Study of the effects of wettability on pool boiling conditions in a quiescent medium

Tomás de Castro Barbosa de Sousa Valente

Thesis to obtain the Master of Science Degree in

Mechanical Engineering

Supervisor: Dr. Ana Sofia Oliveira Henriques Moita

Examination Committee

Chairperson: Prof. Viriato Sérgio de Almeida Semião

Supervisor: Dr. Ana Sofia Oliveira Henriques Moita

Member of the Committee: Prof. Pedro Jorge Martins Coelho

November 2015

ii

iii

Resumo

Este trabalho foca a transferência de calor e dinâmica da bolha para a ebulição nucleada em superficies, em

regimes de molhabilidade extremos de hidrofilicidade e superhidrofobicidade. A molhabilidade é modificada

alterando a química superficial, sem modificar significativamente a sua rugosidade média. Apresenta-se uma

analise detalhada mostrando a evolução temporal do diâmetro das bolhas para os diferentes regimes de

molhabilidade, que poderão servir para futura comparação com simulações numéricas. As curvas de ebulição

obtidas experimentalmente mostram que, para as superficies superhidrofóbicas, existe uma relação linear

entre o fluxo de calor e o sobreaquecimento da parede, embora com um declive inferior ao das hidrofilicas.

Este comportamento é concordante com o efeito “quasi-Leidenfrost” recentemente relatado na literatura.

Relativamente à dinâmica de bolha, os resultados mostraram que os modelos existentes conseguem prever o

crescimento da mesma através do macro-ângulo de contacto (suplementar ao ângulo interno da bolha) para as

superficies hidrofilicas, mas falham ao prever o seu tamanho por não terem em conta os mecanismos de

interacção presentes da ebulição. Estes modelos também falham na previsão do crescimento da bolha para o

caso das superficies superhidrofóbicas. Os resultados mostram também que os ângulos quasi-estáticos não

produzem nenhum resultado coerente quando usados nos modelos existentes. No entanto, estes ângulos

seguem uma tendência semelhante à do ângulo suplementar do ângulo interno da bolha, pelo que se podem

identificar tendências entre o diâmetro de da bolha no instante de emissão da superficie e a frequência para

ambos os ângulos mencionados.

Palavras-chave

Ebulição em piscina, Sistemas Bi-fásicos, Molhabilidade, Inicio de Ebulição, Curva de Ebulição, Dinâmica de

bolha

iv

v

Abstract

This study addresses the detailed description of the heat transfer and bubble dynamics occurring during water

boiling on surfaces with extreme wetting regimes, namely hydrophilicity and superhydrophobicity. The

wettability is changed at the expense of modifying the surface chemistry, without significantly varying the

mean surface roughness. A detailed analysis is presented, showing the temporal evolution of the bubble

growth diameter together with bubble dynamics, which may be useful for comparison with numerical

simulations. A particular trend of the boiling curve is obtained for the superhydrophobic surfaces, as the heat

flux increases almost linearly with the superheat, although with a much smaller slope than that of the

hydrophilic surfaces. This behaviour is in agreement with the so-called “quasi-Leidenfrost” regime recently

reported in the literature.

Regarding bubble dynamics, the results suggest that the existing models can predict the trend of the bubble

growth using the macro-contact angle (complementary to bubble contact angle) for the hydrophilic surfaces,

but cannot accurately predict bubble size, as they do not account for interaction mechanisms. Also

they cannot describe the particular bubble growth phenomenon observed for the superhydrophobic

surfaces. Quasi-static angles cannot provide any satisfactory results when used in the models to predict the

bubble growth diameter, although they follow an evolution similar to that of the macro-contact angle and are

supplemental to the bubble contact angle. In line with this, trends can be observed between the average

bubble departure diameter and bubble departure frequency with both the bubble and the quasi-static

advancing angle.

Keywords

Pool Boiling, Two-phase systems, Wettability, Boiling onset, Boiling Curve, Bubble dynamics

vi

vii

Acknowledgements

I have to start these acknowledgements with Doctor Ana Moita and Almost-Doctor Emanuele Teodori. It was

them that had to put up with me throughout all this time. It was also them that helped me and enlightened me

with all my doubts. To the Professor I thank her for her availability, her genuine niceness and, most importantly

for her friendship. To Emanuele I thank for all the fun that, allied with his unique ingenuity, allowed turning

these hard working months into treasurable memories

I also have to thank Professor Doutor Luis Nobre Moreira for accepting me in this lab, putting onto me an

enormous amount of trust by integrating me within the research group of the project RECI/EMS-

SIS/0147/2012.

I thank my mom and Tio Carlos Presas for putting up with me in the most stressful moments and for, at the end

of each day, providing for fun and relaxed family time. To my father I thank for his constant concern and

constant easiness in dealing with my lack of availability on the tightest moments. To my brother, with all the

love, I thank him for being there and for being proud of what I was doing.

I also have to thank my lab colleagues Miguel Moura and Catarina Laurência, and the lab adoptee and closest

friend João Batista, for all the nights of work in wonderful company, for the breaks where relaxation was the

rule and mind rest the goal and for all the help they gave whenever I needed it.

And if there is one person that deserves to be acknowledged is, without a doubt, Inês. She deserves it because

she was always here. Because without her the day would be much worse. Because it was her unconditional

support, presence and love that gave me the strength to overcome every obstacle in this path. For these and so

many other reasons, Thank you Inês.

Finally I am grateful to Fundação para a Ciência e a Tecnologia (FCT) for partially financing the research under

the framework of the project RECI/EMS-SIS/0147/2012 and for supporting me with a research fellowship.

viii

ix

Contents

Resumo ................................................................................................................................................................... iii

Abstract .................................................................................................................................................................... v

Acknowledgements ................................................................................................................................................ vii

Contents .................................................................................................................................................................. ix

List of figures ........................................................................................................................................................... xi

List of tables ........................................................................................................................................................... xv

Nomenclature ...................................................................................................................................................... xvii

1. Introduction.................................................................................................................................................... 1

1.1 Introduction and Motivation ................................................................................................................. 1

1.2 State of the art ....................................................................................................................................... 2

1.3 Objectives .............................................................................................................................................. 5

1.4 Dissertation outline ............................................................................................................................... 5

2. Theoretical Background ................................................................................................................................. 7

2.1 Wettability ............................................................................................................................................. 7

2.2 Nucleation ........................................................................................................................................... 11

2.3 Bubble dynamics.................................................................................................................................. 13

2.4 Boiling curves ....................................................................................................................................... 16

3. Experimental Set-up and Procedure ............................................................................................................ 19

3.1 Working conditions.............................................................................................................................. 19

3.2 Experimental setup .............................................................................................................................. 20

3.2.1 Overview ......................................................................................................................................... 20

3.2.2 Degassing station ............................................................................................................................ 21

3.2.3 Boiling chamber and auxiliaries ...................................................................................................... 22

3.2.4 Heating Block .................................................................................................................................. 24

3.2.5 Assembly system for the test surfaces ............................................................................................ 25

3.2.5 High-speed imagery ........................................................................................................................ 26

3.3 Improvements to the previous setup .................................................................................................. 26

3.4 Experimental procedure ...................................................................................................................... 28

3.4.1 Surface preparation ........................................................................................................................ 28

x

3.4.2 Surface characterization.................................................................................................................. 30

3.4.4 Pool Boiling tests ............................................................................................................................. 32

4. Experimental data treatment and error quantification ............................................................................... 37

4.1 Data treatment .................................................................................................................................... 37

4.1.1 Boiling Curves .................................................................................................................................. 37

4.1.2 Bubble dynamics analysis ................................................................................................................ 40

4.2 Error Quantification ............................................................................................................................. 46

4.2.1 Boiling Curves .................................................................................................................................. 46

4.2.2 Bubble dynamics analysis ................................................................................................................ 47

5. Results and discussion .................................................................................................................................. 52

6. Conclusions and Future work ....................................................................................................................... 70

6.1 Conclusions .......................................................................................................................................... 70

6.2 Future Work......................................................................................................................................... 71

Bibliography .......................................................................................................................................................... 74

Annexes ................................................................................................................................................................. 80

Annex A – MATLAB code developed for image Post-Processing ...................................................................... 80

Annex B – Poster for LARSyS annual meeting presentation ............................................................................. 90

Annex C – Poster for 14th

UK Heat Transfer Conference presentation ............................................................ 92

Annex D – Abstract of the paper submitted to HEFAT 2015 in South Africa .................................................... 94

Annex E – Abstract of the paper submitted and presented at UKHTC 2015 in Edinburgh ............................... 96

xi

List of figures

Figure 1 - Interfacial tensions acting at the triple contact line ............................................................................... 7

Figure 2 - Wetting regimes ...................................................................................................................................... 8

Figure 3 - Wetting states. Adopted from (Bhushan & Jung, 2011). ........................................................................ 9

Figure 4 - Interfacial tensions for a bubble ........................................................................................................... 10

Figure 5 - Energy factor vs Contact angle ............................................................................................................. 13

Figure 6 - Nukiyama boiling curve(adapted from (Nukiyama, 1934)) ................................................................... 16

Figure 7 - Illustrative pictures of different points in the boiling curve: a) Point A; b) Between A and B; c) Point B

.............................................................................................................................................................................. 17

Figure 8 - Schematic view of the experimental setup ........................................................................................... 21

Figure 9 - Degassing station .................................................................................................................................. 22

Figure 10 - Bare view of the boiling chamber ....................................................................................................... 22

Figure 11 - Final assembly of the boiling chamber ................................................................................................ 23

Figure 12 - a) Resistance power control; b) External heating power control ........................................................ 23

Figure 13 - Back view of the boiling installation ................................................................................................... 24

Figure 14 - Heating block ...................................................................................................................................... 25

Figure 15 - Spring mechanism for contact force control ....................................................................................... 25

Figure 16 - Schematic representation of heating block and detail view of the heat flux sensor ........................... 26

Figure 17 - a) Mounting for high speed camera; b) Mounting for backlight LED .................................................. 26

Figure 18 - Custom built bottom plate and bottom resistance ............................................................................. 27

Figure 19 - Bare view of the boiling chamber ....................................................................................................... 28

Figure 20 - Test surface ......................................................................................................................................... 29

Figure 21 - Ultrasonic bath .................................................................................................................................... 29

Figure 22 - Sealed container for drying ................................................................................................................. 30

Figure 23 - a) Tensiometer; b) Close up view of droplet deposition; c) and d) Contact angle measurement for

hydrophilic and superhydrophobic surfaces, respectively ..................................................................................... 31

Figure 24 - Results from Confocal Microscope ...................................................................................................... 32

Figure 25 - QuickDAQ and Labview Layout ........................................................................................................... 34

Figure 26 – LABVIEW Block diagram ..................................................................................................................... 34

Figure 27 - Inflow of radiation to the camera (adopted from (Usamentiaga, et al., 2014)) ................................. 38

Figure 28 - Setup for thermography ...................................................................................................................... 38

Figure 29 - Sample results from thermography .................................................................................................... 39

Figure 30 - a) Untreated image; b) Image after brightness and contrast adjustment .......................................... 41

Figure 31 - Images before and after cropping for water boiling on: a) Hydrophilic b) Superhydrophobic surfaces

.............................................................................................................................................................................. 42

Figure 32 - Result for background subtraction ...................................................................................................... 42

xii

Figure 33 - a) Result from Gaussian filter; b) Result from imfill function; c) Result from the imclose function; d)

Result from threshold application ......................................................................................................................... 43

Figure 34 - Results for boundary tracing ............................................................................................................... 44

Figure 35 - Example of the input matrix for function bwarea ............................................................................... 44

Figure 36 - Detail view of section for contact angle measurement ....................................................................... 45

Figure 37 - Experimental points obtained for the RAW(Hydrophilic) surface with associated errors ................... 47

Figure 38 - Schematic representation of the error in pixel distribution and its effect on the contact angle

measurement ........................................................................................................................................................ 49

Figure 39 - High speed images of bubble behaviour for hydrophilic (left side) and superhydrophobic (right side)

surfaces at various wall superheats ...................................................................................................................... 53

Figure 40 - Insulating vapour blanket on top of the superhydrophobic surface ................................................... 54

Figure 41 - a) Average bubble departure diameters and b) emission frequencies, as a function of the imposed

heat flux ................................................................................................................................................................ 55

Figure 42 - Boiling curves obtained for water over hydrophilic and superhydrophobic stainless steel surfaces .. 56

Figure 43- Sequence of high-speed images of a bubble departing on a superhydrophobic surface. The

undisrupted vapour layer that remains over the surface is highlighted by white circle. ...................................... 58

Figure 44 - Vaporization rates for hydrophilic and superhydrophobic surfaces as a function of wall superheat . 59

Figure 45 - Berenson's Correlation and Boiling curves for the superhydrophobic surfaces .................................. 60

Figure 46 - Effect of surface topography (quantified by the increase of the mean surface roughness) in the

boiling curves, for extreme wetting scenarios: a) hydrophilic surfaces, b) superhydrophobic surfaces. .............. 61

Figure 47 - Boiling curve showing a “biphilic like” behaviour, resulting from the disruption of the

superhydrophobic coating. The curves obtained for hydrophilic and hydrophobic surfaces are gathered for

qualitative comparison ......................................................................................................................................... 62

Figure 48 - Coating breakage and the different boiling regions ........................................................................... 62

Figure 49 - Different contact angles used throughout these results section: (1) Bubble contact angle; (2) Macro-

contact angle as stated by (Phan, et al., 2009); (3) Apparent Quasi-static contact angle. ................................... 63

Figure 50 - Comparison between the bubble growth on a hydrophilic and a superhydrophobic surfaces at ≈ 10K

of wall superheat .................................................................................................................................................. 64

Figure 51 - Temporal evolution of the bubble contact angle during the growth and detachment of a single

bubble on: a) a hydrophilic surface, b) a superhydrophobic surface ..................................................................... 64

Figure 52 - Temporal evolution of the bubble growth and detachment on: a) a hydrophilic surface, b) a

superhydrophobic surface ..................................................................................................................................... 65

Figure 53 - Bubble departure frequency provided by the expression proposed by Zuber (1963), as a function of

the departure diameter (experimental results). .................................................................................................... 66

Figure 54 - Average a) bubble departure diameter and b) bubble departure frequency, as a function of the

bubble contact angle, macro/supplementary contact angle and quasi-static angle ............................................ 67

Figure 55 - Contact Line Velocity evolution for: a)Hydrophilic surface; b)Superhydrophobic surface................... 67

xiii

Figure 56 - Illustrative post processed images of the growth at: a) Bubble birth (1) b)Contact line movement due

to lateral expansion(2) c)Stable growth(4) d)Bubble just before departure(3) ..................................................... 69

xiv

xv

List of tables

Table 1 - Thermophysical properties of water, taken at saturation temperature at 1.012x105 Pa ...................... 20

Table 2 - Working conditions and variable range ................................................................................................. 20

Table 3 - Characterization results for both surface types...................................................................................... 32

Table 4 - IR camera characteristics ....................................................................................................................... 37

Table 5- Error summary for wall superheat and exemplary values of heat flux ................................................... 46

Table 6 – R2 values for the fitting of the boiling curve of each surface type ......................................................... 47

Table 7 - Relative error for two typical bubble sizes ............................................................................................. 48

Table 8 - Contact angles for both correct and incorrect pixel distributions and the value for the absolute error 49

Table 9 - Bubble dynamics parameters for vaporization rate analysis ................................................................. 58

Table 10 - Results for volume, mass, vaporization rate and heat flux calculations .............................................. 59

Table 11 - Bubble departure diameter as a function of the bubble macro-contact angle: comparison between

the experimental results obtained in the present study and those provided by the expression proposed by Phan

et al. (2010) ........................................................................................................................................................... 65

xvi

xvii

Nomenclature

Latin Letters

Cp Specific heat of a liquid J/KgK Cf Calibration factor Pixels/mm DB Bubble diameter mm edb Error associated with boundary definition Pixels E Error - fr Fraction of the projected surface area that is wetted by the liquid - h Convective heat transfer coefficient W/m

2K

hfg Latent heat of vaporization KJ/Kg k Thermal conductivity W/mK Lc Capillary length m N Number of active nucleation sites - q’’ Heat flux W/cm

2

Ra Average roughness amplitude μm Rb Bubble radius m Rc Cavity radius m rf Roughness factor - R Thermal resistance cm

2K/W

Rz Mean peak-to-valley roughness μm T Temperature K tg Bubble growth time s tw Bubble waiting time s

Greek Letters

α Thermal diffusivity m2/s

β Aperture angle of the conical section o

ε Emissivity - θ Contact angle

o

λr Average wavelength of the surface grooves m ρ Density Kg/m

3

σ Surface tension N/m σ SB Stefan-Boltzmann constant W/m

2K

4

τ Transmissivity - Ψmin Minimum cavity-side angle of a spherical, conical or sinusoidal cavity

o

Subscripts

adv Advancing atm Atmosphere

e Equilibrium d Dynamic g Gas/vapour l Liquid

ls Liquid-solid lv Liquid-vapour

xviii

obj Object r Roughness

rec Receding refl Reflection

sat At saturation conditions

sv Solid-vapour

tot Total

v Vapour

W Wall

1

Chapter 1

1. Introduction

This chapter aims at providing the reader with the context, motivation and objectives of the work developed in

this dissertation. A short state of the art is also included, which summarizes the work reported in the literature

on the effects of surface wettability on pool boiling, to better contextualize the main contributions of the

present study in this topic.

1.1 Introduction and Motivation

Pool boiling heat transfer is explored in many industrial applications at diverse spatial scales, such as

electronics cooling, boilers, nuclear and chemical reactors, refrigeration systems, thermal generation of

electricity, metallurgy or food processing. In this context, several efforts have been made in the last decades, to

further increase the heat transfer coefficients delivered by boiling at low superheat surface temperature.

Enhancement of pool boiling heat transfer is often achieved by altering surface properties. The evolution

observed in micro and nano fabrication techniques within the last decade provides the researchers the

opportunity to test a wide range of surface treatments, which quickly evolved from the micro patterned

surfaces with structures of the order of hundreds of microns, as obtained for instance by (Klein & Westwater,

1971) to nano coatings, (Takata, et al., 2006) and (Phan, et al., 2009). However, many of these treatments

simultaneously alter surface topography and wettability in a non-systematic way, turning it difficult to

understand dominant effects on the boiling mechanisms, which lead to the actual enhancement on the heat

flux that is often reported in these studies. In fact the wettability, which mainly quantifies how well the liquid

spreads over the surface, is affected by the chemistry of the surface (and of the working fluid) and by its

topography. However, it is possible and desirable to separate them at some extent, as recently shown by

(Bourdon, et al., 2012) and (Bourdon, et al., 2013). The surface wettability is usually roughly quantified by the

apparent equilibrium contact angle, θe, which is obtained at the thermodynamic equilibrium between the

interfacial tensions acting at liquid-solid-vapor contact interfaces (often measured on a sessile drop deposited

on the surface). Based on this equilibrium angle, it is widely accepted that a surface is lyophilic (i.e. promotes

the liquid spreading) for 0<θe<90o and lyophobic (i.e. repels the liquid) for θe>90

o. The terms

hydrophilic/hydrophobic, which are commonly used for liquid attractive/repellent surfaces, derive from the

specific attraction/repellence of water. The boundaries for extreme wetting scenarios, namely

superhydrophilicity and superhydrophobicity, are still debated in the most recent literature, as universal

criteria to determine stable extreme wetting regimes are not easily defined. It is known that the heterogeneous

wetting regime associated to superhydrophobicity may not be stable and may not hold, as an activation energy

barrier is transposed, and the contact line slowly moves (He, et al., 2003). Hence, the most representative

measures are given by the quasi-static advancing or receding contact angles and by the hysteresis, which is

basically the difference between the advancing and the receding angles. So, based on this, several authors,

2

such as (Bhushan & Jung, 2011) consider that a surface is superhydrophobic for θadv >150o, as long as the

hysteresis is lower than 10o. These advancing and receding angles are also argued to be more representative of

dynamic processes, which has been demonstrated for drop impacts (for example (Antonini, et al., 2012)), but

may be important also for bubble dynamics (e.g. (Mukherjee & Kandlikar, 2007)) and consequently on the heat

transfer mechanisms. Hence, despite the numerous studies which have been performed so far in describing

pool boiling heat transfer and bubble dynamics, the effect of wettability has not been well described yet. Also,

there is still no consensus on the most appropriate parameters to be used to quantify for this effect on bubble

dynamics and on pool boiling heat transfer.

In this context, the present work addresses the description of the heat transfer and bubble dynamics processes

occurring for the boiling of water on surfaces with extreme wetting regimes, namely hydrophilicity and

superhydrophobicity. The wettability is changed at the expense of modifying the surface chemistry and without

significant variations in the mean surface roughness. Then, the effect of surface roughness is separately

analysed, within each of these extreme wetting regimes.

Furthermore, experimental data on bubble dynamics is still sparsely reported in the literature. A detailed

analysis is also presented, showing effect of the wettability on the temporal evolution of the bubble growth

diameter together with bubble dynamics.

