Effect of Energy Density, Heat of Agglomoration, Pacek,Utomo

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Effect of energy density, pH and temperature on de-aggregation

in nano-particles/water suspensions in high shear mixer

A.W. Pacek ⁎, P. Ding, A.T. Utomo

School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom

Received 22 May 2006; received in revised form 16 November 2006; accepted 3 January 2007

Available online 16 January 2007

Abstract

The effect of energy input, pH and temperature on de-aggregation of hydrophilic silicon dioxide powder (particle size 12 nm) in a high

shear mixer was investigated. It has been found that de-aggregation is a two step process. Initially, at low energy input very large aggregates

(3–1000 μm) are gradually broken into smaller secondary aggregates (2–100 μm) of a single modal size distributions. As the energy input

increases primary aggregates (0.03–1 μm) are eroded from the secondary aggregates leading to bimodal size distributions with the first mode

between 0.03 μm and 1 μm corresponding to the primary aggregates and the second mode between 2 μm and 100 μm corresponding to the

secondary aggregates. At a sufficiently high energy density all secondary aggregates are broken into primary aggregates however, even at the

highest energy density employed the primary aggregates could not be broken into single nano-particles. The temperature and the pH affect de-

aggregation kinetics but do not alter de-aggregation pattern. Increasing pH at low temperature speeds up de-aggregation, whilst increasing pH

at high temperature slows down de-aggregation process.

© 2007 Elsevier B.V. All rights reserved.

Keywords: Silica nano-particles; Suspensions; De-aggregation; Primary aggregates; Secondary aggregates; Energy density

1. Introduction

Nano-particles such as titanium, aluminium or silicon oxides

have wide industrial applications in manufacturing of pigments,

fillers, ceramics, catalysts as well as electromagnetic and optical

devices. In the majority of those applications nano-particles are

processed as suspensions in different aqueous solutions and

frequently the quality of final products depends on the

properties of these suspensions characterized by the particle

size, size distribution, shape and morphology [1]. Therefore,

nano-particles which are often supplied in the form of dry powders have to be re-dispersed in aqueous solutions to give

homogenous, stable dispersions and it is essential that the

aggregates inherently present in dry nano-powders are broken

into primary nano-particles during dispersion process.

Large aggregates suspended in a fluid are broken when the

hydrodynamic forces (determined by the flow field) exceed the

cohesive bonds between particles or smaller aggregates. The

strength of individual bonds depends on the type of nano-

particles (van der Waals interactions), surface properties

(wettability, electrostatic interactions) and the nature of liquid

bridges within an aggregate [2].

Aggregates can be broken by normal or shear stress by

erosion, e.g., a gradual removal of small fragments from the

aggregates periphery or by bulk rupture, e.g., an abrupt

breakage of the aggregates into a number of relatively large

fragments [3]. The mechanism of breakage depends on the size

of the aggregates and the energy intensity [4]. It has been

postulated that as erosion occurs at low energy intensity and as

the energy intensity increases particles are broken by fragmen-tation [5]. As the aggregates become smaller during de-

aggregation, surface forces become more important than mass

forces and for aggregates smaller than 1 μm, surface forces are

more than one million times larger than mass force [6].

Therefore, breakage of large aggregates is relatively simple,

whereas breakage of aggregates smaller than 1 μm might be

very difficult and it has been suggested that the particles smaller

than 10 to 100 nm cannot be broken by mechanical action [7].

Dispersion and de-aggregation of nano-powders in liquids

can be carried out in ball mills, ultrasonic processors and rotor –

stator high shear mixers. The kinetic of de-aggregation in a high

Powder Technology 173 (2007) 203–210

www.elsevier.com/locate/powtec

⁎ Corresponding author.

E-mail address: [email protected] (A.W. Pacek).

0032-5910/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.powtec.2007.01.006

mailto:[email protected]

http://dx.doi.org/10.1016/j.powtec.2007.01.006

http://dx.doi.org/10.1016/j.powtec.2007.01.006

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shear mixer is relatively easy to control and such devices are

frequently used in industry to produce different types of

suspensions. Therefore, in this work the effect of energy input,

pH and temperature on de-aggregation of silica nano-particles

in a Silverson high shear mixer has been investigated and the

results are discussed below.

