Multiphase flow membrane distillation

7/29/2019 Multiphase flow membrane distillation

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Sumit MukhopadhyayCitation:AIP Conf. Proc. , 109 (2010); doi: 10.1063/1.3453795View online: http://dx.doi.org/10.1063/1.3453795View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1254&Issue=1Published by theAmerican Institute of Physics.

Instability of a backward-facing step flow modified by stationary streaky structuresPhys. Fluids 24, 104104 (2012)Direct numerical simulation of stratified turbulencePhys. Fluids 24, 091106 (2012)Influence of a white noise at channel inlet on the parallel and wavy convective instabilities of Poiseuille-Rayleigh-Bnard flowsPhys. Fluids 24, 084101 (2012)The role of boundaries in the magnetorotational instabilityPhys. Fluids 24, 074109 (2012)The onset of steady vortices in Taylor-Couette flow: The role of approximate symmetryPhys. Fluids 24, 064102 (2012)

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A Coupled Multiphase Fluid Flow And Heat And Vapor

Transport Model For Air-Gap Membrane Distillation

Sumit Mukhopadhyay

Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

Abstract. Membrane distillation (MD) is emerging as a viable desalination technology because of its low energy requirementsthat can be provided from low-grade, waste heat and because it causes less fouling. In MD, desalination is accomplished bytransporting water vapour through a porous hydrophobic membrane. The vapour transport process is governed by the vapour

pressure difference between the two sides of a membrane. A variety of configurations have been tested to impose this vapourpressure gradient, however, the air-gap membrane distillation (AGMD) has been found to be the most efficient.

The separation mechanism of AGMD and its overall efficiency is based on vapour-liquid equilibrium (VLE). At present, littleknowledge is available about the optimal design of such a transmembrane VLE-based evaporation, and subsequent condensation

processes. While design parameters for MD have evolved mostly through experimentations, a comprehensive mathematicalmodel is yet to be developed. This is primarily because the coupling and non-linearity of the equations, the interactions betweenthe flow, heat and mass transport regimes, and the complex geometries involved pose a challenging modelling and simulation

problem. Yet a comprehensive mathematical model is needed for systematic evaluation of the processes, designparameterization, and performance prediction. This paper thus presents a coupled fluid flow, heat and mass transfer model toinvestigate the main processes and parameters affecting the performance of an AGMD.Keywords: Membrane distillation, desalination, porous medium flow, multiphase flow and transport, multicomponentdiffusion, mathematical modelingPACS: 47.55-t, 47.56+r, 47.11-j, 44.30+v, 44.35+c, 44.05+e

INTRODUCTION

Sustaining the growing need for freshwater is one of

the most critical challenges of our times. Today, aboutthree billion people around the world have no access toclean drinking water [1]. According to the WorldWater Council, by 2020, the world will be about 17%short of the fresh water needed to sustain the worldpopulation. Moreover, about 1.76 billion people live inareas already facing a high degree of lacking water. Itis predicted that an even larger population will beaffected soon because of the rapid depletion ofgroundwater and surface water resources [1].

While no one single approach (reduction in usage,recycling and reuse, rainwater harvesting, etc.) is

expected to alleviate the problem of freshwaterscarcity, low-cost desalination and purification ofseawater is emerging as an important and viablesource of fresh water. While traditional thermaldesalination technologies (such as multi-stage flashevaporation, multiple-effect distillation, and vapor

compression) are energy intensive processes, theemergence of membrane-based separationtechnologies (such as reverse osmosis, RO) have

reduced the energy requirements associated withdesalination. Consequently, desalination throughmembrane processes as a source of freshwater isbecoming economically more viable [2].

Desalination has received a further impetus throughthe recent advent of a low-cost, energy-efficientmembrane-based separation technology, membranedistillation. (MD). Even though the energyrequirement for MD is comparable to RO processes,RO requires electrical energy, however, MD requiresonly low-grade heat with a temperature of 50-90oC(waste heat or solar energy can be used to heat up the

feed in MD). Also, because MD operates in counter-current mode, efficient use of the energy supplied isobtained. Consequently, it has been predicted that MDwill be able to produce freshwater at about $0.26/m3[2]. Additionally, MD provides some operationaladvantages (such as less susceptibility to fouling) over

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Intl Conference, edited by K. Vafai

2010 American Institute of Physics 978-0-7354-0803-6/10/$30.00


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RO (where fouling and compaction of the foulinglayers poses major operational challenges).Considering all these factors, MD presents substantialpotential as a viable desalination technology.

MD is a separation process that involves transport ofwater vapour through a porous hydrophobicmembrane. The vapour transport process is governed

by the vapour pressure difference between the twosides of the membrane. A variety of configurationshave been tested to impose this vapour pressuregradient, however, the air-gap membrane distillation(AGMD) has been found to be the most efficient. Themain advantage of the AGMD against otherconfigurations is that it allows the collection ofcondensate on a cold surface rather than directly in acold liquid [1-6].

In an AGMD configuration, the expected mass transfersteps involve movement within the liquid feed towardthe membrane surface, evaporation at the membraneinterface, and transport of the vapour through themembrane pores and the air-gap prior to condensation.Thus, the separation mechanism of membranedistillation and its overall efficiency is based onvapour-liquid equilibrium (VLE).