This work is part of a wider project dealing with the experimental and theoretical description of the pool boiling

mechanisms on enhanced surfaces, involving a PhD topic (whose candidate, Mr. Emanuele Teodori, has been a

helpful guidance through the development of the experimental work devised here) and a close collaboration of

Bergamo University in the development of the superhydrophobic surfaces.

The relevance of the present study is better understood in the context of the state of the art of the work

reported in the literature on the effects of surface wettability on pool boiling, as briefly presented in the

following sub-section.

1.2 State of the art

Pool boiling heat transfer has been a subject of study for many decades, from the pioneering work of Lord

Rayleigh, (Rayleigh, 1917), who proposed theoretical relations for the growth or collapse of vapour bubbles, to

the ground-breaking work of (Nukiyama, 1934) who identified the different boiling regimes, on the boiling

curve, which mainly relates, for a liquid boiling on a heated surface, the imposed heat flux with the surface

superheat (i.e. with the increase of the surface temperature above the saturation temperature of the liquid).

This work paved the way for pool boiling to become a hot topic, due to the high heat flux that could be

transferred from the surface to the liquid, within the nucleation regime. The theory on nucleation and on

bubble dynamics, also progressed from here, mostly focusing on nucleation (starting from founding studies

such as (Bankoff, 1958), up to more recent work, as reported for instace by (Qi & Klausner, 2005)) and on the

theoretical or semi-empirical prediction of vital parameters such as the bubble departure or the bubble

3

emission frequency, following the pioneering works of (Jakob & Fritz, 1931) and (Fritz, 1935). These early

studies already recognized the effect of wettability, but without defining a consensual parameter to describe it.

The heat flux in the boiling curve, as defined by (Nukiyama, 1934), is upper limited by the Critical Heat Flux,

which is the maximum heat flux that can be removed by the liquid, for the established working conditions.

Above this value the amount of vapor near the surface insulates it, which leads to a decrease of the heat flux as

the surface superheat is further increased. Therefore, many researchers point to enhance the heat transfer

coefficient within the nucleate boiling region, while trying to increase the critical heat flux and delay the onset

of the critical heat flux conditions, as much as possible (e.g. (Arik, 2001)).

In this context, emphasis has been given in enhancing pool boiling heat transfer. Under this topic, the ground-

breaking study by (Jakob, 1936) showed that surface topography could enhance heat transfer. The rougher

surfaces were shown to produce better results mainly due to the inherent cavities of its topography which

promoted nucleation and increased the heat transfer area. The work reported by (Jakob, 1936) was deepen by

(Corty & Foust, 1955), being then followed by numerous studies on the enhancement of pool boiling heat

transfer based on roughening the surface, as for instance (Kurihara & Myers, 1960), (Hsu & Schmidt, 1961),

(Berenson, 1962) and (Marto & Rohsenow, 1966), which confirmed the results reported by (Jakob, 1936). A

common thread between all the aforementioned studies, and of many more reported in the literature, is that

the so called “surface roughness” was not always precisely defined, mainly because most of these studies were

based on stochastically varying topography. This issue leads to misinterpretations of results and inhibits any

real comparison between them. Universal correlations for the relation between cavities and the nucleation

inception also could not be derived from these results, due to the stochastic modification of the surface

properties, occurring between tests, as argued by (McHale & Garimella, 2010). To cope with this limitation,

several authors took a different approach which led to the surface micro-patterning techniques that allowed

creating surfaces roughened with regular patterns. In this context, several authors patterned the test surfaces

with various regular profiles, such as micro cavities, micro fins and micro pillars. This approach was followed for

instance by (Klein & Westwater, 1971), (Anderson & Mudawar, 1989), (Yeh, 1997) and (Wei & Honda, 2003). In

these studies, maximization of the heat fluxes provided or removed, for liquid heating and cooling applications

were based on a trial-and-error approach which, given the variety of surface treatments easily available, led to

a fast scaling down of these surface patterns (from the micro to the nano scale). Hence, different optimum

patterns were proposed depending on the experimental conditions. This is in line with the argument recently

pointed out by (Cheng, et al., 2014), who stated that despite the numerous studies performed on the

enhancement of pool boiling heat transfer by surface modification, the deep efforts to describe the actual

processes governing the effect of surface modification on the energy, mass and momentum transport at

interfaces only started at the 1980’s and much work has left undone since then.

For instance, interaction mechanisms occurring between nucleation sites are often disregarded. Since the

pioneering work of (Chekanov, 1977), the effect of these mechanisms when roughening the surface have been

sparsely reported even considering they can strongly affect the heat transfer coefficients (e.g. (Teodori, et al.,

4

2013)). Also, the surface treatment is often multi-scaled, but the description of the governing phenomena is

not following this fast scaling down of the surface structuring and modification. As reviewed by (Moreira,

2014), the main processes governing heat transfer at liquid-solid interfaces must be considered within a multi-

scale perspective and in this context, several quantities must be well identified or their effect will be

misinterpreted. A multi-scale approach to describe and control the hydrodynamics, heat transfer and phase

change in droplets and films has been recently proposed by (Gambaryan-Roisman, 2014), which relates surface

modification with changing of the wettability.

Indeed wettability is a key factor controlling interfacial phenomena, but it is affected by surface topography.

This was not taken into account in many of the aforementioned studies, which do not address the need to for

the effect of surface wettability on the heat transfer performance to be isolated from the beneficial effects of

nucleation promotion occurring when the surface topography is modified. Exception is made to some authors,

such as (Wen & Wang, 2002) who tried to focus on the effect of wettability using hydrophilic and hydrophobic

coatings. However, the coating changed the surface topography and the wettability was not changed within

the required extreme regimes to be dissociated with the additional effects of surface topography, in terms of

promotion of nucleation sites.

The study of the effects of surface wettability was only resumed in recent years, when surface treatment

techniques allowed the development of surfaces under extreme wetting scenarios, namely superhydrophilic or

superhydrophobic. These regimes, namely the superhydrophobic, require indeed an additional proper

treatment of surface topography. However, the hydrophobic nature is mainly achieved by modifying the

surface chemistry. With the development of these surfaces, several experimental studies were reported in the

literature, although, once again, they were mostly focused on the maximization of the heat transfer based on a

trial-and-error approach. The various experiments performed on pool boiling over superhydrophobic surfaces

vs hydrophilic surfaces (e.g. (Takata, et al., 2006), (Phan, et al., 2009), (Takata, et al., 2012), (Betz, et al., 2013)

and (Malavasi, et al., 2015)) are consistent in the description of the main trends observed: bubble nucleation

starts at lower superheat values on a superhydrophobic surface, as the energy barrier necessary for nucleus

generation is smaller. However, despite nucleation is favoured, rewetting is not, so the superhydrophobic

surface inhibits bubble release. As a result, the onset of boiling starts at very low superheat values on

superhydrophobic surfaces, but then the force balance does not favour the bubble release from the surface, so

large bubbles stay for longer attached on the surface and coalesce, leading to a Critical Heat Flux condition at

low superheat values. The opposite trend is observed for the boiling curves for hydrophilic surfaces. Based on

these observations, several authors promptly passed on to an “optimum” surface, considering an adequate

superhydrophilic/superphydrophobic patterning of the surface. However, the basic governing mechanisms

occurring at these extreme wetting regimes are far to be understood.

Detailed description of the nucleation process and of bubble dynamics, such as those performed for instance

by (Phan, et al., 2009), (McHale & Garimella, 2010) and (Moita, et al., 2015), are still scarce and do not allow

establishing the accurate relation between bubble dynamics and the aforementioned trends of the boiling

5

curves. Also, the basic nucleation mechanisms were never properly related to the wettability, as it is still

unclear which is the accurate quantity to use. Hence, several authors consider a rough approximation of the

apparent angle to be representative of the contact angle at bubble growth in the expressions to predict the

bubble departure diameter, such for example the Fritz equation (Fritz, 1935). The accuracy of Fritz equation

has been debated several times, particularly when dealing with hydrophobic and superhydrophobic surfaces

(e.g. (Matkovic & Koncar, 2012)) and (Phan, et al., 2009) even report an opposite trend of the bubble growth

with the contact angle, when compared to that given by the Fritz equation. These authors proposed instead

that the macro-angle defined during bubble growth is more appropriate to estimate the bubble diameter,

including it on the so-called energy factor, which basically accounts for the ratio between the volume of a

sphere which has a macro-contact angle and the surface of the full sphere with the same diameter. (Phan, et

al., 2009) further show that this angle is actually very small at nucleation and then increases during bubble

growth for hydrophilic surfaces, occurring the opposite for hydrophobic surfaces. Then, based on geometrical

arguments, the authors show that the energy required to activate the nucleation site and initiate the following

bubble generation is actually larger for a lower macro-contact angle. However, when building up the whole

model, (Phan, et al., 2010) argue similarity between the macro and the apparent contact angles at bubble

departure, for particular conditions.

1.3 Objectives

In line with the context and state of the art provided in the previous paragraphs, the present work aims at

contributing with additional information to allow a more adequate description of the effect of wettability on

pool boiling heat transfer. Particular emphasis is given to its effect on bubble dynamics and to the most

adequate parameters to describe it. To cope with this, the temporal evolution of several quantities used to

describe bubble dynamics, namely bubble diameter, bubble emission frequency and bubble contact angle is

analysed in detail. Bubble dynamics is then expected to be useful in describing boiling curves obtained for

extreme wetting scenarios (hydrophilic vs superhydrophobic). The surface topography is varied within these

extreme wetting conditions, in a systematic and controlled way to assess on its role in a situation for which the

wettability is mainly controlled by the chemical modification of the surface.

The quantification of these variables is also expected to support further numerical simulations of the boiling

process.

1.4 Dissertation outline

The present dissertation is organized in six main chapters, including this Introduction. Chapter 2 introduces the

theoretical background required to understand the main results which are presented and discussed in Chapter

5.

The experimental set-up is described in Chapter 3, together with the experimental procedure and the

diagnostic techniques used to obtain the experimental data. The treatment of the large amount of data and the

particular analysis proposed to be derived here, addressing bubble dynamics, required the development of

6

particular procedures and home-made routines which are presented in Chapter 4, together with the evaluation

of the errors and uncertainties.

Finally, conclusions and future work are addressed in Chapter 6.

7

Chapter 2

2. Theoretical Background

The aim of this chapter is to provide some theoretical insight into the concepts which are required to

understand the discussion of the results that will be presented in Chapter 5. These concepts are introduced,

based on the vast work reported in the literature on pool boiling heat transfer, from a chronological point of

view, from the pioneering studies that served as grounding to the fundamental theories of nucleation and heat

transfer, to the most recent studies.

2.1 Wettability

Wettability quantifies as to which extent a surface is wetted by a liquid. In practice, this wetting capability is

governed by the balance between the interfacial tensions acting on the triple contact line that separates the

three phases, i.e., liquid (l), solid (s) and vapour (v), as represented in Figure 1.

Figure 1 - Interfacial tensions acting at the triple contact line

Several parameters can be used to quantify the wettability. However, the most common is the contact angle of

a sessile droplet onto a flat rigid surface. From a thermodynamic point of view, the equilibrium condition of the

interfacial tensions acting on the droplet is a problem of minimization of the system Gibbs energy, G. Solving

for dG=0 and considering constant temperature and pressure, one obtains the well-known Young’s equation

(Young, 1805), equation (1), which is valid for perfectly smooth and chemically homogeneous surfaces.

𝜎𝑙𝑣𝑐𝑜𝑠𝜃𝑒 + 𝜎𝑙𝑠 = 𝜎𝑠𝑣 (1)

Here 𝜎 is the interfacial tension with its respective indexes, as stated above. Despite being a theoretical

quantity, this equilibrium or static contact angle, 𝜃𝑒 is very useful to provide an indication of the wettability of a

system, which can be obtained a priori of the experimental tests. Namely, based on the value of the static

contact angle one can categorize two main wetting regimes, namely hydrophilic and hydrophobic, as identified

8

in the first two sketches of Figure 2. 𝜃𝑒=0o and 𝜃𝑒=180

o correspond to complete wetting and non-wetting

regimes, respectively. Since these extreme values do not exist in practice, alternative categorizations are used,

namely the superhydrophobic regime, as identified in the last sketch of Figure 2 and the superhydrophilic. The

exact boundaries between the various wetting regimes are still a topic in discussion in recent literature, e.g.

(Sedev, 2011), but for instance (Koch & Barthlott, 2009) consider that a surface is superhydrophilic for 𝜃𝑒<10o

and superhydrophobic for 𝜃𝑒>150o

Figure 2 - Wetting regimes

The equilibrium angle is determined for static conditions, i.e., when the velocity of the contact line is zero.

When dealing with dynamic processes, the most adequate parameters to quantify the wettability are the

dynamic angles. Accurate dynamic contact angle measurements are very difficult to obtain, (Sedev, 2011), so

an alternative way to quantify the wettability is by measuring the quasi-static advancing and receding contact

angles. The difference between the advancing and the receding angles is called hysteresis and is related to the

energy dissipated (irreversibility) at the contact line, (Zhou & Hosson, 1995). The introduction of the hysteresis

values is of the utmost importance because a surface may be considered superhydrophobic by its static contact

angle, but the stability of the triple contact line may be affected by the dynamics of its own motion, mainly due

to possible changes in the wetting regime, that may not be stable. Hence, for a surface to be considered truly

superhydrophobic the hysteresis value should be below 10o, (Bhushan & Jung, 2011). One should note that the

abovementioned classifications and methods are obtained using droplets but in the case of the present work,

bubbles will be the focus with consequences as explained further on.

As aforementioned, the contact angle as defined in Young’s equation is a theoretical measure, which is mainly

valid when assuming a completely perfect smooth and chemically homogeneous surface. This does not occur in

practice. In fact roughness, to some degree, is present in any surface and so, for a droplet resting on a surface,

two limiting states are usually considered, depending on the level of liquid penetration into the rough grooves.

The first state, the so called Wenzel or homogeneous wetting state, (Wenzel, 1936), assumes the liquid fully

penetrates the rough grooves and is in intimate contact with the surface micro structure. In this case, 𝜃𝑒 must

be corrected using Wenzel’s equation,

𝑐𝑜𝑠𝜃𝑟 = 𝑟𝑓𝑐𝑜𝑠𝜃𝑒 (2)

Hydrophilic

10o < θe < 90o 90o < θe < 150o

θe > 150o

Hydrophobic

Superhydrophobic

9

where 𝑟𝑓 is the so called roughness factor and is defined as the ratio between the true wetted area and the

correspondent projected area. The second limiting state assumes the liquid is suspended on the top of the

micro structures and is called the Cassie-Baxter or heterogeneous wetting state, (Cassie & Baxter, 1944). 𝜃𝑒 is

corrected by the Cassie and Baxter equation,

𝑐𝑜𝑠𝜃𝑟 = 𝑟𝑓𝑐𝑜𝑠𝜃𝑒 − 𝑓𝑟(𝑟𝑓𝑐𝑜𝑠𝜃𝑒 + 1) (3)

where 𝑓𝑟 is the fraction of the projected area of the solid surface that is wetted by the liquid.

These wetting states are schematically represented in Figure 3.

Figure 3 - Wetting states. Adopted from (Bhushan & Jung, 2011).

Although the aforementioned equations provide good results, even if their validity and application are still

discussed in the literature, determining 𝑟𝑓 and 𝑓𝑟 factors is not always straightforward and in some cases it may

even not be possible (for instance when dealing with a stochastic topography). To cope with this, several

efforts have been made to establish functional relations between more specific geometrical parameters of the

surface topography and the contact angle. The most commonly used parameters are the average roughness

amplitude, 𝑅𝑎, and the average wavelength of the surface grooves, 𝜆𝑟. In a very early study, (Hitchcock, et al.,

1981) used a dimensionless roughness, 𝑅𝑎/𝜆𝑟, to investigate sixteen substrate and liquid combinations and

reported a linear increase of the contact angle with this new parameter. The exceptions found for good wetting

drops on roughened silica and nickel substrates were associated with the energy required by the advancing

liquid front to overcome the energy barriers associated with surface features. However this trend was not

confirmed by following studies, many of them reporting contradictory results. For instance, (Hong, et al.,

1994), observed a monotonic decrease of the static contact angle of some fluids on metal surfaces with

decreasing roughness, for a mean roughness value below 0,5μm. In a more recent study, (Kandlikar & Steinke,

2001) and (Kandlikar & Steinke, 2002), reported, for water droplets on copper and stainless steel surfaces, that

the contact angle first decreases as the roughness increases, but then starts to increase as surface roughness

reaches the value of about 0,3μm. (Moita & Moreira, 2003) confirmed these results, as they showed a

monotonic increase of the contact angle with increasing mean surface roughness, for values of 0,5<𝑅𝑎<3μm.

Based on an energy analysis (Bico, et al., 2002) show that a hydrophobic surface may not hold its

hydrophobicity, as an energy barrier can be transposed (e.g. the drop oscillates or impacts over the surface at a

10

certain velocity). Following Wenzel and Cassie and Baxter formulations, (Bico, et al., 2002) explains that a

hydrophilic surface becomes more hydrophilic and a hydrophobic one becomes more hydrophobic, with

increasing roughness, as long as the regime is energetically stable and at the point of minimum Gibbs energy.

Up to now, wettability has been discussed considering the interaction between a liquid surrounded by vapour

(e.g. a droplet) and a solid surface. In pool boiling, however, a vapour bubble is attached to the surface and is

surrounded by the liquid, so the direction of the interfacial tensions is completely different from that observed

on the droplet – see Figure 4.

Figure 4 - Interfacial tensions for a bubble

Furthermore, under boiling conditions, the surface and the bubble are not at the same temperature, which

results in an imposed heat flux on the solid-liquid-vapour interface. This creates an unbalance between the

interfacial forces, especially on the triple contact line, where heat transfer is very high and liquid evaporation

occurs at a much higher rate than in the surrounding areas. This will also obviously affect the value of the

contact angle, between the bubble, the surface and the surrounding liquid, which can be much different than

the apparent angle defined for the case of a sessile droplet deposited on a non-heated, flat and rigid surface.

(Phan, et al., 2010) named this new angle, as the macro-contact angle. These authors also propose the

emergence of a micro contact angle in the near region of contact. However, this is a microscopic angle that was

not quantified yet. The experimental techniques available in the present work, also do not allow for the

quantification of this micro angle, so it will not be considered in the discussion of the results. Hence, different

angles are defined, but the appropriate value to use is not yet defined.

To better understand the effect of the wettability and the relevance in defining the appropriate contact angle

associated to bubble formation, growth and departure, an introduction to nucleation, and its relation to

wettability, is addressed in the following paragraph.

11

2.2 Nucleation

Nucleation can be briefly summarized as the birth of a vapour bubble within a liquid. Nucleation can be

homogeneous or heterogeneous. The former is nucleation without preferential nucleation sites and it requires

high degree of superheating (Stefan, 1992) and very particular conditions, namely the purity and complete

degasification of the fluid. Homogeneous nucleation occurs spontaneously and randomly and is more unlikely

to occur, when compared with the heterogeneous nucleation, particularly for experimental conditions of the

present work.

Heterogeneous nucleation involves the entrapment of vapour/gas in the microscopic crevices and cavities of

the boiling surfaces, and these act as nuclei for the bubbles. These cavities may vary in density, size and shape

according to the surface material, finishing and its level of oxidation or contamination. (Corty & Foust, 1955)

were the first to introduce this vapour trapping mechanism based on their observations of pool boiling

experiments, which were later confirmed by (Clark, et al., 1959). In order for a bubble to form and release, i.e.,

for a nucleation site to become active, two different conditions have to be satisfied: vapour/gas has to become

trapped in a crevice and, sufficient energy must be supplied to the trapped vapour/gas to form a stable bubble.

This will grow and detach form the surface, depending on the balance of the applied forces, mainly buoyancy

and surface tension and a new bubble is formed.

(Bankoff, 1958) was the first to provide a criterion, equation (4), for the entrapment of vapour/gas on a wedge,

by an advancing liquid front: the dynamic contact angle 𝜃𝑑 between the surface of the inflowing liquid front

and the wall of the liquid front must be the double of the aperture angle of the conical section 𝛽.

𝜃𝑑 > 2𝛽 (4)

(Lorenz, 1972), (Lorenz, et al., 1974), (Cornwell, 1982) and (Qi & Klausner, 2005) later used this condition in

order to determine the critical conical radius of a boiling site. (Lorenz, 1972), devised a theoretical

homogeneous model that depicts the ratio between the bubble radius and its cavity, 𝑅𝑏/𝑅𝑐, as a function of

the static and dynamic contact angles as well as of the conical cavity angle. This model predicts that, for a fixed

value of the static contact angle, the above mentioned ratio increases with the dynamic contact angle. A

modified model was later proposed by (Tong, et al., 1990).

Another approach to establish a condition for entrapment was proposed by (Wang & Dhir, 1993). By

minimizing the Helmholtz free energy of a system involving a liquid-gas interface in a cavity, (Wang & Dhir,

1993) derived the following criterion:

𝜃𝑒 > 𝜓𝑚𝑖𝑛 (5)

where 𝜓𝑚𝑖𝑛 is the minimum cavity-side angle of a spherical, conical or sinusoidal cavity.