2. Experimental

2.1. Materials

A hydrophilic fumed silicon dioxide (Aerosil® 200 V from

Degussa) was supplied as a dry powder. The primary particles

have density of 2200 kg/m3, SiO2 content higher than 99.8%,

specific surface area of 200 m2/g and the average size of 12 nm

(manufacturer's data). The powder was dispersed in de-ionized,

double distilled water and when necessary pH was adjusted with

H2SO4 or NaOH.

2.2. Nano-particles/aggregates/suspension characterization

Zeta potential of particles/primary aggregates was measured

by Zetamaster (Malvern Instruments) designed for the particles in

size range 20 nm to 3 μm. To ensure that the particles/aggregates

were in the required size range, prior to the measurements of zeta

potential powder was dispersed in liquid and suspension was

sheared in a high shear mixer at 8000 rpm for 1 h.

Particles/aggregates size distributions were measured by

particle size analyzer Mastersizer 2000 (Malvern Instruments)

designed for particles in the size range between 20 nm and 2 mm

which gives particles size as a diameter of the spheres with the

volume equal to the volume of measured particles. In thisinstrument Mie theory was employed to calculate particle size

distributions from the scattered laser light using the refractive

index of silica particles of 1.46. The accuracy of the

measurements was estimated by measuring average size and

size distributions of calibrated standard particles (supplied by

Duke Scientific) of 10.3±0.05 μm and 97±3 nm and for both

sizes experimental error was well bellow 5%. The size and shape

of aggregates/particles were also analyzed with an Environ-

mental Scanning Electron Microscope (ESEM, Philips XL30).

Conductivity of suspension was measured using InLab 730®

conductivity probe from Metler Toledo and pH was measured

using Jenway 3020 pH meter.

2.3. Experimental rig

Experiments were carried out in a high shear, rotor –stator

mixer (L4R from Silverson) with rotor diameter of 0.028 m,

rotor height of 0.015 m and a gap between the rotor and the

Fig. 1. Transient volume distribution functions at different energy dissipation rates: (a) fragmentation of large secondary aggregates at 4.8 W kg−1; (b) fragmentation of

secondary aggregates at 21.7 W kg

−1

; (c) fragmentation of secondary aggregates at 89.9 W kg

−1

during first 20 min of processing; (d) erosion of primary aggregatesfrom the surface of secondary aggregates at 89.9 W kg−1 after longer processing time. 5% Aerosil in water, pH 4, t =20 °C.

204 A.W. Pacek et al. / Powder Technology 173 (2007) 203 – 210



stator of 0.5 mm. To improve macro-mixing in the vessel the

rotor –stator was mounted off centre in a sealed, stainless steel

jacketed vessel (diameter 0.1 m, height 0.15 m) fitted with

sampling port. The measured power number of this mixer is

equal to 1.7 and it is in a good agreement with the literature data

[8]. The temperature was controlled by the water bath and was

measured by the platinum thermocouple.

2.4. Procedure

In all experiments the same procedure was followed. Silica

powder was pre-dispersed in water in a glass stirred vessel fitted

with Rushton turbine, pH was adjusted to required value (4, 7 or

9) and suspension was stirred for 30 min. After that time the

aggregate size distribution was measured in situ using video–

computer –microscope system [9] and in a diluted sample using

Mastersizer 2000. Next the dispersion was transferred to the

high shear mixer from which the air was completely excluded

and the temperature of the water bath was set either to 20 °C,50 °C or 70 °C. The rotor speed was set to the required value

(3000, 5000 or 8000 rpm) and at each speed the dispersion was

sheared for 3 or 4 h. Small samples of suspension were taken

every 10 min and particles/aggregates size distributions were

measured.

3. Results and discussion

3.1. The effect of energy input on kinetics of de-aggregation

Transient volume distributions functions measured at three

different speeds (different energy dissipation rates) over the

period of 3 h are summarised in Fig. 1. Fig. 1a and b illustrates theevolution of aggregate size at energy dissipation rate of 4.8 W

kg−1 (3000 rpm) and 21.7 W kg−1 (5000 rpm) respectively and

Fig. 1c and d illustrates the evolution of aggregate size

distributions at energy density of 89.9 W kg−1 (8000 rpm).