It is worth mentioning that while Bankoff’s criterion is a necessary condition, Wang and Dhir’s criterion

provides a sufficient one.

12

These vapour/gas entrapments then become nuclei for bubbles to grow and release from the surface, as long

as minimum energy conditions are satisfied. Hence, the recently formed nucleus must not shrink, so its internal

temperature must be the saturation temperature for the pressure of the vapour phase determined by the

Young-Laplace Equation. Assuming ideal gas behaviour for the vapour, and applying the Clausius-Clapeyron

equation, the following equation can be derived, which determines the temperature required for the stability

of the nucleus,

𝑇𝑔 − 𝑇𝑠𝑎𝑡 = 2𝜎𝑙𝑣

𝑅𝑐ℎ𝑓𝑔𝜌𝑣

(6)

Here 𝑇𝑔 and 𝑇𝑠𝑎𝑡 are the vapour temperature and the liquid saturation temperature, respectively, 𝑅𝑐 the radius

of the cavity, ℎ𝑓𝑔 the latent heat of vaporization and 𝜌𝑣 the vapour density. A quick overview at the above

equation shows that smaller cavities can become stable with increasing nucleus temperature.

In addition, enough energy must be provided to the nucleus in order for a bubble to grow and reach critical

conditions for exiting that cavity and later detaching from the surface. This is called inception, which can be

summarized as the activation of a nucleation site. Inception is normally viewed as the reaching of the critical

point of instability of the vapour-liquid interface. This interface is said to be stable if its curvature increases

with the increase in vapour volume, as reported by (Mizukami, 1977), (Forest, 1982) and (Nishio, 1985). (Wang

& Dhir, 1993) studied this instability and showed that it occurs when the non-dimensional curvature of the

interfaces reaches a maximum value. Also, by assuming that the interface temperature is the same as the

surface temperature, (Wang & Dhir, 1993) derived the following expression for wall superheat required for

inception with respect to the cavity radius 𝑅𝑐,

𝑇𝑊 − 𝑇𝑠𝑎𝑡 = 2𝜎𝑙𝑣𝑇𝑠𝑎𝑡

𝑅𝑐ℎ𝑓𝑔𝜌𝑣

𝐾𝑚𝑎𝑥 (7)

where:

𝐾𝑚𝑎𝑥 = 1 𝑓𝑜𝑟 𝜃𝑒 ≤ 90∘

𝐾𝑚𝑎𝑥 = 𝑠𝑖𝑛 𝜃𝑒 𝑓𝑜𝑟 𝜃𝑒 > 90∘

These authors also showed, as expected, that larger contact angles (lower wettability) favour the onset of

heterogeneous boiling and increases the density of nucleation sites. This is however a general trend, based on

the apparent contact angle. Hence, an alternative criterion to fully define the effect of the surface wettability

on the appearance and nucleation of was also developed by (Bankoff, 1957), who considers an energy factor to

define the evolution of the energy required to form a bubble with varying contact angles. This energy factor,

equation (8) is defined as the ratio of energy required to form a bubble with contact angle θ on the surface to

that needed to form a homogeneous bubble with the same diameter.

13

𝑓(𝜃) =2 + 3 cos 𝜃 − cos3 𝜃

4 (8)

The same principle has been recently used by (Cheng, et al., 2014) to explain the differences on the nucleation

for hydrophilic and hydrophobic surfaces. In fact, given that the bubble formation energy will be proportional

to this energy factor, high contact angles over 150o, which are obtained at superhydrophobic surfaces, require

much less energy to nucleate a bubble (Figure 5).

Figure 5 - Energy factor vs Contact angle

After nucleation, pool boiling heat transfer is strongly influenced by bubble dynamics, which in term are deeply

affected by wettability, as easily understood from the concepts revised in the following paragraphs.

2.3 Bubble dynamics

Bubble formation and its evolution until detachment is an intricate and complex problem as it depends on

numerous and, mainly unknown, conditions. Several experimental and theoretical studies address bubble

dynamics, usually focusing on three parameters: bubble departure diameter, bubble growth and bubble

departure frequency. Bubble departure diameter is the diameter at which an individual bubble detaches from

the surface. Accurate experimental data are not much available, even considering recent studies, but several

correlations have been suggested to predict its value, usually devised as a function of wall superheat, operating

pressure, gravity and fluid characteristics, but seldom include the effect of the contact angle. This fact is

pointed by (Kolev, 1995) to be the main reason from the scattering in the data obtained. One of the few

exceptions is the correlation proposed by (Fritz, 1935), which is one of the most used and best known

correlations to predict the bubble departure diameter:

𝐷𝐵 = 0.0208𝜃𝑒√𝜎𝑙𝑣

𝑔(𝜌𝑙 − 𝜌𝑣) (9)

14

An extensive review on the existing correlations to predict the bubble departure diameter can be found in

(Carey, 1992). However, as revised in the State of the Art, recent studies still debate how accurately this

correlation addresses the effect of the wettability, with obvious consequences in the prediction of the

experimental data. In fact, (Fritz, 1935) only showed that there was a maximum volume of a vapour bubble

that was a function of the contact angle and of the fluid properties, and the contact angle does not even

appear explicitly in his publication.

Hence, in many studies reported in the literature, the effect of the contact angle is empirically taken into

account, which results in larger disagreement with data for a large number of experimental studies, especially

those with using well-wetting fluids or surfaces, wide pressure ranges or very low gravitational conditions. An

extensive comparison of experimental data from several authors has been performed by (McHale & Garimella,

2010) and more recently by (Moita, et al., 2012). Both studies report that the experimental data gathered from

different studies did not agree with none of the correlations addressed. Besides not accounting with the effects

of surface wettability, the main argument for the disparity in experimental data that the abovementioned

authors use is that many of the studies involve the creation of nucleation sites by altering surface topography

in a stochastic manner, which obviously is difficult to model and replicate between authors and tests. It is

worth mentioning that wettability has not entirely been disregarded in all studies, as its importance with

respect to bubble diameter has been confirmed several times (e.g. (Kakaç & Boilers, 1991), (Pioro, et al., 2004),

(Papon, et al., 2006), , (C.P. Costello & W.J. Frea), (Takata, et al., 2012) and others), but no accurate model has

been devised yet, so only empirical results are reported. In the present work, one does not propose to devise

such model, but to contribute to explain the experimental results.

Bubble growth is defined as the evolution of the size of the bubble with time. This evolution is mainly

controlled by heat flow to the bubble surface, i.e., by the energy equation. (Fritz & Ende, 1936) solved the

transient thermal conduction equation and deduced the following equation for the evolution of the bubble

radius:

𝑅𝑏(𝑡) = √4

𝜋

𝑐𝑝,𝑙

ℎ𝑓𝑔

𝜌𝑙

𝜌𝑣√𝑘𝑙(𝑇𝑤 − 𝑇𝑠𝑎𝑡)𝑡1 2⁄ (10)

where 𝑅𝑏 is the bubble radius and 𝑘𝑙 the thermal conductivity of the liquid.

(Zuber, 1959) disagreed with the fact that bubble growth is only controlled by the energy equation, and took

also into account the momentum equation, i.e., the balance of forces on a growing bubble. However, the

equation derived from this approach only differs from equation (10) by a factor of a number – 2√3 𝜋⁄ . Based

on the absence of considerable differences between these two approaches one can argue that the bubble

growth is mainly governed by the heat flow, addressed in the energy equation. Several other correlations are

proposed in the literature for bubble growth, mostly based on various premises to describe the physical

mechanisms involved in the energy transport from the surface or liquid to the bubble. However, from the

studies reviewed in the present work, none of them takes into account wettability. This may contribute to the

15

large disagreement in experimental data when comparing the results reported by different authors. Also, apart

from the numerical simulations, a detailed analysis on the temporal evolution of bubble growth is not reported.

(Phan, et al., 2009) provides some trends of bubble growth in time and as a function of the surface wettability,

although it is always not so clear which angles are used to quantify the effect of wettability. Despite this, (Phan,

et al., 2009) show that higher contact angles promotes the formation of larger bubble departure diameters,

being the opposite trend observed for more hydrophilic surfaces.

A parameter that is used to assess bubble generation is the bubble departure frequency and can be estimated

using two different procedures, either by measuring the time between two successive events of bubble growth

at a single nucleation site starting at the beginning of the growth, as suggested by (Darby, 1964) or by

measuring the time elapsed between apparent departure events. As for the mathematical relations to predict

the bubble departure frequency, three main equations are often used, as proposed by (Jakob & Fritz, 1931), by

(Zuber, 1963) and by (Mikic, et al., 1970). (Jakob & Fritz, 1931) proposes for water and hydrogen a fixed value

for 𝑓𝑏 . 𝐷𝐵,

𝑓𝑏 . 𝐷𝐵 = 0.078 (11)

(Zuber, 1963) suggests a correlation where 𝑓. 𝐷𝐵 is also constant,

𝑓𝑏 . 𝐷𝐵 = 0.059 [𝜎𝑙𝑣(𝜌𝑙 − 𝜌𝑣)

𝜌𝑙2

]

1 4⁄

(12)

(Mikic, et al., 1970) suggests a non-constant value for 𝑓𝑏 . 𝐷𝐵 that varies according to wall superheat,

𝑓𝑏1 2⁄

. 𝐷𝐵 = (4

𝜋) 𝐽𝑎√3𝜋𝛼 [(

𝑡𝑔

𝑡𝑤 + 𝑡𝑔

)

1 2⁄

+ (1 +𝑡𝑔

𝑡𝑤 + 𝑡𝑔

)

1 2⁄

− 1] (13)

where 𝑡𝑔 is the bubble growth time, 𝑡𝑤 is the waiting time – defined by the time between consecutive bubbles

– and 𝐽𝑎 is the Jakob number defined below,

𝐽𝑎 =𝜌𝑙𝑐𝑝,𝑙(𝑇𝑤 − 𝑇𝑠𝑎𝑡)

𝜌𝑣ℎ𝑓𝑔

(14)

However, these models are in poor agreement with experimental measurements due to the fact that they

simply do not take into account many of the predominant parameters of boiling. For example, nucleation site

geometry may significantly influence the bubble growth and therefore its departure frequency. Some other

variables discarded may be, for instance, nucleation site interaction and bubble coalescence which can both

strongly influence the waiting time.

The review of the theoretical concepts performed so far highlights the fact that for bubble diameter, growth

and frequency, there is no underlying theory or correlation that correctly describes the observed phenomena

and agrees well with the experimental data. So, a more unifying theory must be developed. This trend will be

16

further discussed and confirmed in Chapter 5. In this context, numerical simulations may provide additional

insights into the physics of pool boiling heat transfer and on the nucleation and bubble growth mechanisms,

namely by analysing some parameters that are difficult to obtain experimentally. However, detailed studies are

require providing the accurate boundary conditions, particularly those related to the surface topography and

wettability. The present work is expected to contribute in the definition of these boundary conditions.

2.4 Boiling curves

Besides bubble dynamics, the influence of wettability on the heat transfer mechanisms is perceived on the

boiling curves. The boiling curves are a graphical representation of the variation of heat flux with respect to

surface overheat, ΔT, defined by the difference between the surface temperature and the saturation

temperature of the working fluid:

𝑞′′ = ℎ(𝑇𝑤 − 𝑇𝑠𝑎𝑡) (15)

Various regions can be identified within this curve – the so called boiling regimes – corresponding to different

boiling characteristics, which in turn lead to a different heat flux evolution with ΔT. (Nukiyama, 1934) was the

first to build this curve, represented in Figure 6 and to define these boiling regimes, using a nichrome wire.

Figure 6 - Nukiyama boiling curve (adapted from (Nukiyama, 1934))

17

a)

b)

c) Figure 7 - Illustrative pictures of different points in the boiling curve: a) Point A; b) Between A and B; c) Point B

From this Figure 6, five different regimes can be identified. Before point A, heat transfer occurs by natural

convection. A little bit after point A, for a superheat degree which depends on the working fluid, boiling occurs,

18

being usually identified by a noticeable increase in the curve slope, and single nucleation sites become active

with near surface coalescence limited to bubbles from the same nucleation site, Figure 7 a). Further increasing

the wall superheat, interaction between nucleation sites starts to occur and coalescence between them starts

much closer to the surface, Figure 7 b). Bubble nucleation and interaction keeps increasing until point B is

reached. Now, bubbles from almost every nucleation sites coalesce with one another and vapour starts to

leave the surface as jets or columns, Figure 7 c). This interaction obviously affects the heat transfer coefficient

as it precludes fluid circulation near the surface, where heat transfer is occurring. This effect on the heat

transfer coefficient is associated to the change in slope of the curve, which will eventually reach point C,

defined as the critical heat flux. Beyond this point, bubble coalescence is so intense that, almost

instantaneously, the surface becomes completely covered by a vapour film. This vapour film acts almost as an

insulant for the surface, thus reducing dramatically the heat transfer coefficient. This leads to a sharp increase

of surface temperature to point E, which often results to the system burnout, damaging the surface. If the

surface is not damaged, point D is obtained by steadily decreasing the temperature until the boiling becomes

stable again and bubbles start to release from the surface naturally.

The present work focus on region II, defined as partial nucleate boiling. As the results will be often explained

relating the boiling curves with bubble dynamics, it is worth introducing the governing theory and model on the

heat transfer mechanisms, occurring within this region. Pool boiling heat transfer can be quantified as the sum

of three main mechanisms, as early suggested by (Han & Griffith, 1962) and by (Hsu & Graham, 1976).

Following this approach, which was later materialized into the so-called RPI model, as proposed by (Kurul &

Podowski, 1990), these three mechanisms are: i) the heat transferred by the actual vaporization of liquid

(latent heat term), ii) the heat transfer associated to the fluid motion within the near surface region, in which

the surface is rewetted by liquid when the existing thermal boundary layer is disrupted by bubble departure

and iii) The heat transferred by natural convection.

It is also worth mentioning that the first two mechanisms are often responsible for most part of the heat that

is transferred from the surface, as reported by (Han & Griffith, 1962) and later confirmed in more recent

studies (e.g. (Gerardi, et al., 2009)).

19

Chapter 3

3. Experimental Set-up and Procedure

This chapter provides a detailed description of the set-up, the measurement techniques and the methodology

followed to perform the experiments. Although most part of the setup was already assembled, following

previous work, (Teodori, et al., 2013), the particular experimental conditions considered in the present work

demanded for several modifications, which are presented here.

3.1 Working conditions

The main focus on this work is to describe the effect of extreme wetting conditions (and particularly

superhydrophobicity) on pool boiling heat transfer. Emphasis is given to the impact of wettability on two major

aspects: the boiling curves and bubble dynamics (taking into account that the first is strongly affected by the

second).

The boiling curves are generated by running pool boiling experiments under imposed heat flux conditions on

the surface, with continuous control and monitoring of the surface temperature, liquid temperature and

pressure inside the pool boiling chamber. The curves were obtained at a pressure of 1bar±10mbar and the

maximum heat flux imposed was 10W/cm2 for hydrophilic surfaces and about 3W/cm

2 for the

superhydrophobic ones. The curves are constructed based on consecutive increase of the imposed heat flux in

small steps of 0,5-1W/cm2. Bubble dynamics was studied qualitatively and quantitatively by high-speed imaging

of the vicinity of the surface, being the videos recorded for each heat flux step, to capture all the possible

bubble dynamic behaviour and enable analysing the possible relation between bubble dynamic characteristics

and particular trends observed at the boiling curves. Quantitative data are then obtained by extensive post-

processing procedures of the recorded images, using a home-made routine that was specifically developed in

MATLAB for this purpose, as further detailed in Chapter 4.

The wettability was quantified by the dynamic advancing and receding contact angles and by the contact angle

hysteresis. In this context, the wettability, quantified by the quasi-static advancing contact angle, was varied

between the extreme values of θadv=85,3o and θadv=166

o. Particular care was taken with the preparation and

characterization of the test surfaces before, during and after each experimental test.

These extreme wetting conditions were mostly obtained at the expense of modifying the surface chemistry, as

further explained in the following paragraphs. Under these extreme wetting conditions, and following the

fundamental concepts described and reviewed in Chapter 2, the surface topography is expected to play a

secondary role when compared to the change of the contact angles (the main parameter used to quantify the

wettability). However, surface topography was also carefully characterized and quantified using the mean or

20

average roughness, Ra, and the average of single peak-to–valley Rz. Also, the effect of the surface topography

was also evaluated for the surfaces with and without the chemical treatment.

The working fluid is water, whose main physicochemical properties are depicted in Table 1.

Table 1 - Thermophysical properties of water, taken at saturation temperature at 1x105 Pa

Property Value

Tsat (°C) 99.7

ρl (kg/m3) 957.8

ρv (kg/m3) 0.5956

µl (mN m/s2) 0.279

cpl (J/kgK) 4217

kl (W/mK) 0.68

hfg (kJ/kg) 2257

σ (N/m)x10-3

58

Table 2 summarizes the main working conditions addressed in the experimental tests and the range covered by

the main working variables.

Table 2 - Working conditions and variable range

Variable Working range Units

Pressure 1000±10 mbar Fluid temperature 372.85±0,5 K

Top surface temperature ≈ [373.15 – 438.15] K Temperature below the surface ≈ [373.15 – 453.15] K

Heat flux ≈ [0 – 9] W/cm2

3.2 Experimental setup

3.2.1 Overview

The set-up is mainly composed by a boiling chamber, where the experiments are performed, a degassing

station in which the fluid is degassed, pressurized and constantly heated and a filling and evacuating circuit that

connects the boiling chamber respectively to the degassing station and to the waste fluid container, being the

later at ambient pressure. A schematic view is presented in Figure 8. The pressure and the temperature inside

the boiling chamber are accurately controlled (the temperature is controlled with a precision of 1K and for the

pressure control the precision is 1,6 mbar). The entire heating block of the pool boiling test section is isolated

with Teflon, and the pool boiling chamber is isolated from the outside with rubber and glass wool. Heaters

disposed inside, controlled by a PID controller (index 2 of Figure 12 a)), and on the outer surfaces of the boiling

chamber, assure that the liquid inside the chamber remains at saturation temperature. The pressure is

controlled by means of two electronic valves that are controlled to respond based on the measures given by a

21

pressure transducer (OMEGA DYNE Inc) inside the pool, using a home-made routine based loop control. This

control system reacts to pressure variations in the order of 1,6 mbar. The refilling and the entire measurement

processes are automatically controlled by this routine. The temperatures are sampled using K-Type

thermocouples. The signal is acquired and amplified by a National Instruments DAQ board plus a BNC2120. The

acquisition frequency is 100Hz. The heating block, which heats and accommodates the different surfaces is

formed by a copper cylinder inside which a cartridge heater (315W) is placed. As aforementioned, also the

cylinder is isolated with Teflon.

Figure 8 - Schematic view of the experimental setup

A more detailed description of the main parts of the set-up is provided in the following paragraphs.

3.2.2 Degassing station

Degassing the working fluid is of extreme importance, as the gas dissolved in the liquid will affect the

saturation temperature for the working pressure, which consequently influences the experimental results,

namely the boiling curves.

The degassing station, shown in Figure 9, is composed by the main parts, as numbered, according to the figure:

22

Figure 9 - Degassing station

1. Two 5 litre reservoirs equipped with one pressure gauge for internal pressure monitoring – mainly for

safety concerns. The left reservoir, herein named as primary reservoir is connected to the test

chamber; the reservoir on the right side, herein named as secondary reservoir is used to refill the

primary reservoir, after the test chamber is filled;

2. Connecting tube between the primary and secondary reservoirs;

3. Condenser for harnessing steam that is released by the reservoirs.

3.2.3 Boiling chamber and auxiliaries

The test chamber is an aluminium tank that will hold the working fluid at the working temperature and

pressure conditions. A bare view of the test chamber can be seen in Figure 10, in which one can identify:

Figure 10 - Bare view of the boiling chamber

1. Slot for pressure transducer;

2. Coupling slot for thermocouple for internal temperature control via the PID;

3. Slot for thermocouple that measures the temperature of the liquid near the test surface;

1

2

3

23

4. Bottom internal electrical resistance;

5. Electrical connectors for top resistance;

6. External heating pads location.

The test tank was also insulated with rubber and Glass wool and fitted with external heating pads (6) to

minimize thermal dissipation to the environment. Its final assembly can be viewed in Figure 11.

Figure 11 - Final assembly of the boiling chamber

Two rheostats are also placed as the test tanks auxiliaries: one to control the power to the internal resistances

(Figure 12 a) index 1) and the other (Figure 12 b)) to control the power input to the exterior heating cartridges

and assure they do not overcome their safe working temperature.

a) b)

Figure 12 - a) Resistance power control; b) External heating power control

Figure 13 depicts a back view of the boiling set-up, showing the connections to the degassing station and outlet

reservoirs

24

Figure 13 - Back view of the boiling installation

Here, one may also identify:

1. Primary reservoir outlet for tank filling and pressure control;

2. Test tank exit electro valve for pressure control;

3. Manual valve for security reasons;

4. Test tank inlet connection;

5. Test tank inlet electro valve for pressure control.

3.2.4 Heating Block

The heating block itself is a fundamental and crucial part of the set-up. It holds the surface on which boiling

occurs and is equipped to measure the heat flux and surface temperature. It is composed of a Teflon block

(index 2 of Figure 14), for insulation purposes, that accommodates the heating cylinder (index 4 of Figure 14).

The heat flux is measured using a thin heat flux sensor (Captec Entreprise ®) custom made to fit perfectly to the

heating block. This sensor, which is placed between the copper cylinder and the surface has a sensitivity of

2,21mV/(W/m2). The surface temperature is measured with a T-Type thermocouple that is coupled with

Captec’s heat flux sensor.

The surfaces is mounted on and fixed to the heating block by PEEK (polyether ether ketone) screws (index 1 of

Figure 14) and nuts, to ensure that the least possible amount of heat is dissipated from the surface by the

screws. Vitton O-rings (index 5 of Figure 14) are placed to prevent leakage from beneath the surface to the

heating area. The Teflon block is firmly coupled with an aluminium base (index 6 of Figure 14) to allow for

25

insertion and strong attachment of the heating block to the boiling chamber. This base is also fitted with Vitton

O-rings for leakage prevention.

Figure 14 - Heating block

Figure 16 provides a schematic section representation of the heating block as well as a detail view of the

placement of the heat flux sensor and the T-Type thermocouple.

3.2.5 Assembly system for the test surfaces

The test surfaces must be characterized (as explained in sub-section 3.4.2) being fixed to the heating block,

before the entire assembly is inserted and fixed into the tank. Before accommodating the surfaces, the top of

the heating cylinder is thoroughly cleaned and covered with a controlled amount of thermal paste. Afterwards,

the surface is attached by means of eight PEEK nuts that press them against the Viton O-rings to prevent leaks.

Obviously, the contact force between the top of the cylinder head and the surface plays an important role on

the thermal resistance between them. Hence, to assure a constant force is similarly applied in all the testes

performed, a spring mechanism has been designed. In this system, 4 springs press on a lower Teflon part that is

attached to the cylinder, being the exerted force controlled by adjusting the height of the lower nuts that are

holding the other end of the spring. This system is illustrated in Figure 15.

Figure 15 - Spring mechanism for contact force control

26

Figure 16 - Schematic representation of heating block and detail view of the heat flux sensor

3.2.5 High-speed imagery

To record the high speed footage for qualitative analysis of boiling dynamics and for the quantitative

description of bubble dynamics obtained with the post-processing algorithm, two separate mountings were

assembled. One for the high speed camera, to ensure that the camera is fixed in a known and well defined

position for the various tests , and one for the backlight LED, to improve image quality. Both of them are

depicted in Figure 17. The camera used was the Phantom 640 with the following operating specifications:

Resolution of 512x512 @ 2200 FPS.

a) b)

Figure 17 - a) Mounting for high speed camera; b) Mounting for backlight LED

3.3 Improvements to the previous setup

Several studies were already performed in a previous setup, e.g., (Teodori, et al., 2013), and based on the

sensitivity acquired on performing those experiments, there were some modifications that could be

implemented in order to improve the performance and quality of the pool boiling tests. These improvements,

listed below, were implemented before beginning the experimental campaign for the present work:

1. Addition of the secondary reservoir and of the required connections to the primary one. This

secondary tank allows the refilling of the primary one without expose the water inside to the

atmosphere;

27

2. Change of the attachment method of the heating block: this required a complete makeover of the

bottom plate of the tank, which was custom built in the present work – index 1 of Figure 18;

3. Refurbishing of the whole heating block for further adaptation to the new bottom plate;

4. Addition of an extra internal resistance at the bottom of the tank, to ensure a more homogenous

temperature distribution in the bulk fluid – index 2 of Figure 18;

5. Strengthening of the outer surface to improve leakage containment and to allow for higher tightening

forces when fixing the base to the test tank – index 1 of Figure 19;

6. Addition and wiring of a power rheostat for controlling the power supplied to the internal resistances,

to allow for better control of its heating – See Figure 12;

7. Addition and wiring of a power rheostat to control the external heating pads and maintain them at a

safe workable temperature of about 120oC – See Figure 12;

8. Addition of external insulation to the test tank, mainly with natural rubber and an outer coating of

glass wool – See Figure 11;

9. Addition of a near surface thermocouple to measure saturation temperature, given that the previous

one, which was located near the tank wall, could be influenced by heat losses to the environment;

10. Addition of a vacuum compressor to reduce as much as possible the initial amount of non-

condensable gases within the tank.

Figure 18 - Custom built bottom plate and bottom resistance

28

Figure 19 - Bare view of the boiling chamber

3.4 Experimental procedure

The experimental procedure for this work is quite extensive and time consuming. It is composed of many

separate steps, all of which require explanation and description. The general steps to follow in the

experimental procedure are:

1. Surface preparation;

2. Surface characterization;

3. Assembly of the test surface;

4. Pool boiling test;

5. Characterization of surface ageing (after the pool boiling tests).

3.4.1 Surface preparation

Stainless steel surfaces are prepared to have dissimilar topographic and wetting properties. The numerous

surfaces used in this study (nearly 40) are categorized in 4 main groups: RAW – “smooth” hydrophilic surfaces,

ROUGH – “rough” hydrophilic surfaces, RAW SHS and ROUGH SHS, representing superhydrophobic surfaces

with identical roughness amplitude as that of the hydrophilic ones.

The 62x62x1 mm surfaces used are provided by Bergamo University and can be seen in Figure 20 below.

29

Figure 20 - Test surface

A number of surfaces were sent to IST already prepared and ready to use, but many were prepared at IST. First,

the surfaces must be very well cleaned of any fat residues, dust or other particles, as they may alter the

wettability. Afterwards, the surfaces are coated with a commercial chemical compound called Glaco, which is

mainly a perfluoroalkyltrichlorosilane combined with perfluoropolyether carboxylic acid and a fluorinated

solvent. The cleaning procedure must follow the steps listed below:

1. 30 min in a ultrasonic bath (Figure 21) in water at 40oC;

2. Drying with compressed air;

3. 30 min in a ultrasonic bath in acetone at 40oC.

Figure 21 - Ultrasonic bath

The procedure for creating the superhydrophobic coating envolves the following steps:

1. Cleaning process described above;

2. Coating with Glaco spray;

3. Drying for 24 hours in a sealed container (Figure 22);

4. Apply second coating and repeat point 3;

5. Apply a total of 5 coatings.

30

Figure 22 - Sealed container for drying

It is worth mentioning that even after the surface is coated, the wettability is easily changed by contamination,

so the cleaning procedure described above must be repeated for each of the surface, and for all the boiling

tests performed.

3.4.2 Surface characterization

Wettability

After the cleaning and preparation processes, and immediately before each test, the surfaces are characterized

in terms of wettability and topography. Wettability is quantified by the apparent quasi-static advancing and

receding angles. The measurements are performed at room temperature (20oC), using an optical tensiometer

(THETA from Attension). The angles are evaluated from the images taken within the tensiometer, using a

camera adapted to a microscope. The images (with resolution of 15,6 μm/pixel, for the optical configuration

used here) are post-processed by a drop detection algorithm based on Young-Laplace equation (One Attension

software). The tensiometer and a detail view of the droplet while the contact angle is being measured can be

viewed in Figure 23 a) and b) respectively. Also, a frame from the software as it measures the contact angle for

each of the wetting regimes, hydrophilic and superhydrophobic, is shown in Figure 23 c) and d).

a) b)

31

c) d)

Figure 23 - a) Tensiometer; b) Close up view of droplet deposition; c) and d) Contact angle measurement for hydrophilic and superhydrophobic surfaces, respectively

For each frame (which is associated to the subsequent time instant), the software provides the left, right and

mean values. These data points are retrieved, neglecting those that correspond to waiting time between

stopping inflating the droplet and beginning to deflate, and a spreadsheet is created in Excel. For the advancing

contact angle, an average of the values and its standard deviation is taken so that one has a representative

mean value for that contact angle. In the case of the receding contact angle, the value considered is the one

that corresponds to the first motion of the contact line after deflating has begun. When performing the analysis

for the superhydrophobic surface the hysteresis i.e., the difference between the advancing and receding

contact angles is also quantified, which, recalling the arguments presented in Chapter 2, should be below 10o.

The blue lines on the above figure is a mere representation of the drop boundary the software is creating.

This procedure must be repeated for three different points on the centre part of each surface, mainly to verify

the homogeneity of the wetting regime of the surface, but also to increase the accuracy of the measurements.

Surface topography

A qualitative analysis of surface topography was also conducted, mainly to detect abnormal grooves or

scratches that could act as predominant nucleation sites and consequently could influence the boiling curves

and bubble dynamics. This analysis was performed with a Laser Scanning Confocal Microscopy (Leica SP8

Confocal Microscope) using the reflection mode, and consisted on the visual inspection of the surface

topography. A sample of the 3D reconstruction of a surface performed in this microscope is illustrated in Figure

24.

32

Figure 24 - Results from Confocal Microscope

Stochastic roughness was also quantified to allow for inference on its effects on the results of the present

work. This will allow confirming that roughness plays a secondary role when compared to the abrupt

wettability change. The roughness profiles are measured using a Dektak 3 profile meter (Veeco) with a vertical

resolution of 200Angstroms. These profiles are further processed to obtain the mean roughness (determined

according to standard BS1134) and the mean peak-to-valley roughness (determined following standard

DIN4768). Average representative values of Ra and Rz are taken from 10 measurements distributed along the

entire surface. Table 3 summarizes surface characterization for each type of surface as explained before.

Table 3 - Characterization results for both surface types

Category Surface material

Ra [μm] Rz [μm] θadv [o] θrec [

o]

Hysteresis [

o]

RAW Stainless steel 0.06 0.09 85.3 <20 >10

ROUGH Stainless steel 1.20 1.58 90.75 <20 >10

RAW SHS Stainless steel coated with

Glaco 0.06 0.09 166 164 2

ROUGH SHS Stainless steel coated with

Glaco 1.20 1.58 166 164 2

3.4.4 Pool Boiling tests

The pool boiling test procedure starts by degassing the distilled water. This is performed by boiling the water in

the degassing station for about half an hour at 1.9 bar and then opening the valves from the primary reservoir,

to lower the pressure to about 1.4 bar before filling the boiling chamber. Also, before filling the chamber, a

vacuum compressor is used to remove as much air as possible from inside the tank. This vacuum pump stays on

throughout the filling process to make sure no air becomes trapped. After filling the tank, the vacuum pump is

turned off and the primary pressure cooker is refilled by allowing the water from the secondary one – which is

still at 1.9 bar – to flow to it. The secondary reservoir is refilled and both continue to boil the water throughout

33

the test, further degassing the water. After the test tank is filled, the internal resistances and the PID controller

are turned on and the water, which was cooled due to the losses in the filling process, is heated until the

saturation temperature for the inside pressure is reached. At this point, computer monitoring starts using

LABVIEW and QUICK DAQ. For a visual aid throughout the following description Figure 25 shows the LABVIEW

and QUICK DAQ layout. The inside pressure is monitored in LABVIEW – right bottom graph and numeric value –

and the limiting values, for which the inlet and exit electro valves turn on or off to maintain a quasi-constant

internal pressure, are set in the red highlighted boxes of Figure 25.

The initial power supplied to the cartridge heater is set by configuring the variable transformer to 20V. This

value, which was determined empirically, is required to compensate all losses, thus assuring that the surface

achieves the saturation temperature of the working fluid, as this is the initial condition to start the

experimental test. The top graph from the QUICK DAQ layout provides a view of the temperature evolution on

the surface and enables checking its stabilization. Once the initial value of the saturation temperature has been

reached, the data registry process is initialized. In the LABVIEW, three seconds of data are recorded at 100 Hz

and for every one hundred data points, its average and standard deviations are written to a spreadsheet. This

data includes heat flux measurements and pressure. Simultaneously, in the QUICK DAQ, one thousand points

are recorded and the average and standard deviation values of the surface and water temperatures are also

recorded to a spreadsheet. Also at the same time, a movie is recorded through the high-speed camera for

future analysis of the bubble dynamics at each temperature and flux level.

The voltage input to the cartridge heater is further increased in 5V, and after waiting for the surface

temperature to stabilize – this takes about 20 min for the hydrophilic surfaces and 40 min for the

superhydrophobic ones – the data registry process is repeated.

This entire procedure is repeated, with subsequent voltage increase of 5V until the maximum working

temperature of the heat flux sensor is reached. This temperature value is about 180oC. This procedure allows

to obtain 10-11 points per test.

The boiling curves presented in the results chapter (Chapter 5) are averaged from 4 tests (for each surface type

tested). Several authors in literature repeat the measurements for descending flux steps to infer on hysteresis.

However, due to time constrains of each test, this was not performed. The whole process allowing to obtain

one single curve (and the corresponding visualization of the bubble dynamics), excluding surface preparation,

takes about 6 hours for hydrophilic surfaces and 10 hours for the superhydrophobic ones, which would lead to

an overall test time of about 15-18 hours if a hysteresis analysis was included. A total of about 35-40 pool

boiling tests were conducted, including those which had to be discarded.

34

Figure 25 - QuickDAQ and Labview Layout

The LABVIEW block diagram developed for data recording and display as well as pressure control can be viewed

in fig Figure 26.

Figure 26 – LABVIEW Block diagram

After each test and the whole experimental facility has cooled down, the test surface is removed from the

heating block and is again characterized following the procedures described in point 3.4.2 to check on

significant changes in wettability (i.e. in the contact angle measurements) and/or in surface topography which

35

may have occurred during the experimental test. The most usual effect is the decrease of the contact angles,

particularly on the θadv.

This procedure is also important as it provides important information on the durability of the treated surfaces.

However, to assure reproducibility of the high contact angles obtained with the superhydrophobic surfaces,

even if the contact angle had not decreased to values below the superhydrophobicity threshold, a new surface

was always used for each test.

36

37

Chapter 4

4. Experimental data treatment and error

quantification

This chapter explains the data reduction procedures, which were followed to obtain the results that will be

further presented and discussed in Chapter 5. This description includes the analysis and quantification of the

errors associated with data measurement and treatment.

4.1 Data treatment

4.1.1 Boiling Curves

As a first step in treating the data for obtaining the boiling curves it is worth mentioning that there is a non-

negligible thermal resistance between the heat flux sensor and the top of the surface, which can be estimated

from equation (16):

𝑞′′ [𝑊

𝑚2] =

∆𝑇

𝑅𝑡𝑜𝑡

=𝑇𝑠𝑒𝑛𝑠𝑜𝑟 − 𝑇𝑊

𝑅𝑡𝑜𝑡

(16)

Where 𝑇𝑠𝑒𝑛𝑠𝑜𝑟 and 𝑞′′ are known variables representing the temperature measured underneath the surface

and the heat flux, respectively. 𝑇𝑊 is unknown and must be determined. To cope with this, an Infrared

Thermographic camera was used to measure the temperature on the top of the surface. Table 4 depicts the

main characteristics of the camera used, an ONCA MWIR InSb (from the ONCA 4969 series) from Xenics.

Table 4 - IR camera characteristics

Camera characteristics Optical system Image characteristics

Sensor: InSb (MWIR) Focal lens: 13 mm Video rate: 60 Hz

Spectral sensibility 3,5 to 5 µm Optics material: Germanium Max. framerate: 3000 fps

Resolution: 320x256 pixels Minimum Region of Interest ROI: 15x5 pixels

Pixel dimension. 30x30 µm Exposition time > 1 µs

Refrigeration: Stirling engine

Thermal sensibility < 17 mk

Pixel operability > 99.5 %

At this stage one should briefly explain the basic working principles and procedures to perform accurate

measurements with this camera.

38

Figure 27 - Inflow of radiation to the camera (adopted from (Usamentiaga, et al., 2014))

The target object temperature can be related with all the variables that control the radiation flow to the

camera (schematically represented in Figure 27) by means of the following equation:

𝑇𝑜𝑏𝑗 = √𝑊𝑡𝑜𝑡 − (1 − 𝜀𝑜𝑏𝑗) ∙ 𝜏𝑎𝑡𝑚 ∙ 𝜎𝑆𝐵 ∙ (𝑇𝑟𝑒𝑓𝑙)

4− (1 − 𝜏𝑎𝑡𝑚) ∙ 𝜎𝑆𝐵 ∙ (𝑇𝑎𝑡𝑚)4

𝜀𝑜𝑏𝑗 ∙ 𝜏𝑎𝑡𝑚 ∙ 𝜎𝑆𝐵

4

(17)

When configuring the camera, several steps have to be performed. The first step consists in positioning the

camera on a stable and safe location and measure its lens distance from the target object. Figure 28 provides a

view of the mounting of the camera and the setup.

Figure 28 - Setup for thermography

To measure and quantify the variables related to the transmission and reflection through the surrounding air,

the camera has two different inputs: atmosphere temperature and ambient temperature. Atmosphere

temperature is measured with a Type-K thermocouple and it is used by the camera’s own software to compute

39

air transmittance. Ambient temperature is a variable that will account for reflection. This theoretical

temperature is measured by placing a reflective object (e.g. aluminum thin foil) at the same distance from the

camera that the test surface will be. This temperature is an input value of the software. The target object

emissivity is also an input value of the software of the camera. For the purpose of this analysis, a test surface

painted in black was used, with 𝜀𝑜𝑏𝑗 = 0,95 − 0,96. Next, one should set the integration time – defined as the

time of each scan of the surface - keeping in mind that this defines the temperature range that the camera can

measure. A low integration time yields a wider temperature measurement range, but also increases image

noise. Taking this into account, an integration time of 200 ms was chosen. Finally, to account for changes in the

integration time, as well as to avoid the occurrence of the “Dionisio” effect – i.e., the reflection in the infrared

image of the camera’s own lens – an offset calibration has to be performed. This is done using a target object

with a known temperature and, by means of the camera’s own calibration algorithm, one can match the

measured values with the known ones, considering the reference target object temperature.

Having performed the entire above steps, one is now able to evaluate the thermal resistance. This is performed

by measuring the temperature beneath the surface, with the Type-T thermocouple, and above the surface,

with the infrared camera, in steps, i.e., these temperatures are recorded for various steps of increasing and

stabilized surface temperature and the thermal resistance for each of this steps is calculated using equation

(16), recalling that the heat flux is acquired by the heat flux sensor. This procedure is repeated for different

points within the region of interest of the surface. The thermal resistance, which is considered to be an average

of four points of these resistance values, is calculated to yield the final result of 𝑅𝑡𝑜𝑡 = 4,715 𝑐𝑚2. 𝐾𝑊⁄ .

Figure 29 depicts some qualitative results from the thermal imaging analysis.

Figure 29 - Sample results from thermography

After calculating the thermal resistance, the temperature values provided by the T-Type sensor, placed

beneath the surface, are corrected by the thermal resistance, to obtain the actual surface temperature on the

boiling side.

40

This correction is performed for each boiling curve obtained, following the procedure previously described.

Each boiling curve presented in the Results chapter (Chapter 5) is an average of 4 experiments, obtained in

similar and reproducible conditions and is obtained by curve fitting of the corrected data (intercepted at point

0,0).

4.1.2 Bubble dynamics analysis

To have detailed information on the effect of surface wettability in bubble dynamics, which can be related to

the pool boiling curves, high speed footage has been recorded for each heat flux step, for every single curve

used to generate the average boiling curves and for each surface type.

As explained in Chapter 2, the most usual quantities used to quantify bubble dynamics are the bubble

departure diameter and the bubble departure frequency. However, quantitative information on how the

bubbles contact angle and the contact line velocity change during bubble growth and how they are affected by

surface wettability (quantified by the quasi-static, bubble and macro contact angles) is still sparsely reported in

the literature, although is vital to describe the effect of wettability on pool boiling. Also, it is important to infer

on possible correlations between the bubble and the macro contact angles. In this scope, in the present work,

bubble dynamics was described based on the temporal evolution of the following quantities:

Bubble Diameter;

Contact angle at the contact line between surface and bubble;

Contact line horizontal velocity;

Departure frequency.

Which are evaluated for each recorded frame. This results into an extremely large amount of data to be

analysed. To cope with this, a specific code was developed in MATLAB, which allowed a semi-automation of the

whole measuring process. The measurement process cannot be fully automatic, so, a pre-processing manual

measurement is also required, as detailed in the following paragraphs. Given the different procedures followed

by several authors to quantify the departure frequency (as revised for instance in (Moita, et al., 2015)), it is

worth mentioning that in the present work, the departure frequency is obtained by dividing the number of

departure events captured within a defined data set/high-speed movie (evaluated by the user of the code), by

the time of the recorded high-speed video.

Hence, the image processing algorithm addressed the main steps:

1. Manual image pre-processing;

2. Image cropping;

3. Image background subtraction;

41

4. Image treatment;

5. Bubble boundary tracing and centroid determination;

6. Diameter measurement;

7. Contact angle measurement;

8. Contact line velocity measurement;

9. Conversion from pixel values to mm values.

Each of these steps is briefly explained in the following paragraphs. The entire code is provided in Annex A.

Manual image pre-processing

The image background and contrast are not homogeneous. Hence, the first step is the adjustment of the

brightness and contrast levels to maximize the contrast and turn the image background as homogeneous as

possible. This adjustment is made using the software of the high-speed camera, Phantom 640.