From Fig. 1 it appears that de-aggregation of silica powder

can be seen as a two step process. In the first step, at a relatively

low energy input (short processing time at 8000 rpm or low

energy dissipation rates at 3000 and 5000 rpm) large aggregates

(between 5 and 500 μm) of initially dry powder shown in Fig. 2a

are broken into a smaller, secondary aggregates with the size

between 3 and 80 μm. The transient, single modal volume

distribution functions shown in Fig1a, b and c are approximatelyself preserving and as the time progresses they are gradually

shifting towards the smaller size aggregates. The shape of

volume distribution functions indicates that in this step

fragmentation of secondary aggregates is the main mechanism

of de-aggregation [5]. It is worth to stress that the smallest

aggregates obtained in this step are of the order of 2 μm which is

in a good agreement with literature information that the

aggregates/particles larger than 1 μm are relatively easy to break.

In the second step, at sufficiently high energy input

(processing at 8000 rpm for approximately 30 min or more)

large secondary aggregates start breaking into a small primary

aggregates clearly seen in Fig. 2 b. The transient volume

distributions functions (Fig. 1d) become bimodal, with the first

mode ranging from approximately 50 nm to 0.9 μm (primaryaggregates) and the second mode ranging from 3 μm to 80 μm

(secondary aggregates). Increase of energy input leads to a

gradual reduction of volume fractions of the aggregates in the

second mode and an increase of the volume fractions of

aggregates in the first mode. The widths of both modes

practically do not change and the median diameters are

practically constant. It has to be stressed here that even at the

highest investigated energy density (1500 kJ kg−1) reported

here and at even higher energy density during ultrasonication

(of the order of 4300 kJ kg−1), the aggregates in the first mode

(primary aggregates) could not be broken into a single nano-

particles. The qualitative results obtained with Mastersizer 2000 were confirmed by ESEM analysis and the ESEM image

in Fig. 2 b clearly shows many primary aggregates in the range

50 nm to 100 nm and practically no single nano-particle (of the

order of 12 nm).

Similar behaviour of polymer latex nano-particles suspended

in surfactant solutions was recently reported by the authors [10]

who postulated that the single nano-particles in the close-

packed primary aggregates are close enough to enter into the

primary energy well leading to irreversible aggregation. The

same explanation can be offered here.

The median diameters of the secondary aggregates as a

function of the processing time and as a function of the energy

density are shown in Fig. 3. The median diameters at the two

Fig. 2. Images of silica aggregates: (a) secondary aggregates in dispersion

charged into high shear mixer after premixing with Rushton turbine (time 0 in

high shear mixer), width of the image is equal to 1.1 mm; (b) primary aggregates

in the same dispersion after 4 h of shearing at 8000 rpm.




lowest energy dissipation rates were calculated from the size

distributions of all aggregates having single modal sizedistributions. At the highest energy dissipation rate where size

distributions become bimodal (see Fig. 1d) median diameter

was calculated from the second mode only e.g., median

diameter in the latter case corresponds to the population of

the secondary aggregates only.

The reduction of the median diameter (or any other mean

diameter) during de-aggregation process can be described in

terms of a processing time and the energy dissipation rate or in

terms of the energy density (size–energy model). For high shear

mixer the energy dissipation rate was calculated from:

e ¼ Pod N 3d D5d q ð1Þ

and the energy density from:

E ¼ ed t ð2Þ

Experimental median diameters plotted as a function of time

(Fig. 3a) in the log–log coordinates fall at three distinctive,

nearly parallel straight lines with the slope ranging from 0.23 to

0.20 with coefficient of determination (r 2) larger than 0.98.

The reduction of the aggregates mean diameters with time

during grinding/de-aggregation is frequently described by the

so called size–energy model [5,7]:

d av ¼ C d E

−

a ð3Þ

This simple experimental model developed in the mid-1950s

is still used to calculate the mean (usually median) particle size in

a different type of grinding devices. The exponent α can be

interpreted as a reduction rate of the median diameter and

constant C as a size of aggregate at unit specific energy input.

This simple two parameter model allows the quick prediction of

the mean size in a given grinding device and it also allows easy

comparison between different types of grinding devices. The

major disadvantage of this model is that it does not allow the

prediction of size distributions and it can be used to model

grinding processes where size distributions are single modal.

Considering that the alternative way of predicting the mean

particle size and size distribution is the solution of the population

balance model (integro-differential equation usually convertibleto a set of differential equations) which is rather complex and

time consuming, it is not surprising that this model has been

successfully used in literature to describe the grinding of solid

particles [5,7] where α of the order of 0.68–0.72 was obtained. It

has also been adopted to correlate average drop size with energy

input during liquid/liquid emulsification in different types of

high shear mixers and in those processes in which α of the order

of 0.4 was reported [11].