An example illustrating the result of this pre-processing procedure is depicted in Figure 30 in which, a)

corresponds to the untreated image and b) to the image with adjusted levels of brightness and contrast.

a) b) Figure 30 - a) Untreated image; b) Image after brightness and contrast adjustment

Image cropping

After being loaded into the MATLAB program, the image is cropped to focus on the region of interest, a single

nucleation site. When analysing boiling on the superhydrophobic surfaces, the cropping is applied to the whole

part of the image focusing on the single large bubble that is formed, covering the entire surface. However,

when dealing with boiling on the hydrophilic surfaces one may have numerous nucleation sites active at the

same time, so the cropping is made to minimize superpositioning of bubbles, which is not well handled by the

bubble boundary tracing algorithms. Figure 31 displays uncropped and cropped images for both hydrophilic

and superhydrophobic surfaces, a) and b) respectively.

42

a) b)

Figure 31 - Images before and after cropping for water boiling on: a) Hydrophilic b) Superhydrophobic surfaces

Image background subtraction

Before each test, a background image is recorded for subtraction on the actual bubble image frame.

Background subtraction is helpful in reducing the background noise in the image. All the images loaded are

converted to a matrix of greyscale intensity values, in which 0 represents black and 255 white.The function

used here basically subtracts the matrix corresponding to the background image to each matrix corresponding

to the frame with the bubbles. The order used in the subtraction operation seems odd, but is done to provide

reversal tones, i.e., whites become black and black becomes white, which makes the visual analysis easier for

the user of the code. The result of this procedure is exemplified in Figure 32.

Figure 32 - Result for background subtraction

Image treatment

As seen in Figure 32, there are some parts of the inside of the bubble that are not completely defined and that

were, in most cases, the result of light reflection on the bubble’s outer surface. In some other cases there is still

some white spots in the image from secondary bubbles, e.g., generated from boiling at the internal electrical

resistances, that must be eliminated. This requires a multi-step process of image enhancement and bubble

filling. Hence, a Gaussian filter is applied, which removes some of the above mentioned noise (Figure 33a).

“Black holes” inside the bubble may lead to erroneous measurements, so they must be filled. The Gaussian

43

filter already adds some blur to the image to aid the filling process, however, it often does not entirely solve

this problem. To cope with this, different strategies are used, such as, for instance using the imfill function of

MATLAB (Figure 33b). Alternatively, the most effective way of filling the holes within the bubble is using

MATLAB’s strel function with “ball” specification, which creates structuring elements with specified sizes and

shapes. These structuring elements are then inserted into the figure by means of the imclose function. This

function follows the borders of pixels where major changes occur in its vicinity – which typically represent

holes, and using the strel structuring elements as an input, insert those elements in order to fill the hole and

close it. The result of this process is exemplified in Figure 33 c). A consequence of this imclose function is that it

also inserts these structuring elements in the outside border that defines the bubble, which results in the

blurriness seen in Figure 33 c). However, this has a minor effect when applying a simple edge detection

approach consisting on converting the greyscale into a binary image where value 1 is inserted into the indexes

that satisfy an imposed condition which, in this case, is that the pixel value for that index is higher than a

specified threshold. This threshold relates to the intensity of the white of that analysed pixel, which means that

by setting a correct threshold one can eliminate the blurry part and end up with the defined bubble, as shown

in Figure 33 d).

a) b)

c) d)

Figure 33 - a) Result from Gaussian filter; b) Result from imfill function; c) Result from the imclose function; d) Result from threshold application

Bubble boundary tracing and centroid determination

Another upside of performing this operation is that one ends up with a binary image, with values of 1 where

the bubble exists (white colour) and 0 where it does not (black colour). This allows for a much easier location of

pertinent pixels, namely those associated to the bubble boundaries. Using the bwtraceboundary function, the

44

boundary of the bubble is traced. This function requires one pixel of the boundary for it to start its trace to the

following pixels as well as the initial direction of trace. Obviously this starting point cannot be set by hand by

analysing each frame, so the solution to this problem was to use the find function to uncover the first value of 1

on the last line – which corresponds to the contact line – of the binary matrix that composes the image and set

those coordinates as the starting point. This point is the furthermost left point of the bubble at the contact line

and is identified in red, in Figure 34 (pointed by the blue arrow) which also shows the boundary traced over the

bubble. The trace direction was set to North for reasons explained further on. With the initial point set, the

function is applied to the entire matrix (i.e. to the binary image) in the direction specified and finds the pixels

that have the largest gradient in value between neighbouring pixels. These pixels correspond to the boundary

of the bubble. This process yields a matrix of coordinates of the boundary pixels.

Figure 34 - Results for boundary tracing

The centroid is determined by calculating an average of the matrix resulting from the boundary tracing, in both

horizontal and vertical directions. This is possible because, as this is an image, the index values are also

locations within pixel distribution, i.e., the number of rows and columns of the image are related to image size,

in pixels, in vertical and horizontal directions, respectively. The centroid is plotted as a blue cross in Figure 34.

Diameter measurement

The bubble diameter is measured using the bwarea function, which applied to the matrix of the binary image

resulting from the previous step returns the areas of regions filled with 1’s. For instance applying the bwarea to

the matrix exemplified in Figure 35 (which represents a binary image for definition of the bubble) the value

returned by the function is 4 𝑝𝑖𝑥𝑒𝑙𝑠 𝑥 4 𝑝𝑖𝑥𝑒𝑙𝑠 = 16 𝑝𝑖𝑥𝑒𝑙𝑠2.

0 0 00 1 10 1 1

0 0 01 1 01 1 0

0 1 10 1 10 0 0

1 1 01 1 00 0 0

Figure 35 - Example of the input matrix for function bwarea

45

To use this function, and in order to make sure there are no tiny holes left after image treatment that would

affect the accuracy of the area measurement, an additional step is performed, to assure that there are no 0

values in the region defined as the bubble. The final diameter is then computed making use of the circle area

equation.

Contact angle measurement

In order to measure the contact angle at the contact line, one must define the tangent lines that form the

angle. Reminding that the initial direction of trace for the bwtraceboundary function was North (red arrow in

Figure 36), the first points that appear in the matrix, resulting from the application of that function, are the

coordinates of the upward pixels on the bubble boundary from that starting point. Using a set of those values,

a linear equation is created to fit those points using the polyfit function. By calculating the inverse tangent of

the slope of that linear equation one gets the contact angle. For a visual aid, Figure 36 represents a detailed

view of the bubble and the definition of the contact angle.

Figure 36 - Detail view of section for contact angle measurement

Contact line velocity measurement

Contact line velocity is the speed at which the contact line moves on top of the surface as the bubble grows.

The process for the calculation of this velocity is to use the same point that was set for the tracing of the

boundary and by using v = x/t, in which 𝛥𝑥 is the difference in the horizontal coordinate of that reference

point, between two consecutive frames and 𝛥𝑡 is the time between consecutive frames.

Conversion from pixel values to mm values

The final obvious required step is to apply a calibration factor Cf that provides the relation pixels/mm. This was

evaluated using a pixel ruler on an image of a millimetric grid, taken for the same conditions as those used to

record the bubble dynamics phenomena. For the present work, the calibration factor is

𝐶𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟(𝐶𝑓) = 31.4 𝑝𝑖𝑥𝑒𝑙𝑠

𝑚𝑚 ⁄

46

4.2 Error Quantification

4.2.1 Boiling Curves

The uncertainties associated to the boiling curve have two major sources: the errors associated with the

measurement equipment, such as the thermocouples and the heat flux sensor, and the uncertainty related to

the curve fitting.

The error associated with the temperature values measured from the thermocouples, affects the calculation of

the wall superheat, as given in equation (18):

𝐸∆𝑇 = √𝐸𝑇𝑠𝑎𝑡2 + 𝐸𝑇𝑠𝑢𝑟𝑓𝑎𝑐𝑒

2 (18)

In which each temperature error follows (Abernethy, et al., 1985),

𝐸𝑇 = √𝑈2 + (2𝜎)2 (19)

U is the uncertainty of the measurement instrument itself, which in this case is ±0,5o for both thermocouples

used, and σ is the standard deviation of the measurements.

On the other hand, the error associated with heat flux measurement in the sensor can be evaluated as:

𝐸𝑞′′ = √𝑈2 + (2𝜎)2 (20)

In this case, the uncertainty value, given by the manufacturer, is of ±3%. The values of standard deviation used,

for temperature and heat flux individually, were the maximum found throughout all the tests which were 0,244

for the temperature and 0,058 for the heat flux.

Table 5 depicts the value of the error associated with the wall superheat and also the error for exemplary

values of the heat flux.

Table 5- Error summary for wall superheat and exemplary values of heat flux

Temperature [K] Heat flux [W/cm2]

Variable value - 0 3 6 9

Error ±0.949 0.116 0.147 0.214 0.294

Figure 38 shows, as an example, the error bars for a representative boiling curve obtained for water on a

hydrophilic surface. It depicts the experimental data obtained for the 4 tests used to derive the average curve.

47

Figure 37 - Experimental points obtained for the RAW(Hydrophilic) surface with associated errors

The experimental points in association with its error, in both wall superheat and heat flux, show good

reproducibility of the results. The curve fitting is obtained with no significant deviations from the experimental

points, leading to satisfactory values of the R2. Table 6 depicts the values of the R

2 for each of the boiling curves

generated.

Table 6 – R2 values for the fitting of the boiling curve of each surface type

Surface type R2

(%)

RAW 99.1

ROUGH 98.6

RAW SHS 99.7

ROUGH SHS 97.4

The values of this R2 are not entirely decisive when it comes to classifying a fitting as good or bad. The residual

plot must also be analysed to see if there is a pattern among the scattering of the residual points. In all the

cases addressed here, no pattern was identified, so R2 values can be considered trustworthy.

4.2.2 Bubble dynamics analysis

This subsection addressed the evaluation of the uncertainties for each parameter measured using the post-

processing routine that was developed.

Diameter measurement

In order to estimate the uncertainty of the measurements of the bubble’s diameter one must take into account

two different factors. The first, 𝛥𝐶𝑓 is the uncertainty associated with the conversion from pixel values to

48

millimetre values. As this is subjected to a random error depending on the positioning of the pixel ruler on the

image, a conservative estimate of about ±5% is taken as the uncertainty. The latter is related to the error

associated to the definition of the boundary of the bubble in the post-processing procedure, ebd, which is of the

order of 4 pixels. This value was obtained by multiple pre and after processing image qualitative analysis. The

resulting relative error can be expressed as the square root of the quadratic sums of both of the single relative

errors pertaining to each parameter, as represented in equation (21):

𝛥𝐷𝐵

𝐷𝐵

= √(𝛥𝐶𝑓

𝐶𝑓

)

2

+ (2𝑒𝑑𝑏

𝐷𝐵 . 𝐶𝑓

)

2

(21)

Table 7 shows the uncertainty for two of the maximum typical bubble sizes obtained at the boiling on each

type of surface tested.

Table 7 - Relative error for two typical bubble sizes

Bubble diameter (mm) Relative error (%)

3 9.86

10 5.61

Departure frequency

As briefly stated in the previous chapter, the departure frequency values were obtained by dividing the number

of events counted by the user of the code, by the elapsed time, which in turn, is the duration of the video

analysed. Hence, the error associated with this measurement is related to the error in the total number of

frames analysed, i.e., one could easily consider that the bubble detached ±1 frame from the chosen one at

beginning of the counting and at the end. Therefore the error can be evaluated as:

𝛥𝑓𝑏

𝑓𝑏

= [𝑛𝑒𝑣𝑒𝑛𝑡𝑠 (𝑛𝑓𝑟𝑎𝑚𝑒𝑠 + 2)⁄ ]

𝑓𝑏

(22)

The maximum uncertainty obtained was 0.045%. At first glance, this value is quite low. However, due to the

stochastic nature of the nucleation process, the frequency value at a certain heat flux step may be affected by

much higher variations. As neighbouring nucleation sites become active, the energy removed from their

activation may greatly reduce the bubble departure frequency of the site that is being analysed. Despite, for

the boiling over hydrophilic surfaces, where this effect is more likely to affect the measures, the frequency

value was averaged from two different data sets, which consider different nucleation sites, in an attempt to

minimize this limitation of the data. Repeatability of the results may be an issue, so analysis based on

frequency values, was performed with care, mainly considering qualitative trends.

Contact angle measurement

Regarding the analysis of the uncertainties associated with the measurement of the contact angle, they are

strongly related to the uncertainty in the definition of the boundary of the bubble and then in the definition of

49

the tangent lines. The highest uncertainties occur when the bubble boundary is well defined at the contact line,

but the following 2 pixels of the boundary – as 3 is the minimum number of pixels used to fit the line that

allows for the contact angle measurement – are off by 1 pixel location. This reasoning is schematically

represented in Figure 38.

Figure 38 - Schematic representation of the error in pixel distribution and its effect on the contact angle measurement

In this case the contact line is correctly represented, i.e., both tangent lines (green for the correct pixel

distribution and red for the incorrect pixel distribution) start at the same point. However, the following pixels

of the wrong distribution were traced 1 pixel to the left, as a consequence of the uncertainty when defining the

boundary of the bubble. By fitting a line through the pixels for each distribution one can obtain its slope, and

consequently its contact angle. The difference in the measured angles is assumed to be the highest error

possible.

Table 8 represents the results obtained.

Table 8 - Contact angles for both correct and incorrect pixel distributions and the value for the absolute error

Correct pixel distribution angle (o)

Wrong pixel distribution Angle (

o)

Absolute error (o)

45 56.31 11.31

Contact line velocity measurement

The error for the measurement of the contact line velocity can be evaluated as:

𝛥𝑣

𝑣=

√(𝛥𝐶𝑓

𝐶𝑓)

2

+ (2 𝑝𝑖𝑥𝑒𝑙𝑠

𝛥𝑥. 𝐶𝑓)

2

𝛥𝑡

(23)

where Cf is the error associated to the calibration factor, Cf. At each frame, the ending points of the contact

line, can be out of place by ±1 pixel. The maximum uncertainty occurs when the contact line moves only 1 pixel,

which leads to an uncertainty value of 91%. All the measurements under these conditions are naturally,

50

disregarded. However, in most of the cases addressed here, the contact line motion always covers nearly 10

pixels in average, so the uncertainty is of the order of 10%.

51

52

Chapter 5

5. Results and discussion

This chapter presents and discusses the main results obtained in the present work. The effect of wettability on

bubble dynamics is discussed in detail, based on qualitative (boiling morphology) and quantitative analysis. This

effect on the heat transfer mechanisms is then evaluated by relating the bubble dynamics with boiling curves

experimentally obtained. Furthermore, the experimental data is compared with theoretical and empirical

predictions.

Changing the wettability within extreme scenarios leads to significant differences in bubble dynamics, covering

various phenomena which occur at different temporal and spatial scales. This is clearly shown in Figure 39,

which depicts the bubble generation process for various values of wall superheat and for pool boiling of water

on a hydrophilic (on the left side) and superhydrophobic (on the right side) surface.

a) Wall superheat: 21 K b) Wall superheat: 21 K

53

c) Wall superheat: 32 K

d) Wall superheat: 32 K

e) Wall superheat: 40 K f) Wall superheat: 44 K

Hydrophilic surface Superhydrophobic surface

Figure 39 - High speed images of bubble behaviour for hydrophilic (left side) and superhydrophobic (right side) surfaces at various wall superheats

From the sequence of images illustrating the boiling phenomena on the hydrophilic surface one can identify

several characteristics which are often reported in the literature, for similar wetting conditions (e.g. (Berenson,

1962)): at low superheat, (Figure 39 a), the nucleation sites are sparsely located within the heated area

(Φ20mm) with very few active sites. Further rising the surface superheat up to 32K, (Figure 39 c), the heated

area becomes much more active with bubbles rising from a broader number of nucleation sites. Also, lateral

coalescence starts to occur. This trend in increasing the number of active nucleation sites continues until the

wall superheat is increased typically up to 40K, (Figure 39 e). Then, bubble interaction becomes chaotically

evident with strong coalescence occurring in both vertical and horizontal directions.

This behavior contrasts with the boiling process observed on the superhydrophobic surfaces: even at the

lowest wall superheat value, corresponding to Figure 39 b), the heated area of the superhydrophobic surface is

54

already completely covered with a single bubble. In fact, the wall superheat value of 21K was chosen for

comparative purposes, but for the superhydrophobic surface, the boiling starts immediately at 1-2K of wall

superheat, but single nucleation sites are not distinguished. Instead the boiling process is only visible by the

growing of this single large bubble. Hence, further increasing the surface temperature, Figure 39 d) and f), the

boiling process is not qualitatively different from that observed at lower surface superheat, except for the

bubble size, since the bubble slightly grows as the wall superheat increases.

This particular behavior, in which this single bubble covers the entire heated area, can be explained based on

the theoretical description for the boiling on superhydrophobic surfaces introduced in Chapter 2. Bubble

nucleation starts at lower superheat values on a superhydrophobic surface, as the energy barrier necessary for

nucleus generation is smaller. Hence, very small bubbles appear on the surface already at 1-2K superheat.

However, being the surface superhydrophobic, there is no interfacial tension component promoting bubble

detachment, so these bubbles tend to stay attached on the surface and start to coalesce in the horizontal

direction, generating an initial insulating vapor blanket from which the single bubble starts to depart, as

enabled by the force balance. The particular superhydrophobicity of this surface allied to its stochastic micro

roughness, strongly promotes this behavior which occurs very fast and at very low wall superheat values, as

aforementioned, so the growth and coalescence of these small bubbles is almost impossible to capture.

However, the formation of this insulating vapor blanket, depicted in Figure 40 is coherent with the “quasi-

Leidenfrost” effect recently reported by (Malavasi, et al., 2015) that occurs on surfaces similar to those used in

the present study, both in the topography and in the chemical treatment.

Figure 40 - Insulating vapour blanket on top of the superhydrophobic surface

The insulating layer of vapour will also affect the evolution of the bubble departure diameter, Db, as depicted in

Figure 41 a).

55

a) b)

Figure 41 - a) Average bubble departure diameters and b) emission frequencies, as a function of the imposed heat flux

For the hydrophilic surfaces, there is no obvious change in diameter with increasing heat flux. Although several

correlations predict the increase of the bubble diameter with the heat flux for hydrophilic surfaces, as revised

for instance in (McHale & Garimella, 2010), these authors show that this trend depends on several parameters,

such as on the interaction mechanisms between nucleation sites. Similar observations are reported in (Moita,

et al., 2015). Hence, this result is not in disagreement with the literature.

On the other hand, for the water boiling on the superhydrophobic surface, the higher heat flux increases the

amount of vaporization. Considering that the large bubble is growing over the insulating vapor layer, this leads

to an almost steady increase in bubble departure diameter.

The difference in size of the bubble on the superhydrophobic surface, when compared to those detached from

the hydrophilic surface also contributes to dissimilar results in terms of the bubble emission frequency, fb, as

depicted in Figure 41 b), being the emission frequency much lower for the superhydrophobic surfaces. For the

boiling on hydrophilic surfaces, the emission frequency follows a decreasing trend, in agreement with the

behavior proposed by (Zuber, 1963). The bubble diameter and emission frequency do not follow necessarily

the relation proposed by several the authors, such as (Jakob & Fritz, 1931) or (Mikic, et al., 1970), in which the

bubble departure frequency is inversely proportional to the departure diameter, as this behavior is also

strongly dependent on the interaction mechanisms, (McHale & Garimella, 2010). For the boiling on the

superhydrophobic surface, there is a steady increase of the emission frequency with increasing heat fluxes. This

trend is naturally contrary to that typically reported for the hydrophilic surfaces, as expected. In this case the

bubble formation and release process occurs over the vapor layer, so the entire growth and departure process

can be enhanced with the increase in the amount of vaporization.

These different bubble behaviour observed on these surfaces with extreme wetting scenarios will probably

affect the heat transfer processes of each surface. The most common way of analyzing this is through boiling

curves which represent the evolution of the surface superheat versus the imposed heat flux.

Figure 42 depicts the boiling curves obtained for the hydrophilic and superhydrophobic surfaces with the

lowest roughness amplitudes. The curves show significantly different trends, which are qualitatively in

56

agreement with the results reported in the literature (e.g. (Takata, et al., 2006), (Phan, et al., 2009), (Takata, et

al., 2012), (Betz, et al., 2013)) and with quite good agreement with the results recently reported by (Malavasi,

et al., 2015), whose experimental conditions are very close to those considered in the present work, except for

the highest heat fluxes considered here.

Figure 42 - Boiling curves obtained for water over hydrophilic and superhydrophobic stainless steel surfaces

From this Figure, the difference in the heat that is transferred from the hydrophilic and from the

superhydrophobic surfaces to the liquid is obvious and can be related to the bubble dynamics behavior

discussed in the previous paragraphs. Hence, the onset of boiling for the hydrophilic surface occurs

approximately for a superheating of 12K, followed by the typical increase in the curve slope, caused by

triggering of the nucleate boiling regime. On the other hand, the boiling curve obtained for the

superhydrophobic surface has a quite atypical trend. The onset of boiling occurs usually during the first power

step, at about 1-2 K of wall superheat. After that, the heat flux increases almost linearly with surface

superheating, with much lower slope than that of the hydrophilic surface.

Based on the RPI model introduced in Chapter 2, (Kurul & Podowski, 1990), there are two major heat transfer

mechanisms, that occur in the boiling process: the heat transferred by the actual vaporization of liquid (the

latent heat) and a second very important mechanism, related to the fluid motion within the near surface

region, in which the surface is rewetted by liquid when the existing thermal boundary layer is disrupted by

bubble departure. The heat transfer that occurs until a new equilibrium thermal boundary layer is formed is

not negligible. In the case of the hydrophilic surfaces, these mechanisms occur in every single nucleation site

and at every bubble departure event, which leads to a high heat transfer performance, being this high

performance related to the higher heat flux that is removed at the same wall superheat. However, in the case

of the superhydrophobic surfaces, the mechanism associated with surface rewetting is not present. As the

bubble grows and departs, the insulating vapour layer is not disrupted and remains covering the surface, acting

57

as an additional thermal resistance to the heat transferred from the surface to the liquid. This phenomenon is

illustrated in Figure 43, which depicts a high-speed sequence of images of a bubble departing from the surface

and leaving the aforementioned insulating vapour layer undisrupted.

a) 0 ms b) 0,455 ms

c) 0,91 ms d) 1,365 ms

58

e) 1,82 ms f) 2,275 ms

Figure 43- Sequence of high-speed images of a bubble departing on a superhydrophobic surface. The undisrupted vapour layer that remains over the surface is highlighted by white circle.

The absence of the rewetting mechanism on the superhydrophobic surfaces is unlikely to be the single reason

explaining the difference between the boiling curves obtained with the hydrophilic vs the superhydrophobic

surface. In fact, the vapor insulation layer on the superhydrophobic surface will also reduce the amount of

liquid vaporization, when compared to the hydrophilic surface, which can be shown based on a simple analysis,

explained as follows. Making use of the post-processing routine developed in MATLAB and already explained in

Chapter 4, one can quantify two of the three parameters that influence the vaporization rate, namely the

bubble departure diameter Db and the bubble departure frequency fb. The other required parameter is the

number of active nucleation sites, which must be manually counted for the hydrophilic surface. In the case of

the superhydrophobic surfaces, this is not required, as the extreme wettability causes all the nucleation sites to

coalesce at a microscopic distance from the surface, creating a single much larger bubble that covers the whole

heated area. Table 9 depicts the results for these parameters, as well as the temperature and heat flux

conditions.

Table 9 - Bubble dynamics parameters for vaporization rate analysis

Surface Wall superheat

[K] q’’ [W/cm

2] Db [mm] fb [Hz]

Active nucleation sites

RAW 27 4.88 3.25 15.21 21

RAW SHS 32 1.1 9.17 7.75 1

Assuming each bubble as sphere, one can evaluate its volume and, multiplying that value by ρv, its mass.

Multiplying the mass value by fb and by the number of active nucleation sites, N, one obtains a rough

estimation of the amount of liquid that is vaporized, per second, following equation (24). Considering the value

59

for the latent heat of vaporization, hfg, provided in Table 1, one can re-estimate the power removed per surface

area using the vaporization values. Comparative values obtained for the hydrophilic and for the

superhydrophobic surface are depicted in Table 10.

𝑉𝑎𝑝𝑜𝑟𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒[𝑔 𝑠⁄ ] =4

3𝜋 (

𝐷𝐵

2)

3

ρ𝑣𝑓𝑏𝑁 (24)

Table 10 - Results for volume, mass, vaporization rate and heat flux calculations

Surface Volume [mm3] Mass [g]

Vaporization rate [g/s]

q’’ [W/cm2]

RAW (hydrophilic) 17.97 1.1x10-5

3.51x10-3

2.52

RAW SHS (superhydrophobic)

403.75 2.4x10-4

1.86x10-3

1.33

Even though these results should be considered as a rough estimative, they are accurate enough to identify

trends. Hence, the vaporization rate is much lower for the superhydrophobic surface, as the insulating vapor

layer will preclude the heat transfer from the surface to the liquid, thus limiting the vaporization rate. On the

other hand, the fact that the large bubble stays attached for longer periods of time significantly reduces the

bubble emission frequency for the superhydrophobic surface, further contributing to the lower value of the

vaporization rate.

The re-estimate value of the heat flux removed by vaporization for the hydrophilic surface is almost half of the

total amount of the heat flux that was measured by the sensor. This can be related to the strong weight of the

term associated to the heat removed by the re-wetting mechanism (as the thermal boundary layer is

disrupted), as proposed in the RPI model, (Kurul & Podowski, 1990). This may be so, since, for the

superhydrophobic surface, for which this mechanism is unlikely to occur, according to the arguments discussed

in the previous paragraphs, the heat flux removed by vaporization is very close to the measured one.

Based on this argument, the heat flux removed from each of these surfaces, as a function of the wall superheat

should follow the trend depicted in Figure 44.

Figure 44 - Vaporization rates for hydrophilic and superhydrophobic surfaces as a function of wall superheat

60

From the results depicted in Figure 44 and supported by the discussion presented up to now, the

superhydrophobic surface starts to vaporize liquid at a much lower wall superheat, when for the hydrophilic

surface the heat is only transferred by natural convection. Hence, for lower surface superheat values, one may

argue that higher heat flux is removed from the superhydrophobic surface, for similar superheat values, when

compared to the hydrophilic one. This should be further confirmed by the experimental results, refining the

measurements, up to 14K, to try capturing the boiling incipience point, which was not possible for the accuracy

available in the present set-up.

As the wall superheat increases, and the insulating vapor layer is generated over the superhydrophobic surface,

the heat that is transferred from the surface to the liquid is strongly limited, so that the heat flux removed for

the same wall superheat become much lower when compared to that obtained for the hydrophilic surface.

This phenomenon of the quick generation of the insulating vapour layer over the superhydrophobic surface has

been recently identified as a “quasi-Leideinfrost” effect, by (Malavasi, et al., 2015). Hence, these authors

consider that there is a sudden change in the boiling regime, from nucleation to the film boiling (or Leidenfrost)

regime, associated to this vapour layer. To confirm this trend, a correlation for film boiling (i.e. when the heat

transfer occurs steadily over a vapour layer), developed by (Berenson, 1961), as depicted in equation (25), was

compared to the experimental boiling curve obtained for the superhydrophobic surface (as shown in Figure

42). The comparison between the experimental data and Berenson’s correlation is depicted in Figure 45.

𝑞′′ = 0.325 [𝑘𝑣

3𝜌𝑣𝑔(𝜌𝑙 − 𝜌𝑣)(ℎ𝑓𝑔 + 0.4𝐶𝑝𝑣(𝑇𝑊 − 𝑇𝑠𝑎𝑡))

𝜇𝑣(𝑇𝑊 − 𝑇𝑠𝑎𝑡)√𝜎 𝑔(𝜌𝐿 − 𝜌𝑣)⁄]

14⁄

(𝑇𝑊 − 𝑇𝑠𝑎𝑡) (25)

Figure 45 - Berenson's Correlation and Boiling curves for the superhydrophobic surfaces

The Figure clearly shows that the experimental results closely follow the correlation proposed by (Berenson,

1961), thus supporting the hypothesis of the change in the boiling regime.

The Figure also depicts results obtained for surfaces with different roughness amplitudes.

61

Surface topography is known to be an influential variable in pool boiling. However, within these extreme

wetting regimes, it clearly plays a secondary role, as the mild increase of the surface roughness does not

introduce significant changes in the boiling curve. This is observed for both hydrophilic and superhydrophobic

surface, as shown in Figure 46. In fact, a mild increase of the mean roughness is not likely to introduce a

significant modification in the wettability, at least in a monotonic and quantifiable way, which can be related to

the apparent angles as stated by (Valente, et al., 2015). Also, it is difficult to relate the boiling mechanisms with

the average parameters that must be used to characterize surfaces with stochastic profiles, e.g. (McHale &

Garimella, 2010). Given that, within the range of roughness amplitude considered here, the increase of the

mean roughness does not significantly change the apparent contact angles, so, it is more likely that the

roughness will mostly affect the pool boiling heat transfer by promoting the potential increase of the number

of active nucleation sites. However, to successfully achieve this goal, one needs to take into account numerous

factors such as bubble and nucleation sites interaction, so that a more systematic approach should be

considered, in which the surface topography is altered within a wider range of geometrical parameters,

particularly regarding the distance between the potential active nucleation sites, e.g. (Teodori, et al., 2013).

a) b)

Figure 46 - Effect of surface topography (quantified by the increase of the mean surface roughness) in the boiling curves, for extreme wetting scenarios: a) hydrophilic surfaces, b) superhydrophobic surfaces.

At this point of the discussion, it is worth mentioning that the curves represented here are limited to the low

heat flux values, which can be reached with the superhydrophobic surfaces. In fact, further rising the imposed

heat flux leads to the disruption of the superhydrophobic coating, which completely modifies the trend of the

boiling curve, generating a “biphilic like“ behaviour, i.e. resembling the behaviour of a hydrophilic surface with

superhydrophobic spots, as reported for instance by (Betz, et al., 2013). This trend is illustrated in Figure 47.

62

Figure 47 - Boiling curve showing a “biphilic like” behaviour, resulting from the disruption of the superhydrophobic coating. The curves obtained for hydrophilic and hydrophobic surfaces are gathered for qualitative comparison.

This occurs at heat flux values much lower than the Critical Heat Flux expected for the hydrophilic surface, so

the curves represented here are quite below this critical value. The change in bubble dynamics due to the

“biphilic” nature of the surface, which consequently should affect the induced flow near the surface, seems to

be the governing factor leading to the enhancement of the heat transfer performance of these surfaces

(reminding that a better performance is associated to the higher heat flux that is removed for the same wall

superheat value, when comparing the various surfaces). Figure 48 illustrates the regions depicting different

boiling behaviour on this biphilic surface, created as the coating breaks.

Figure 48 - Coating breakage and the different boiling regions

These results support the argument that hydrophilic surfaces with superhydrophobic spots may provide the

best compromise in optimizing pool boiling heat transfer. However, deeper research is required in this topic, to

optimize the patterns, which must be supported by an accurate description of bubble dynamics and resultant

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

0

10

20

30

40

50

RAW (Hydrophilic)

RAW SHS (Superhydrophobic)

RAW SHS with coating failure

Heat

flu

x q

'' [

W/c

m2]

Wall superheat [ºC]

“biphilic like” behaviour

Coating failure

Single large bubble

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

0

10

20

30

40

50

RAW (Hydrophilic)

RAW SHS (Superhydrophobic)

RAW SHS with coating failure

Heat

flu

x q

'' [

W/c

m2]

Wall superheat [ºC]

“biphilic like” behaviour

Coating failure

Single large bubble

63

flow dynamics. In these particular conditions, the “biphilic” like behaviour results from a stochastic process,

which cannot be controlled and therefore will not be further discussed.

A general description of the surface wettability on pool boiling conditions and its resulting performance in heat

transfer has been provided. However, making use of the post-processing routine especially developed for this

work (see Chapter 4), it is possible to perform an additional analysis on the bubble growth and detachment

mechanisms and carry out a comparative analysis between the superhydrophobic and the hydrophilic surfaces.

Before starting the various descriptions of the parameters of this single bubble analysis, and in order to provide

an easier understanding of the following paragraphs, it is important to summarize the various definitions of the

contact angles that can be used to describe the effect of the wettability on boiling and that are considered in

the present work. This is important when trying to understand which parameter is more suitable to describe

the effect of wettability. These angles are displayed in Figure 49 with each index being: (1) Bubble contact

angle as measured by the developed post-processing routine; (2) Macro-contact angle as defined by (Phan, et

al., 2009), which is also the supplementary angle of the bubble contact angle; (3) Apparent Quasi-static contact

angles obtained using the sessile drop method.

Figure 49 - Different contact angles used throughout these results section: (1) Bubble contact angle; (2) Macro-contact angle as stated by (Phan, et al., 2009); (3) Apparent Quasi-static contact angle.

Having established this ground base in terms of contact angles, one may now start the aforementioned single

bubble analysis. Figure 50 depicts the temporal evolution of the bubble growth (one bubble) on the

superhydrophobic surface compared to that of the hydrophilic one. It is worth noting that, as expected, the

growth time, tg, for bubble detachment on the superhydrophobic surface is much larger than that on the

hydrophilic. This can be easily confirmed by looking at the temporal evolution of the bubble growth in which, in

the time one single bubble grows for the superhydrophobic surfaces, nearly 10 have grown and detached for

the hydrophilic one. Hence, while the bubble diameter slowly grows on the superhydrophobic surface over

more than 300ms, attaining values larger than 10mm, the bubbles over the hydrophilic surface grow up to 2-

2,5mm, within around 10-16ms. The abrupt decrease of the diameter corresponds to the bubble detachment

instant. The corresponding bubble departure instant for the superhydrophobic surface could not be captured in

this data set, as the growth period is too long.

64

Figure 50 - Comparison between the bubble growth on a hydrophilic and a superhydrophobic surfaces at ≈ 10K of wall superheat

Regarding the temporal evolution of the contact angle of the bubble for the hydrophilic surface, Figure 51 a),

the bubble contact angle starts at a low value and then increases, during bubble growth, until the point the

contact line starts receding and then further decreases until bubble detachment. Actually, the bubble contact

angle starts with very low values (less than 50o), which are not represented here, as the bubble at this period is

yet too small to be accurately tracked and measured by the post-processing routine. The macro-contact angle

on the side of the surface (supplementary to the bubble contact angle) has the opposite evolution. This is

qualitatively in agreement with the process reported by (Phan, et al., 2009). On the other hand, given that for

the superhydrophobic surface, the large bubble is formed already over a thin vapor film, the bubble already

appears with a shape that is indeed very close to that reported by (Phan, et al., 2009) for hydrophobic surfaces,

but, as seen in Figure 51 b), the contact angle remains practically constant during the entire slow growing

process of the bubble, until it suddenly detaches from the surface.

a) b)

Figure 51 - Temporal evolution of the bubble contact angle during the growth and detachment of a single bubble on: a) a hydrophilic surface, b) a superhydrophobic surface

These bubble growing processes are schematically illustrated in Figure 52. The images shown in this Figure are

mainly the post-processing of the real images taken during the bubble growth process; they are not simulations

or schematic representations.

65

0 ms 0,45 ms 4,95 ms 11,25 ms 16,2 ms 17,1 ms

a)

0 ms 1,8 ms 6,3 ms 10,8 ms 22,95 ms 33,75 ms

b) Figure 52 - Temporal evolution of the bubble growth and detachment on: a) a hydrophilic surface, b) a superhydrophobic

surface(0 ms is not bubble birth but is simply an initial time point for the subsequent images)

By comparison of the contact angles depicted in Figure 51 with the schematic evolution shown in Figure 52, it is

not obvious that these angles approach the static or the quasi-static values at bubble formation and departure,

as argued by (Phan, et al., 2010), but the bubble contact angle follows supplementary values to those of the

macro-contact angle, which in turn are approximately (in average) close to the quasi-static angles. Hence, one

may perform a simple quantitative evaluation of the validity of the use of this macro-contact angle using an

existing correlation. Table 11 depicts the bubble diameter as a function of the macro-contact angle, comparing

the experimental results for the hydrophilic surface obtained here with those computed using the following

equation proposed in (Phan, et al., 2010):

𝐷𝑏 = (6√3

2)

1 3⁄

(𝜌𝑙

𝜌𝑣

)−1 2⁄

(𝜌𝑙

𝜌𝑣

− 1)1 3⁄

(tan 𝜃)−1 6⁄ 𝐿𝑐 (26)

in which 𝐿𝑐 = √𝜎

𝑔(𝜌𝑙−𝜌𝑣) is the capillary length.

Table 11 - Bubble departure diameter as a function of the bubble macro-contact angle: comparison between the experimental results obtained in the present study and those provided by the expression proposed by Phan et al. (2010)

Macro-contact angle (o)

Predicted data model Phan et al. (2010) (mm)

Present Work (experimental data)

(mm) Relative deviation (%)

54 1.34 3.11 132.09 57 1.31 2.27 73.28

One can observe a general decreasing trend of the bubble diameter, however there is a significant disparity in

terms of the values obtained for the bubble diameter. The main reason for this disparity is the fact that (Phan,

et al., 2010) considers a single bubble nucleating from a single nucleation site. In the experimental conditions

of the present work, the emerging bubble that was analyzed by the post-processing algorithm was most

Bubble contact

angle

66

certainly the resultant from the interaction of a few very close and very small nucleation sites. They became

activated at the same time due to microscopic thermal and mechanical interaction mechanisms, which resulted

in a larger bubble emerging. One must note that even by having a bubble formed by various nucleation sites,

the value for the contact angle becomes unchanged due to the fact that it only depends on fluid and surface

properties and not the size of the bubble. Any satisfactory results are obtained for the superhydrophobic

surfaces, mainly because (Phan, et al., 2010) equation is only valid for contact angles lower than 90o, which is

not the case for superhydrophobic surfaces. Nevertheless, these results suggest that the macro-contact angle

provides a good qualitative way, in terms of general trends followed to describe the role of wettability on

bubble dynamics, although there are several additional effects that must be considered, such as interaction

mechanisms. Also, this analysis must be extended to explain the more complex processes occurring at

superhydrophobic surfaces, for contact angles much larger than 90o.

The bubble departure frequency, evaluated by Zuber’s equation, (Zuber, 1963), as a function of the

experimental results obtained here for the bubble diameter is depicted in Figure 53.

Figure 53 - Bubble departure frequency provided by the expression proposed by Zuber (1963), as a function of the departure diameter (experimental results).

The experimental results of the present work closely follow the trend predicted by (Zuber, 1963) – equation

(12). However one must approach this result with caution, as the experimental work only rendered three

different bubble departure diameters for three different surfaces, which is not enough to define a clear trend.

This means that despite the fact that a general trend appears to be followed, deeper analysis must be

performed.

Regardless of the particular description of the processes that is required to accurately predict the temporal

evolution of bubble growth, qualitative analysis of Figure 50, Figure 51 and Figure 52 suggest that in average,

there may be a trend for the bubble and quasi-static contact angles to be supplemental, so that averaged

quantities may follow trends with these angles. This is inferred in Figure 54, which considers the average

bubble departure diameter, Figure 54 a), and emission frequency, Figure 54 b), as a function of bubble contact

and macro-contact angles but also with the quasi-static angles.

67

a) b)

Figure 54 - Average a) bubble departure diameter and b) bubble departure frequency, as a function of the bubble contact angle, macro/supplementary contact angle and quasi-static angle

The figure shows a clear trend of the bubble diameter to increase and consequently the frequency to decrease

with the quasi-static and with the macro-contact angle, thus supporting some similarity between them and

consequently supplementary evolution with the bubble contact angle. One must note that the results displayed

in Figure 54 b) are obtained at a relatively high surface overheat, about 33 K, for a more stable boiling process

with fewer influence of interaction mechanisms that differ between wetting regimes. Results at lower surfaces

overheat often depict disparities in one or more points.

One may also infer on the stability of the actual bubble’s growth process in the case of hydrophilic and

superhydrophobic surfaces. Hence, looking at Figure 50 it can be seen that, in the case of the hydrophilic

surfaces, the bubble grows constantly and without oscillations or stops in the growth. However, this is not the

case for the bubble generated on the superhydrophobic surface. In fact, these bubbles, as already shown in

Figure 50, have a much more unstable growing process with many oscillations occurring. These oscillations

occur in terms of bubble diameter, e.g. growth becomes steady for a few milliseconds and suddenly the slope

changes evolving until another stable zone and so on; bubble shape, caused by fluid motion along the bubble’s

interface; and also at the contact line where it does not have a stable movement along bubble growth. Taking

again advantage of the post-processing algorithm developed, the contact line velocity evolution for the growth

period of a single bubble was obtained for each surface type as depicted in Figure 55.

a) b)

Figure 55 - Contact Line Velocity evolution for: a) Hydrophilic surface; b) Superhydrophobic surface

68

It is clear that on the hydrophilic surface, the bubble has a stable contact line movement during the whole

growth process, having peaks at three different instants: Bubble birth (1), when the bubble is visible on the

high-speed movie for the first time; a second instant (2) which corresponds to the instant when the bubble

starts its growing process at the contact line, thus swiftly expanding and stabilizing; and a third instant (3) that

corresponds to the line receding, just before the bubble departs. This motion is also characterized by a stable

movement and a very tiny descending slope (4) in the contact line velocity plot over time that is barely

noticeable in Figure 55. This is the characteristic evolution of these bubbles, given that the velocity of the

contact line has a positive value, as the bubble grows, but then starts to decrease and becomes negative, when

buoyancy effects start to lift the bubble and pulling it away from the surface. Illustrative post processed images

of the three instants are displayed in Figure 56, together with stabilized growth process, characterized by a very

slow (barely noticeable) movement at the contact line. The indexes in Figure 56’s caption are related to those

on Figure 55.

a) (1)

b) (2)

c) (4)

69

d) (3)

Figure 56 - Illustrative post processed images of the growth at: a) Bubble birth (1) b) Contact line movement due to lateral expansion (2) c) Stable growth (4) d) Bubble just before departure (3)

In the case of the superhydrophobic surface, the contact line depicts an unstable movement, with many

oscillations occurring throughout the growth process, with no characteristic instants for its occurrence. The

contact line follows almost like a wave movement along the growth process, which is also associated to the

abovementioned instabilities in growth. These instabilities and waviness of the bubble are clearly visible when

analysing the high speed footage. This instability can be due to three main reasons. The most likely is the

“quasi-Leidenfrost” effect reported by (Malavasi, et al., 2015), given that the vapour layer on top the surface,

from which the bubble rises is much larger than the actual bubble, thus allowing it to go back and forth on top

of this layer. In addition, the actual bubble size may also contribute to this instability, as the larger size of the

bubble is mainly associated to the fact that buoyancy is balanced against the forces maintaining the bubble

close to the surface, which can induce instabilities. Finally, the actual slowness of the growth process may also

allow for the local pressure variations to produce some effect on the bubble shape, which in turn would affect

the size and position of the contact line.