Fig. 3 b shows that by plotting experimental d 50 as a function

of energy density in log–log coordinates all data points can be

collapsed (with engineering accuracy) into a straight line with

an average slope α=0.26 and r 2=0.91 which indicates that that

first step of de-aggregation of silica powder (when sizedistributions are single modal) can also be described by this

model.

Whilst the breakage of secondary aggregates having the

single modal size distributions can be analyzed in terms of

rather simple size–energy model, the analysis of de-aggregation

when size distributions become bimodal is more complex. In

case of bimodal size distributions the mean sizes cannot be used

to describe the changes of the population of the aggregates and

in principle the evolution of bimodal size distribution with time

should be analyzed within the framework of population balance

model [12]. Whilst such analysis is currently performed and the

results will be reported soon, the whole process of de-aggregation can be qualitatively discussed in terms of transient

aggregate size distributions (Fig. 1) or it can be quantified in

terms of breakage of the secondary aggregates (Fig 3) combined

with the analysis of the increase of a cumulative mass fraction of

the primary aggregates (Fig 4).

The volume fraction of the primary aggregates and d 90 as a

function of the processing time at 8000 rpm are summarised in

Fig. 4. It is interesting to note that primary aggregates are

generated only after a certain amount of energy has been put

into the dispersion (or after a certain processing time, see Fig. 1c

and d). As the volume fraction of the primary aggregates levels

at an approximately 0.95, d 90 falls below 1 μm and stays

practically constant indicating that practically all the secondary

Fig. 3. Median diameters (d 50) of the secondary aggregates at pH 4 and T =20 °C as function of: (a) processing time and (b) energy density at different energy

dissipation rates: ε =4.8 W kg−1 (•), ε =21.7 W kg−1 (○), ε =89.9 W kg−1 (▾). Solid lines — linear regression.




aggregates were broken. Until the secondary aggregates are present in the suspension the volume fraction of primary

aggregates increases linearly with the processing time at the rate

of the order of 0.01 s−1. After d 90 falls below 1 μm the rate of

increase of the volume fraction of the primary aggregates

reduces to approximately 0.0005. It is worth to notice that even

after 4 h of processing at 8000 rpm nano-particles were not

observed in the suspension (see Fig. 1d) which indicates that the

primary aggregates were not broken.

Similar pattern of breakage of silica aggregates built from

0.3 μm nano-particles was reported by Kusters et al. [4] where,

based on similar evid ence as presented above, authors

concluded that silica aggregates are broken by erosion in the

whole range of the energy density. In our case it appears that at low energy density fragmentation of the large aggregates occurs

and at a high energy density primary aggregates are sheared

from surface of the secondary aggregates.

3.2. The effect of pH and temperature on kinetics of

de-aggregation

The change of pH of the suspension leads to a change of

electrostatic charges on the aggregates surfaces which in turns

affects the repulsive forces between them and might alter the

kinetics of de-aggregation. To assess and to quantify the effect

of pH on de-aggregation kinetics the relation between pH andthe charge of the particles surface, zeta potential at different pH

has been measured and the results are summarised in Fig. 5a.

The combined effect of pH and temperature on the kinetics of

de-aggregation is summarised in Fig. 5 b and typical transient

distributions during de-aggregation at pH 4 and pH 9 are

compared in Fig. 6.

The higher the absolute values of zeta potential, the larger the

electrostatic repulsive forces and the separation of the particles

becomes easier. In investigated system zeta potentials at pH 7

and higher are of the order of −40 mV and zeta potential at pH 4

is approximately −15 mV which indicates that the repulsive

forces at pH 9 are larger than at pH 4. This suggest that de-

aggregation at pH 9 and pH 7 should be faster than at pH 4 but

the analysis of aggregate size/size distributions (Figs. 5 b and 6)

shows that this is the case only at a low temperature. At 20 °C an

increase of pH from 4 to 9 speeds up de-aggregation as can be

seen from an increase of median size reduction rate α from 0.23

at pH 4 to 0.29 at pH 9. Also, at pH 9 after 10 min 30% of the

secondary aggregates were broken into the primary aggregates,

whereas at pH 4 after 30 min only 21% of the secondaryaggregates were broken however, in both cases after 4 h of

shearing 95% of the secondary aggregates were broken into the

primary aggregates. Fig. 6a also shows that even when the

breakage rate was highest (at pH 9, t =20 °C) the primary

aggregates (size range 50–100 nm) were not broken into a

single nano-particles (average size 12 nm).