The analysis performed here provides a better understanding of the macroscopic behaviour of bubbles when

wettability varies. The detailed description of the temporal evolution of the various bubble dynamic

parameters, discussed here, together with the evaluation of the contact angles evolution, is expected to be

relevant for validation of future computer simulations.

70

Chapter 6

6. Conclusions and Future work

6.1 Conclusions

This study addresses the effect of the wettability on pool boiling heat transfer. For this purpose, surfaces with

extreme wetting regimes (namely hydrophilic and superhydrophobic) were prepared and characterized. A mild

increase of the surface roughness amplitude was also considered to infer on its possible effect within each of

these extreme wetting regimes. The effect of the wettability was investigated on the pool boiling curves,

experimentally obtained for each type of surface tested here. Furthermore, a detailed analysis on the

wettability effect on bubble dynamics, with emphasis on the monitoring of the temporal evolution of relevant

parameters (e.g. bubble growth, contact angles, contact line velocity) was performed by extensive post-

processing procedures of the high-speed images taken to characterize boiling morphology. To cope with this a

home-made routine was specially developed in MATLAB during this study.

Extreme changes in wettability lead to significantly different boiling curves with atypical trends observed for

the boiling over superhydrophobic surfaces. Hence, the boiling is triggered at very low wall superheat values (1-

2K) with a high number of small nucleation sites. The bubbles, in the absence of a governing force that

promotes their departure, stay attached to the surface and coalesce, forming an insulating vapour layer from

which large bubbles are generated, covering the entire heated surface. Consequently, the heat flux increases

almost linearly with wall superheat, closely following the empirical trend predicted within the film boiling

regime. This behaviour is in agreement with the so called “quasi-Leidenfrost”, recently reported in literature.

Consequently , for the same wall superheat, the heat flux on the superhydrophobic surface is much lower than

that on the hydrophilic ones, except at very low superheats, (<14K) for which boiling is already observed over

the superhydrophobic surface, and for which heat is only removed by natural convection on the hydrophilic

surface. The differences observed in the heat flux are also strongly related to the bubble dynamics

characteristic of the boiling on each of these surfaces. Hence, for the boiling on the superhydrophobic surface,

the bubble generated on the surface is extremely large (with all the nucleation sites coalescing to a bubble

approximately the size of the heater) and its frequency is very low. Hence, the resulting vaporization rate is

lower than that obtained for the hydrophilic surfaces. Furthermore, for the hydrophilic surfaces, boiling is

characterized with regular size bubbles emerging from multiple sites within the surface, promoting rewetting

and increasing the heat that is transferred from the surface to the liquid. This rewetting mechanism, which is

reported by several authors to be a main term in the pool boiling heat transfer, is precluded on the

superhydrophobic surfaces due to the generation of the insulating layer. Quantitative estimation on the

various terms of the heat flux supports these assumptions

71

Regarding the temporal evolution of the various parameters characterizing bubble dynamics, the results show

that the growth period of a bubble emerging from a superhydrophobic surface is much larger – about 20 times

larger – than that taken by the bubbles emerging from the hydrophilic one. Prediction of bubble growth and

bubble departure diameters are addressed for several years in the literature, but many fail the predictions due

to the inaccurate account for the effect of wettability. In line with this, the present work also explores the

temporal evolution of the contact angles, as differently defined by several authors, to infer on possible trends

between them and the bubble growth mechanisms. Particularly, the evolution of the bubble contact angle

during the growth process is evaluated, together with the supplementary values of that angle – here called the

macro-contact angle – which are observed to approach the quasi-static contact angles, as defined by (Phan, et

al., 2010). However, using these values on relations to predict bubble diameter, as proposed in (Phan, et al.,

2010), allows obtaining good agreement in the general trend, although does not render accurate quantitative

results. This can be attributed to different causes, namely to the interaction mechanisms, which are not usually

considered in these correlations. Hence, the analysis performed here suggest existing models/theoretical

correlations can predict the trend of the bubble growth using the macro-contact angle (complementary to

bubble contact angle) for the hydrophilic surfaces, but cannot accurately predict bubble size. Consequently,

they are unable to describe the particular bubble growth phenomenon observed for the

superhydrophobic surfaces.

Finally, the stability of the bubble formation process was also inferred, by analysing the stability of the contact

line motion. The contact line velocity profiles obtained for the bubbles growing on the superhydrophobic

surfaces was shown to be highly unstable, contrasting to the stable growing process depicted by the bubbles

on the hydrophilic surfaces.

These results are expected to be useful in devising future correlations accounting for the effect of the

wettability, particularly on the extreme wetting conditions considered in the present study. The experimental

data produced is also expected to be useful in validating future numerical simulations.

6.2 Future Work

There are still many questions to be addressed in order to achieve an accurate characterization of the effect of

wettability on pool boiling heat transfer. A limited number of correlations and models were investigated, so the

validity of a wider range of theoretical relations to predict bubble dynamic features, such as bubble growth and

departure diameter, must be analysed and explored at the light of how adequate the contact angles studied

here are useful in improving the theoretical predictions.

Although several authors have recently reported the improved heat transfer coefficients for pool boiling over

the aforementioned biphilic surfaces (i.e. hydrophilic surfaces with suerhydrophobic spots) a detailed analsysis,

similar to that performed in this study, should be extended for those surfaces, to understand the governing

phenomena and optimize the biphilic pattern in a systematic way.

This study should also be extended considering the boiling on superhydrophilic surfaces and the boiling of

other fluids, such as ethanol and mixtures, due to their significantly different properties, when compared to

72

those of water, which will render significant differences in the bubble dynamics and, consequently in the

boiling curves.

The routine developed here to process the high-speed images can further be improved, mainly considering the

following items: 1) Improve the routine (e.g. the boundary detection algorithm) so it could disregard pre-

coalescence in the vertical direction which occurs when the lower boundary of the last released bubble and the

upper boundary of the new one are almost touching – and still detect the bubble as a single unit and not as

strange shape, resulting from the beginning of the coalescence; 2) a secondary algorithm should be derived in

which the contact angles are calculated based on the boundaries described using the Young-Laplace equation,

to fully define the curve at the interface and minimize the error obtained in this measurement.

To further improve the effectiveness of the software developed, the lighting and the camera support must also

be improved in order to enhance the quality of the high-speed images and further reduce the error associated

with the boundary tracing.

73

74

Bibliography

Abernethy, R., Benedict, R. & Dowdell, R., 1985. ASME measurements uncertainty. J. Fluids Eng., 107(2), pp.

161-164.

Anderson, T. & Mudawar, I.,1989, Microelectronic cooling by enhanced pool boiling of a dielectric

fluorocarbon liquid. ASME J. Heat Transf., Volume 111, pp. 752-760.

Antonini, C., Amirfazli, A. & Marengo, M., 2012. Drop impact and wettability:from hydrophilic to

superhydrophobic surfaces. Phys. Fluids, Volume 24.

Arik, M., 2001. Enhancement of Pool Boiling Critical Heat Flux in Dielectric Liquids. Ph.D. Dissertation, Dept.

Mechanical Eng., Univ. Minnesota, Minneapolis.

Bankoff, S., 1957. Ebullition from solid surfaces in the absence of a pre-existing gaseous phase. Trans. Am.

Mech. Eng., Volume 79, pp. 735-740.

Bankoff, S., 1958. Entrapment of gas in the spreading of a liquid over a rough surface. AlChE J. , Volume 4, pp.

24-26.

Berenson, P., 1961. Film-Boiling Heat Transfer From a Horizontal Surface. J. Heat Transfer, Volume 83, pp. 351-

356.

Berenson, P., 1962. Experiments on pool-boiling heat transfer. Int. J. Heat and Mass Transfer, Volume 5, pp.

985-999.

Betz, A., Jenkins, J., Kim, C. & Attinger, D., 2013. Boiling heat transfer on superhydrophobic, superhydrophilic,

and superbiphilic surfaces. Int. J. Heat and Mass Transf., Volume 57, pp. 733-741.

Bhushan, B. & Jung, Y., 2011. Natural and biomimetic artificial surfaces for superhidrophobicity, self cleaning,

low adhesion and drag reduction. Progress in Material Sciences, Volume 56, pp. 1-108.

Bico, J., Thiele, U. & Quéré, D., 2002. Wetting of textured surfaces. Colloids and Surfaces A: Physicochemical

and Engineering Aspects, Volume 206, pp. 41-46.

Bourdon, B. et al., 2013. Enhancing the onset of pool boiling by wettability modification and nanometrically

smooth surfaces. Int. Comm. Heat and Mass Transf., Volume 45, pp. 11-15.

Bourdon, B. et al., 2012. Influence of the wettability on the boiling onset. Langmuir, Volume 28, pp. 1618-1624.

Carey, V. P., 1992. Liquid–vapor phase‐change phenomena

Cassie, A. & Baxter, S., 1944. Wettability of porous surfaces. Transactions of the Faraday Society, Volume 40,

pp. 546-551.

75

Chekanov, V., 1977. Interaction of centers in nucleate boiling. Teplofiz. Vys. Temp., Volume 15, pp. 121-128.

Cheng, P., Quan, X., Gong, S. & Hong, F., 2014. Recent studies on surface roughness and wettability effects in

pool boiling. Proc. 14 th IHT.

Clark, H., Strenge, P. & Westwater, J., 1959. Active sites for nucleate boiling. Chem. Eng. Prog., Symp. Ser.,

Volume 55, pp. 103-110.

Cornwell, K., 1982. On boiling incipience due to contact‐angle hysteresis. Int. J. Heat and Mass Transfer,

Volume 25, pp. 205-211.

Corty, C. & Foust, A., 1955. Surface variables in nucleate boiling, 51 (17) (1955) . Chem. Eng. Prog. Symp. Ser.,

Volume 51, pp. 1-12.

Costello, P. & Frea, J., 1963, A salient non hydrodynamic effect on pool boiling burnout of small semicylindrical

heaters,American Institute of Chemical Engineers Progress Symposium Series Preprint No. 15, Sixth US National

Heat Transfer Conf.

Darby, R., 1964. The dynamics of vapour bubbles in nucleate boiling. Chemical Engineering Science, Volume 19,

pp. 39-49.

Forest, T. W., 1982. The stability of gaseous nuclei at liquid‐solid interfaces. J. Appl. Phys., Volume 53, pp. 6191-

6201.

Fritz, W., 1935. Maximum Volume of vapour bubbles. Phys.Z, Volume 36, pp. 379-388.

Fritz, W. & Ende, W., 1936. Uber den verdam-pfungsvorgang nach kinematographischen aufnahmen an

dampfblasenr. Physik Zeitsch, Volume 37, pp. 391-401.

Gambaryan-Roisman, T., 2014. Controlling hydrodynamics, Heat transfer and phase change in thin films and

drops. Proc.14th IHT.

Gerardi, C., Buongiorno, J., Hu, L. W. & McKrell, T., 2009. Measurement of nucleation site density, bubble

departure diameter and frequency in pool boiling of water using high-speed infrared and optical cameras. Proc.

of 7th ECI International Conference on Boiling Heat Transfer.

Han, C. & Griffith, P., 1962. The mechanism of heat transfer in nucleate boiling. Technical Report No. 7673-19,

Department of Mechanical Engineering, Massachusetts Institute of Technology.

He, B., Patankar, A. & Lee, J., 2003. Multiple equilibrium droplet shapes and design criterions for rough

hydrophobic surfaces. Langmuir, Volume 19, pp. 4999-5003.

Hitchcock, S. J., Carrol, N. T. & Nicholas, M. G., 1981. Some effects of substrate roughness on wettability.

J. Mat. Sci., Volume 16, pp. 714-732.

76

Hong, K. T., Imadojemu, H. & Webb, 1994. Effects of oxidation and Surface Roughness on Contact Angle.

Exp. Thermal Fluid Sci, Volume 8, pp. 279-285.

Hsu, S. & Schmidt, 1961. Measured variations in local surface temperatures in pool boiling of water.

J.Heat Transfer, Volume 83, pp. 254-260.

Hsu, Y. & Graham, R., 1976. Transport processes in boiling and two-phase systems, including near-critical fluids.

Washington, D.C.: Hemisphere, .

Jakob, M., 1936. Heat Transfer in Evaporation and Condensation. Mech. Eng. Am. Soc. Mech. Eng., Volume 58,

pp. 643-660.

Jakob, M. & Fritz, W., 1931. Versuche uber den Verdampfungsvorgang. Forschungsgebiete des

Ingenieurwesens, Volume 2, pp. 435-447.

Kakaç, S. & Boilers, S., 1991. Evaporators and Condensers.

Kandlikar, S. & Steinke, M., 2001. Contact angles of droplets during spread and recoil after impinging on a

heated surface. Chemical Engineering Research and Design, Volume 79, pp. 491-498.

Kandlikar, S. & Steinke, M., 2002. Contact angles and interface behaviour during rapid evaporation of liquid

on a heated surface. Int. J. Heat and Mass Transfer, Volume 45, pp. 3771-3780.

Klein & Westwater, 1971. Heat transfer from multiple spines to boiling liquids. AIChE J., Volume 17, pp. 1050-

1056.

Koch, K. & Barthlott, B., 2009. Superhydrophobic and superhydrophilic plant surfaces: An inspiration for

biomimetic materials. Philosophical Transactions of the Royal Society: Mathematical, Physical Engineering

Sciences,, pp. 1487-1509.

Kolev, N., 1995. How Accurately Can We Predict Nucleate Boiling? Exp. Thermal Fluid Sci 10 (1995) 370‐.

Exp. Thermal Fluid Sci., Volume 10, pp. 370-378.

Kurihara, H. & Myers, J., 1960. The effects of superheat and surface roughness on boiling coefficients. AIChE J.,

Volume 6, pp. 83-91.

Kurul, N. & Podowski, M., 1990. Multidimensional effects in forced convection subcooled boiling. Proceedings

of the 9th International Heat Transfer Conference, pp. 21-25.

Lorenz, J. J., 1972. The effects of surface conditions of boiling characteristics, Cambridge, Massachusetts:

Ph. D Thesis, Massachusetts Institute of Technology.

Lorenz, J. J., Mikic, B. B. & Robsenow, W. M., 1974. Effect of surface conditions on boiling characteristics.

Proceedings of 5th International Heat Transfer Conference, Volume 4, pp. 35-39.

77

Malavasi, I. et al., 2015. Appearance of a low superheat “quasi-Leidenfrost” regime for boiling on

superhydrophobic surfaces. Int. Comm. Heat and Mass Transfer, Volume 63, pp. 1-7.

Marto, . & Rohsenow, ., 1966. Effects of surface conditions on nucleate pool boiling of sodium.

ASME J. Heat Transf., Volume 88, pp. 196-204.

Matkovic, M. & Koncar, B., 2012. Bubble departure diameter prediction uncertainty. Science and Tech. Nuclear

Inst., Volume 2012.

McHale, J. & Garimella, S.,2010, Bubble nucleation characteristics in pool boiling of a wetting liquid

on smooth and rough surfaces, International Journal of Multiphase Flow, Volume 36, pp. 249-260.

Mikic, B., Rohsenow, W. & Griffith, P., 1970. On bubble growth rates. Int. J. Heat and Mass Transfer, Volume

13, pp. 657-666.

Mizukami, K., 1977. Entrapment of vapor in reentrant cavities. Lett. Heat and Mass Transfer, Volume 2, pp.

279-284.

Moita, A. S. & Moreira, A. L. N., 2003. Influence of surface properties on the dynamic behaviour of impacting

droplets. Sorrento, Italy, Proceedings of the 9th ICLASS‐Europe2003.

Moita, A. S., Teodori, E. & Moreira, A. L. N., 2012. Enhancement of pool boiling heat transfer by surface micro‐

structuring. Journal of Physics: Conf. Series 395: 012175 .

Moita, A., Teodori, E., Moreira & A.L.N., 2015. Influence of surface topography in the boiling mechanisms. Int. J.

Heat and Fluid Flow, Volume 52, pp. 50-63.

Moreira, A., 2014. Multi-scale interfacial phenomena and heat transfer enhancement. Proc.14th IHT.

Mukherjee, A. & Kandlikar, S., 2007. Numerical study of single bubbles during nucleate pool boiling. ASME J.

Heat Transfer, Volume 126, pp. 1023-1039.

Nam, Y., Aktinol, E., Dhir, V. & Ju, Y., 2011. Single bubble dynamics on a superhydrophilic surface

with artificial nucleation sites. Int. J. Heat and Mass Transfer, Volume 54, pp. 1572-1577.

Nishio, S., 1985. Stability of pre‐existing vapor nucleus in uniform temperature field. Tran. JSME (Ser.B), Volume

54, pp. 1802-1807.

Nukiyama, S., 1934. Maximum and minimumvalues of heat Q transmitted from metal to boiling water under

atmospheric pressure. J. of Japan Society of Mechanical Engineering, Volume 37, p. 367.

Papon, P., Leblond, J. & Meijer, P. H. E., 2006. The Physics of Phase Transitions. Second ed., Springer‐Verlag ,

pp. 35-51.

78

Phan, H., N. Caney, P. Marty & S. Colasson, ., 2009. Surface wettability control by nanocoating: the effects on

pool boiling heat transfer and nucleation mechanism, Int. J. Heat and Mass Transfer , Volume 52, pp. 5459-

5471.

Phan, H. et al., 2010. A model to predict the effect of contact angle on the bubble departure diameter during

heterogenous boiling. Int. Comm. Heat Mass Transf., Volume 37, pp. 964-969.

Pioro, I. L., Rohsenow, . & Doerffer, S. S., 2004. Nucleate pool‐boiling heat transfer: review

of parametric effects of boiling surface. Int. J. Heat and Mass Transfer, Volume 47, pp. 5033-5044.

Qi, Y. & Klausner, J. F., 2005. Heterogeneous nucleation with artificial cavities. Journal of Heat Transfer, Volume

127, pp. 1189-1196.

Rayleigh, L., 1917. On the pressure developed in a liquid during the collapse of a spherical bubble. Philosophical

Magazine, Volume 34, pp. 94-98.

Sedev, R., 2011. Surface tension, interfacial tension and contact angles of ionic liquids. Current Opinion in

Colloid & Interface Science, Volume 16, pp. 310-316.

Stefan, K., 1992. Heat transfer in condensation and boiling. x, Berlin Germany, (1992) 127‐128. . Springer, pp.

127-128.

Takata, Y., Hidaka, S. & Hu, L., 2006. Boiling feature on a super water-repellent surface. Heat Transf. Eng.,

Volume 27, pp. 25-30.

Takata, Y., Hidaka, S. & Kohno, M., 2012. Effect of surface wettability on pool boiling: enhancement by

hydrophobic coating. Int. J. of Air‐Conditioning and Refrigeration, Volume 20.

Teodori, E., Moita, A. & Moreira, A., 2013. Characterization of pool boiling mechanisms over micro-patterned

surfaces using PIV. Int. J. Heat Mass Transf., Volume 66, pp. 261-270.

Teodori, E., Moita, A. & Moreira, A., 2013. Pool boiling heat transfer over micro-patterned surfaces:

Experiments and Theory. World Conference on Experimental Heat Transfer.

Tong, W., Bar‐Cohen, A., Simon, T. W. & You, S. M., 1990. Contact angle effect on boiling incipience of highly‐

wetting liquids. Int. J. Heat Mass Transfer, Volume 33, pp. 91-103.

Usamentiaga, R. et al., 2014. Infrared Thermography for Temperature Measurement and Non-Destructive

Testing. Sensors, Volume 14.

Valente, T., Teodori, E., Moita, A. S. & Moreira, A. L. N., 2015. Effect of wettability on nucleate boiling.

Proceedings of the 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics –

HEFAT 2015, pp. 168-177.

79

Wang, C. H. & Dhir, V. K., 1993. Effect of surface wettability on active nucleate site density during pool boiling

of water on a vertical surface. Trans. ASME J. Heat Transfer, Volume 115, pp. 670-679.

Wei, J. & Honda, H., 2003. Effects of fin geometry on boiling heat transfer from silicon chips with micro‐pin‐

fins immersed in FC‐72. Int. J. Heat and Mass Transfer, Volume 46, pp. 4059-4070.

Wen, D. & Wang, ., 2002. Effects of surface wettability on nucleate pool boiling heat transfer

for surfactant solutions. Int. J. Heat and Mass Transfer, Volume 45, pp. 1739-1747.

Wenzel, R., 1936. Resistance of solid surfaces to wetting by water. Industrial and Engineering Chemistry,

Volume 28, pp. 988-994.

Yeh, 1997. Analysis of thermally optimized fin array in boiling liquids. Int. J. Heat and Mass Transf., Volume 40,

pp. 1035-1044.

Young, T., 1805. An essay on the cohesion of fluids. Philosophical Transactions of the Royal society of Long,

Volume 95, pp. 65-87.

Zhou, B. X. & Hosson, J. M., 1995. Influence of surface roughness on the wetting angle. J. Mat. Res., Volume 10.

Zuber, N., 1959. Hydrodynamic aspect of boiling heat transfer. Ph.D. Thesis.

Zuber, N., 1963. Nucleate boiling: the region of isolated bubbles and the similarity with natural convection. Int.

J. Heat Mass Transf., Volume 6, pp. 53-78.

80

Annexes

Annex A – MATLAB code developed for image Post-Processing

% Matlab Code for bubble dynamics analysis of pool boiling experiments % Image-Processing Toolbox is required to execute!

% Author: Tomás Valente, 2015, IN+

clc close all clear all

%%

%---------------------->P A R A M E T E R S<-----------------------------

%CHANGE THE FOLLOWING STRINGS if paths and filenames are not in accordance: % %>> delete empty excel-sheets ver_excel = 'Sheet'; %>> search for background image background_file = 'Background.bmp'; %>> search for images containing img_files = '*129_*.bmp'; %>> set camera frames per second cam_fps = 2200;

%------------------------------------------------------------------------

%%

%Start timer and program tic workspace; disp('Running script..');

%Open image directory dirname = uigetdir;

if (dirname==0) disp('>>>> You need to enter a valid path..Aborting execution!'); error('Invalid Pathname!'); else disp(['Selected input dir: ' dirname]); end

%%

try

calib = 62.80; %calibration factor in pixels per 2 mm

81

start_at = int16(1);%number of the frame for start of algorithm for

analisys limit_bw = int16(30);%threshold if isinteger(start_at) && (start_at>0) %Do just nothing else error('It seems as if the second entry is not of type integer!'); end

if isinteger(limit_bw) && (limit_bw>0) %Do just nothing else error('It seems as if the third entry is not of type integer!'); end catch err fprintf('\nSomething went wrong! Please check for errors.\n'); rethrow(err); end

calib_factor = calib/2; %>> calibration factors in pixels per mm fprintf('\nCalibration-factor: %g Pixels per mm\n', calib_factor); fprintf('Starting at image #%u\n',start_at); fprintf('Black-White threshold is: %u\n', limit_bw);

%Count number of existing images in dir cont_dir = dir(img_files); no_img = length(cont_dir);

fprintf('\nDetected %u images for %s!\n\n',no_img, img_files); %Verify that images are correctly counted and if the start value does not %exceed the number of images if (start_at>no_img) disp('..cannot execute loop for image analysis.'); error('ATTENTION: The chosen start-at value exceeds the total number of

images!');

%Preallocate output-vector for loop A = zeros(1,3);

%Select the backround image and background image cropping [backgr_img1] = imread(background_file); [backgr_img] = imcrop(backgr_img1,[70,152,225,324]);

%Create *.xls for output with actxserver (MS only!) -> formating enabled cd(dirname); warning('off','MATLAB:xlswrite:AddSheet');

current_date = datestr(clock,0); str_valid = strrep(current_date, ':' , '-'); output_name = ['Analysis_' str_valid '.xlsx'];

loc_excel = 'A1:F1'; xlswrite(output_name,{'#','File','Diameter [mm]','Contact

angle(º)','Centroid Velocity','Contact Line

Velocity'},'Results',loc_excel); loc_excel_d = 'G1:H1'; xlswrite(output_name,{'Init. Diameter [mm]','Max. Diameter

[mm]'},'Results',loc_excel_d);

82

str_excel = [dirname '\' output_name]; str_sheet = ver_excel; %>> EN: Sheet, DE: Tabelle, etc. (= Lang. dependent)

myExcel = actxserver ('Excel.Application'); myExcel.Visible = 0; %>> Make Excel visible while processing myExcel.DisplayAlerts = 0;

%Open Excel file and delete unnecessary sheets myExcel.Workbooks.Open(str_excel);

try %Throws an error if the sheets do not exist myExcel.ActiveWorkbook.Worksheets.Item([str_sheet '1']).Delete; myExcel.ActiveWorkbook.Worksheets.Item([str_sheet '2']).Delete; myExcel.ActiveWorkbook.Worksheets.Item([str_sheet '3']).Delete; catch err %Do just nothing end

%Format the worksheet myExcel.Columns.Item(1).columnWidth = 10; myExcel.Columns.Item(2).columnWidth = 40; myExcel.Columns.Item(3).columnWidth = 20; myExcel.Columns.Item(5).columnWidth = 25; myExcel.Columns.Item(6).columnWidth = 25; cells = myExcel.ActiveSheet.Range(loc_excel); cells.Font.Bold = 1; cells.HorizontalAlignment = 3; cell_d = myExcel.ActiveSheet.Range(loc_excel_d); cell_d.Font.Bold = 1; cell_d.HorizontalAlignment = 3;

myExcel.ActiveWorkbook.Save;

%Setting background color for Excel cell-formating rgb_val = [255 255 102]; my_color_1 = rgb_val * [1 256 256^2]'; rgb_val = [96 204 99]; my_color_2 = rgb_val * [1 256 256^2]';

%%

%Define initial values mandatory for the loop d_zero = 0; d_max = 0; centroide_real1=[0 0]; centroide1=[0 0]; contacto1=0;

%Check and, if necessary, convert data type to maintain integrity of loop

index check_type = strcmp(class(no_img),'double');

if (check_type) start_at = double(start_at); else

83

%Do just nothing end

%Image processing algorithm and data writing for k=start_at:no_img

%Reset important parameters to prevent incorrect analysis img3=0; img4=0;

%Load the image for processing str_img = cont_dir(k).name; [imgh] = imread(str_img);

%Image cropping [img] = imcrop(imgh,[70,152,225,324]);

%Background subtraction img_sub=imsubtract(backgr_img,img);

%Gaussian filter hy = fspecial('gaussian', [3 3], 1); hx = hy'; img_y = imfilter(double(img_sub), hy, 'replicate'); img_x = imfilter(double(img_sub), hx, 'replicate'); img_gauss = sqrt(img_x.^2 + img_y.^2);

%Image enhancement and hole filling img3_a = imfill(img_gauss, 'holes'); img3_b = 256 * (img3_a >= limit_bw);

se = strel('disk', 17); se2 = strel('ball', 1, 1); img3_c = imclose(img3_b, se2); img4_a = imopen(img3_c, se);

img3 = img3_b; img4 = img4_a > 10;

img3_d = img3_c > 10; %Working variables setup row=0; col=0; boundary=0; tamanho=size(img3_d); x=tamanho(1); y=tamanho(2); coluna=min(find(img3_d(x,:))); %Bubble variables calculation if (img3_d(x,coluna)==1)%Detects if there is a bubble present in the

current working frame

%Boundary tracing boundary = bwtraceboundary(img3_d,[x, coluna],'N');

%Diameter measurement mat = zeros(x, y);%Creation of a zero matrix for use with bwarea mat(sub2ind(size(mat), boundary(:,1), boundary(:,2))) = 1;%Filling that

matrix with 1 on boundary coordinates

84

imgb=im2bw(mat); imgb2=imfill(imgb,'holes');%Filling the boundary set by the previous

manipulation with one's area=bwarea(imgb2);%Area measurement diametro=2*sqrt(area/pi);%Diameter calculation dia_drop_real2=diametro/calib_factor;%Diameter conversion to mm

%Centroide calculation centroide=[mean(boundary(:,2)) mean(boundary(:,1))]; centroide_real2=centroide/calib_factor;%Centroid conversion to mm values

%Contact angle measurement boundary2=[x - boundary(1,1) boundary(1,2) ;x - boundary(2,1)

boundary(2,2);x - boundary(3,1) boundary(3,2); x - boundary(4,1) boundary(4,2);x - boundary(5,1) boundary(5,2);x -

boundary(6,1) boundary(6,2)];%Boundary manipulation for polyfit ab2 = polyfit(boundary2(:,2), boundary2(:,1), 1);%Linear equation fit to

boundary points near contact line angle=atand(ab2(1));%Angle calculation

% Conditions to avoid coalescence detection, angle inversion % and other factors if (angle > 0) angle=angle; else angle=180+angle; end if (boundary==0) angle=0; end if (centroide1(2)-centroide(2) > 40) dia_drop_real=0; centroide_real2=[0 0]; centroide_real1=[0 0]; vel_drop=0; else dia_drop_real=dia_drop_real2; end if (dia_drop_real>6) dia_drop_real=0; centroide_real2=[0 0]; centroide_real1=[0 0]; vel_drop=0; else dia_drop_real=dia_drop_real2; end if (centroide(2)< x - 120) dia_drop_real=0; centroide_real2=[0 0]; centroide_real1=[0 0]; vel_drop=0; end else dia_drop_real=0; centroide=[0 0]; centroide_real2=[0 0]; centroide_real1=[0 0]; angle=0; end if (boundary==0) angle=0;

85

end

%Mark d_max try if (dia_drop_real>d_max) d_max = dia_drop_real; k_max = k; end catch err fprintf('There was a problem obtaining the droplet diameter! Maybe start_at

needs to be adjusted?'); rethrow(err); end %Velocity calculations

%Centroide velocity if (centroide_real2 ~= 0) y_1 = centroide_real2(2); y_2 = centroide_real1(2); dy = y_2 - y_1; dt = 1/cam_fps*1000; vel_drop = dy/(dt); else vel_drop=0; end if (vel_drop < 0) vel_drop = 0; end

%Contact line velocity if (boundary ~=0) contacto2=boundary(1,2)/calib_factor; dy_cont=contacto1-contacto2; dt = 1/cam_fps*1000; vel_cont = dy_cont/(dt); else vel_cont=0; end if (contacto1==0) vel_cont=0; end if (contacto2==0) vel_cont=0; end

%variable setting and resetting for loop purposes contacto1=contacto2; centroide_real1=centroide_real2; centroide1=centroide;

%Write and process the current data to Excel A = {k str_img dia_drop_real angle vel_drop vel_cont};

m = k+3-start_at; cell_no = num2str(m); loc_excel = ['A',cell_no,':F',cell_no]; loc_excel_d = ['G',cell_no];

cell_d = myExcel.ActiveSheet.Range(loc_excel_d); cell_d.Interior.Color = my_color_1;

86

cell_d.NumberFormat = '0,000';

cells = myExcel.ActiveSheet.Range(loc_excel); cells.HorizontalAlignment = 3; cells.Value = A;

%Image display with boundary and angle plotting imshow(img3_d); axis equal; hold on if (img3_d(x,coluna)==1) plot(boundary(:,2),boundary(:,1),'g','LineWidth',3); hold on plot(centroide(:,1),centroide(:,2), 'b*') hold on text(50, 50, [sprintf('%1.3f',angle),'{\circ}'],... 'Color','y','FontSize',14,'FontWeight','bold'); end drawnow; end

%Mark cell containing d_max m = k_max+3-start_at; cell_no = num2str(m); loc_excel = ['A',cell_no,':G',cell_no]; cell_d = myExcel.ActiveSheet.Range(loc_excel); cell_d.Interior.ColorIndex = 45; cell_d.Font.Color = 2; cell_d.Font.Bold = 1;

%Print d_zero and d_max to Excel B = {d_zero d_max};

loc_excel = 'G3:H3'; cells = myExcel.ActiveSheet.Range(loc_excel); cells.Interior.Color = my_color_2; cells.NumberFormat = '0,000'; cells.HorizontalAlignment = 3; cells.Value = B;

%Add a new chart to Excel and select data

%Diameter graph myChart = myExcel.ActiveSheet.Shapes.AddChart; editChart = myChart.Chart; editChart.SeriesCollection.NewSeries; m = k+3-start_at; cell_no = num2str(m); loc_excel = ['C3:C',cell_no]; loc_excel_d = ['A3:A',cell_no]; editChart.SeriesCollection(1).Value = myExcel.ActiveSheet.Range(loc_excel); editChart.SeriesCollection(1).XValue =

myExcel.ActiveSheet.Range(loc_excel_d); %Format the chart properties myChart.Chart.ChartType = 4; posChart = myExcel.Activesheet.get('Range', 'I7'); myExcel.ActiveSheet.ChartObjects.Left = posChart.Left; myExcel.ActiveSheet.ChartObjects.Top = posChart.Top; myChart.Chart.HasTitle = 1; myChart.Chart.ChartTitle.Text = 'Spreading diameter over img-#'; myChart.Chart.HasLegend = 0;

87

editChart.ChartArea.Width = 500;

%Contact angle graph myChart2 = myExcel.ActiveSheet.Shapes.AddChart; editChart2 = myChart2.Chart; editChart2.SeriesCollection.NewSeries; m = k+3-start_at; cell_no = num2str(m); loc_excel = ['D3:D',cell_no]; loc_excel_d = ['A3:A',cell_no]; editChart2.SeriesCollection(1).Value =

myExcel.ActiveSheet.Range(loc_excel); editChart2.SeriesCollection(1).XValue =

myExcel.ActiveSheet.Range(loc_excel_d); %Format the chart properties myChart2.Chart.ChartType = 4; posChart2 = myExcel.Activesheet.get('Range', 'I22'); myExcel.ActiveSheet.ChartObjects.Left = posChart2.Left; myExcel.ActiveSheet.ChartObjects.Top = posChart2.Top; myChart2.Chart.HasTitle = 1; myChart2.Chart.ChartTitle.Text = 'Contact angle variation'; myChart2.Chart.HasLegend = 0; editChart2.ChartArea.Width = 500;

%Centroid vertical velocity graph myChart3 = myExcel.ActiveSheet.Shapes.AddChart; editChart3 = myChart3.Chart; editChart3.SeriesCollection.NewSeries; m = k+3-start_at; cell_no = num2str(m); loc_excel = ['E3:E',cell_no]; loc_excel_d = ['A3:A',cell_no]; editChart3.SeriesCollection(1).Value =

myExcel.ActiveSheet.Range(loc_excel); editChart3.SeriesCollection(1).XValue =

myExcel.ActiveSheet.Range(loc_excel_d); %Format the chart properties myChart3.Chart.ChartType = 4; posChart3 = myExcel.Activesheet.get('Range', 'I38'); myExcel.ActiveSheet.ChartObjects.Left = posChart3.Left; myExcel.ActiveSheet.ChartObjects.Top = posChart3.Top; myChart3.Chart.HasTitle = 1; myChart3.Chart.ChartTitle.Text = 'Bubble vertical Velocity(m/s)'; myChart3.Chart.HasLegend = 0; editChart3.ChartArea.Width = 500;

%Contact line velocity graph myChart4 = myExcel.ActiveSheet.Shapes.AddChart; editChart4 = myChart4.Chart; editChart4.SeriesCollection.NewSeries; m = k+3-start_at; cell_no = num2str(m); loc_excel = ['F3:F',cell_no]; loc_excel_d = ['A3:A',cell_no]; editChart4.SeriesCollection(1).Value =

myExcel.ActiveSheet.Range(loc_excel); editChart4.SeriesCollection(1).XValue =

myExcel.ActiveSheet.Range(loc_excel_d); %Format the chart properties myChart4.Chart.ChartType = 4; posChart4 = myExcel.Activesheet.get('Range', 'I55');

88

myExcel.ActiveSheet.ChartObjects.Left = posChart4.Left; myExcel.ActiveSheet.ChartObjects.Top = posChart4.Top; myChart4.Chart.HasTitle = 1; myChart4.Chart.ChartTitle.Text = 'Contact Line Velocity'; myChart4.Chart.HasLegend = 0; editChart4.ChartArea.Width = 500;

%Save and close myExcel.ActiveWorkbook.Save; myExcel.Visible = 1; %>> Make Excel visible % myExcel.ActiveWorkbook.Close; % myExcel.Quit; % myExcel.delete;

t_elapsed=toc; fprintf('Analysis finished!\n\nTotal time elapsed: %g seconds.',

t_elapsed);

89

90

Annex B – Poster for LARSyS annual meeting presentation

91

92

Annex C – Poster for 14th UK Heat Transfer Conference

presentation

93

94

Annex D – Abstract of the paper submitted to HEFAT 2015 in

South Africa

EFFECT OF WETTABILITY ON NUCLEATE BOILING

Valente T, Teodori E., Moita A.S. * and Moreira A.L.N. *Author for correspondence

IN + - Department of Mechanical Engineering,

Instituto Superior Técnico, Universidade de Lisboa,

Av. Rovisco Pais, 1, 1049-001 Lisbon,

Portugal,

E-mail: anamoita@dem.ist.utl.pt

ABSTRACT

Heat transfer enhancement at liquid-solid interfaces is often achieved by modifying the surface properties.

However, deep efforts to describe the actual role of surface modification only started at the 1980’s and much

work has left undone since then. The wettability is a key parameter governing heat, mass and momentum

transport at liquid-solid interfaces. However it is usually quantified using macroscopic quantities, which cannot

be related with the micro and nano scale phenomena occurring at the interface. In this context, the present

paper revises the potential and limitations of using macroscopic apparent contact angles to predict the wetting

regimes. Then, these angles are used to relate the wetting regimes with bubble dynamics and heat transfer

processes occurring at pool boiling. The results show that the macroscopic angles are useful to establish

general trends and differentiate bubble dynamics behaviour occurring for opposite wetting regimes. However,

milder wetting changes occurring within each regime, caused, for instance, by surface topography are not well

captured by the apparent angle, as the surface topography is not scaled to affect this macroscopic angle,

although it can clearly influence the bubble formation and departure mechanisms and, consequently the heat

transfer coefficients. In line with this, the concept of the micro scale contact angle, as introduced by Phan et al.

[1] is used here together with a geometrical parameter to include the effect of surface topography, to describe

the role of the wettability on bubble dynamics. Based on this analysis, a multi-scale approach is proposed to

include the role of wettability on correlations predicting the pool boiling heat transfer coefficients.

95

96

Annex E – Abstract of the paper submitted and presented at

UKHTC 2015 in Edinburgh

EFFECT OF EXTREME WETTING SCENARIOS ON POOL BOILING

T. Valente1, tomas.valente@tecnico.ulisboa.pt

I. Malavasi2, ilenana.malavasi@gmail.com

E. Teodori1, e.teodori@dem.ist.utl.pt

A.S. Moita1*, anamoita@dem.ist.utl.pt

M. Marengo2,3

, m.marengo@brighton.ac.uk

A.L.N. Moreira1, moreira@dem.ist.utl.pt

1IN+ - Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

2Dept. of Eng. and Applied Sciences, University of Bergamo, Viale Marconi 5, 24044 Dalmine, Italy

3University of Brighton, School of Computing, Engineering and Mathematics, Lewes Road, BN2 4GJ Brighton, UK

ABSTRACT

This study focuses on the detailed description of the heat transfer and bubble dynamics processes

occurring for the boiling of water over surfaces with extreme wetting regimes, namely hydrophilicity and

superhydrophobicity. The wettability is changed at the expense of modifying the surface chemistry and without

strong variations in the mean surface roughness. Furthermore, a detailed analysis is presented, showing the

temporal evolution of the bubble growth diameter together with bubble dynamics, which may serve for future

comparison with numerical simulations.

The results show a particular trend of the boiling curve obtained for the superhydrophobic surfaces, as the heat

flux increases almost linearly with the superheat, until reaching a maximum value after which it does not

further increase. This occurs because a large bubble is formed over the entire surface just at 1ºC superheat, as

a result of the almost immediate coalescence of the bubbles formed at the surface. This behaviour is in

agreement with the so-called “quasi-Leidenfrost” regime recently reported in the literature.

Regarding bubble dynamics, the results suggest that the existing models can predict the trend of the bubble

growth using the macro-contact angle (complementary to bubble contact angle) for the hydrophilic surfaces,

but cannot accurately predict bubble size, as they do not account for interaction mechanisms. Also they cannot

describe the particular bubble growth phenomenon observed for the superhydrophobic surfaces. Quasi-static

angles cannot provide any satisfactory results when used in the models to predict the bubble growth diameter,

although they follow an evolution similar to that of the macro-contact angle and are supplemental to the

bubble contact angle. In line with this, trends can be observed between the average bubble departure

diameter and bubble departure frequency with both the bubble and the quasi-static advancing angle. These

results suggest that the parameter which can accurately relate the bubble growth with the surface wettability

97

is the bubble contact angle (or from the wall side, the so-called macro-contact angle), but apparent angles

follow supplemental evolution, being therefore useful to identify qualitative trends.

KEYWORDS

Pool Boiling, Two-phase systems, Wettability, Boiling onset, Boiling Curve