As the temperature increased to 50 °C, the opposite effect of

pH on breakage kinetics was observed and at pH 4 (small

repulsive forces) de-aggregation was faster than at the higher pH.

Further increase of temperature to 70 °C leads to a further, very

strong reduction of the breakage rate at the highest pH (more than

4 h was needed to break 90% of secondary aggregates, α=0.19) but at pH 4 the breakage rate increased (90% of secondary

aggregates were broken within 55 min, α=0.27).

Whilst, as discussed above and as shown in Fig. 5 b, both the

temperature and the pH have a strong effect on the kinetics of de-

aggregation and breakage rate, the effect of both those parameters

on the final size distribution of the primary aggregates is

negligible. There is a pronounced difference between the transient

volume distributions functions shown in Fig. 6a and b with much

faster shift towards smaller particles in Fig. 6a (pH 9, t =20 °C)

Fig. 5. (a) Zeta potential of primary aggregates as a function of pH for 1% (•)

and 5% (○) w/w silica in water; (b) the effect of pH and temperature on time

necessary to break 95% of secondary aggregates into aggregates smaller than1 μm; (•) pH 4, (○) pH 7, (▾) pH 9.

Fig. 4. Fraction of aggregates smaller than 1 μm (primary aggregates) and d 90 of

whole population of aggregates as a function of processing time at pH 4,

T =20 °C and ε =89.9 W kg−1.




than in Fig. 6 b (pH 4, t =20 °C), but again the final volume

distributions (after 240 min) are practically identical.

In principle the effect of pH and temperature on the

interactions between particles/aggregates can be analyzed

using extended DLVO (Derjaguin–Landau–Verwey–Over-

beek) model. In this model the interaction force between two

spheres of the same radii ( R) is expressed in terms of the van der

Waals energy (V A), the electrostatic energy (V E) and the

hydration energy (V H) between two flat surfaces [13,14]:

F ¼ p RðV A þ V E þ V HÞ ð4Þ

Attractive van der Waals energy (V A) between two flat

surfaces can be calculated from [13]:

V A ¼ −

A

12ph2 ð5Þ

where values of Hamaker constant for silica–silica in water

reported in literature [14–16] are in the range 0.46×10−20 J to

1.02×10−20 J.

The electrostatic repulsive energy (V E) depends on the

charge on particles surface and the properties of the liquid. For

constant surface potential it can be estimated from Eq. (6) in

which Stern potential can be replaced with the measured zeta

potential [15,17]:

V E ¼ 2 Z 2nkT eWs

kT

21

j1−tanh

jh

2

ð6Þ

Hydration energy (V H) has an effective range of fewnanometers and exponentially decays with distance [18]. It

can be calculated from the experimental correlation [15]:

V H ¼ V 1d e−h=h1 þ V 2d e−h=h2 ð7Þ

where: V 1/2π R =0.14 J/m2, h1=0.057 nm, V 2/2π R =5.4×10−3

J/m2 and h2= 0.48 nm are experimentally determined para-

meters [14].

All components of the interaction energy between two silica

particles of the same diameter were calculated from Eqs. (4)–(7)

and the results are summarised in Fig. 7a for the particles

separated by more than 1 nm and in Fig. 7 b for the particles

separated by less than 1 nm. In both cases it is clear that the

interactions between the silica particles in water are dominated by

the repulsive hydration force. The repulsive electrostatic energies

at different pH (see insert in Fig. 7a) are two orders of magnitude

Fig. 6. Transient volume distribution functions in 5% Aerosil/water suspension

at rotor speed of 8000 rpm at the following processing conditions: (a) pH 9,

T =20 °C after processing times of: 0 min (•), 10 min (○), 20 min (▾), 240 min

(▽); (b) pH 4, T =20 °C after processing times of: 0 min (•), 20 min (○),

50 min (▾), 240 min (▽).

Fig. 7. Components of interaction energy between particles: V A — attractive van

der Waals energy, V E — repulsive electrostatic energy, V H – repulsive hydration

energy; (a) particles separated by more than 1 nm (aggregates); (b) particlesseparated by less than 1 nm (single particles).




lower than van der Waals and hydration energies and they are

practically negligible both at shorter and at longer separation

distances. It is possible to postulate that as the surface of

aggregates is not very smooth the shortest distance separating

them is probably larger than 1 nm and at such a distance the

repulsive hydration energy does not allow entry into the deep

primary well. This means that the secondary aggregates whichare built from the primary aggregates are relatively weak and can

be broken at low energy input as discussed above. Very strong

repulsive hydration interactions also explain exceptional stability

of the suspensions of primary silica aggregates even at pH

corresponding to the iso-electric point [11,14]. On the other hand,

the distance between smooth, small single particles (of the order

of 12 nm) can be below 0.1 nm which allows them to aggregate

irreversibly by entering the primary well. It is also possible that

the strength of these very small, primary aggregates might

depend on the solubility of silica in water. As the pH and

temperature increase from 20 °C to 70 °C the solubility of silica

increases drastically [19] which might lead to a faster conversionof the liquid bridges containing relatively large amounts of

dissolved silica into very strong solid silica bridges.

Theoretically predicted effect of pH on the electrostatic

repulsive forces is very small and it does not allow explanation

of rather strongeffect of pH on de-aggregationkinetics at elevated

temperature observed experimentally. This confirms the literature

suggestions that electrostatic interactions within DLVO model

have serious limitations in the case of silica nano-particles.

4. Conclusions

This study has revealed the two stage mechanism of de-

aggregation of large (+50 μm) secondary aggregates made of silica nano-particles (size 12 nm) and the effect of the

temperature and pH on the kinetics of de-aggregation and size

distributions of the primary aggregates. In the first stage, at low

energy density, the large aggregates of single modal size

distributions are broken by fracture and the transient size

distributions slowly shift towards smaller sizes as energy

density increases. The median size of the aggregates at this stage

is well correlated by the size–energy model. At higher energy

density, the mechanism of breakage changes into erosion of

primary aggregates (50 nm to 1 μm) from the surface of the

secondary aggregates. This leads to bimodal volume distribu-

tions with the first mode between 50 nm and 1 μm and thesecond mode between 3 and 80 μm. At a sufficiently high

energy density, the secondary aggregates disappear leaving only

small primary aggregates in the suspension.

The effect of pH on the kinetics of de-aggregation depends on

the temperature; at low temperatures the increase of pH increases

the de-aggregation rate but as the temperature increases the

increase of pH leads to a significant reduction of de-aggregation

rate. Even at the most favourable conditions (low temperature,

high pH, high energy density), breakage of the primary

aggregates which were smaller than 1 μm into single nano-

particles was not observed. This implies that primary aggrega-

tion is an irreversible process, e.g., primary aggregates cannot be

broken into single silica oxide nano-particles.

Nomenclature

A Hamaker constant [J]

C Constant defined by Eq. (3)

d 32 Sauter mean diameter [m]

d 90- 90% (volume) of aggregates below d 90% [m]

D Rotor diameter [m]

e Electron charge [C] E Energy density [kJ kg−1]

h Distance between particles [m]

k B Boltzman constant [J K −1]

N Rotor speed [s−1]

Po Power number [–]

V Interaction energy [J/m2]

R Particle radius [m]

r 2 Coefficient of determination [–]

t Time [min]

t 95% Time necessary to break 95% of secondary

aggregates below 1 μm

[min]

T Absolute temperature [K] z Valency [–]

α Constant defined by Eq. (3) [–]

ψ Electrostatic potential [V]

ε Average energy dissipation rate [W kg−1]

κ Inverse Debye length [m−1]

ρ Liquid density [kg m−3]

Acknowledgement

This work is a part of the PROFORM (“Transforming Nano-

particles into Sustainable Consumer Products Through Ad-

vanced Product and Process Formulation” EC Reference

NMP4-CT-2004-505645) project which is partially funded bythe 6th Framework Programme of EC. The contents of this

paper reflect only the authors' view. The authors gratefully

acknowledge the useful discussions held with other partners of

the Consortium: Bayer Technology Services GmbH; BHR

Group Limited; Centre for Computational Continuum Mechan-

ics (C3M); Karlsruhe University, Inst. of Food Process Eng;

Loughborough University, Department of Chemical Eng;

Poznan University of Technology, Inst. of Chemical Technol-

ogy and Eng; Rockfield Software Limited; Unilever UK Port

Sunlight, Warsaw University of Technology, Department of

Chemical and Process Eng.

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