Although the potential of AGMD has been recognizedfor some time now, its growth at the industrial scalehas been rather limited [3]. This slow growth is mainlybecause of the lack of reliable optimal designparameters. While design parameters for AGMD havebeen evolving mostly through experimentations, acomprehensive conceptual and mathematical model isyet to be developed. To date, the modeling studies

reported in literature on AGMD mainly investigate thetemperature polarization phenomena, and heat andmass transport processes based on empiricalrelationships [4,5]. These previous modelingapproaches do not actually solve for the multiphaseflow distribution associated with AGMD. This isprimarily because the coupling and non-linearity of theequations, the interactions between the flow, heat andmass transport regimes, and the complex geometriesinvolved pose a challenging modelling problem. Yet acomprehensive mathematical model that solves for thecoupled equations is needed for systematic evaluationof the processes, design parameterization, and

performance prediction. This work thus proposes thedevelopment of a coupled flow, heat and mass transfermodel to investigate the main processes andparameters affecting the performance of an AGMD.

COUPLED PROCESSES IN AGMD

Figure 1 presents a schematic drawing of a singleAGMD module [6]. The water on the high temperatureside of the hydrophobic membrane vaporizes from theliquid-vapor interface. The vapor is transportedthrough the membrane pores and is condensed on thecold surface, separated from the membrane by the air-

gap. A porous hydrophobic membrane is used becauseit allows permeation of vapor only, not liquid. Highlyhydrophobic membranes with an appropriate pore size

Figure 1. Schematic representation of AGMD processes [6]

are therefore generally used.

In general terms, understanding the physics of flow inan AGMD module requires an analysis of fluid flow,heat and mass transport processes through a porousmedium in a multiphase, multicomponent system.More specifically, we need a conceptual modelconsisting of two phases (liquid and gas) and twocomponents (water and air). The liquid phase consistsof water, which can have some dissolved air and anumber of dissolved solutes (in the feed seawater).The gas-phase may be consisted of air plus any watervapor generated through evaporation.

For an accurate description of the coupled fluid flow,heat and mass transport processes in AGMD, aconceptual model needs to account for the followingphysical processes: Fluid flow by advection under

pressure, viscous, and gravity (if any) forces; heattransport through conduction and convection,vaporization and condensation, phase change andlatent heat effects; transport of dissolved solutes, andtheir concentration changes because of evaporation;capillary pressure and relative permeability effects atthe vapor-liquid interface and in the membrane pores;

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and multicomponent diffusion in a multiphase system.In addition to these physical processes, the conceptualmodel also needs to account for the complex andtortuous flow paths in the membrane and condenserchannels, resulting from the placement of the spacers.

MATHEMATICAL MODEL OF AGMD

COUPLED PROCESSES

In developing the mathematical model, whileincluding most of the physical processes describedabove, we make some simplifying assumptions. First,we will conceptualize both the membrane andcondenser channels as equivalent porous media, withthe effective porosities, permeabilities, and tortuositiesestimated from the shape and configuration of thespacers. Second, we will assume that evaporation doesnot alter the dissolved solute concentration in themembrane channel, and that the impact of thedissolved solutes on vapor pressure is negligible.

Third, it will also be assumed that the feed water hasno particulate solids. Fourth, membrane foulingresulting from deposition/adsorption of solutes on themembrane surface will be excluded from the model.

Governing Equations For Multiphase Flow

And Transport

For a flow system with two components (water andair) and two phases (liquid and gas), Gibbs phase ruledictates that two degrees of freedom (e.g., pressure andtemperature) are needed. Additionally, there are the

phase saturations (sl and sg) that need to bedetermined. However, only one of the saturationsneeds to be resolved as the two are related by

(1)1 gl ss

In other words, there are three unknowns (e.g.,pressure, temperature and one of the phasesaturations), and thus to resolve the flow systemcompletely, we need to have three equations. Theseequations could be the mass conservation equations ofthe two components and the energy balance equation[7].

The mass balance equation for water in any arbitrary

subdomain (with dimensions x, y, and z) of theflow system can be written as

l

w

g

w

gg

w

l

w

llg

w

ggl

w

ll

w

ggg

w

lll

qXDXDXX

XsXst

uu

(2)

where is porosity, s is saturation, is density, X ismass fraction, u is specific flux (or fluid velocity),D is

for air can be similarlypressed as

the diffusive strength factor (see below), and q is thesource or sink term. Subscripts l and g refer to theliquid and gas phases, respectively. Superscripts wand a are used to specify the water and air componentsin the system, respectively.

The conservation equationex

a

a

g

a

gg

a

l

a

llg

a

ggl

a

ll

ggg

qXDXDXX uu(3)

Finally, The energy balance equation for thsubdomain is

aalll XsXs

t

e same

ll UUsUst

1

hggglll

ssgggl

qThuhu (4)

ion 3, U is the internal e

enthalpy, is the thermal conductivity, and T is

d that the phase velocities can beetermined from Darcys law such that

In Equat nergy, h is the

temperature.

It is assumed

gu

Pk

kr (5)

where kis ility, kr is the relativethe absolute permeab

velocity of phase , and g is the acceleration due to

gravity. The fluid pressure in phase (P) is the sumof a reference pressure P (assumed equal to thepressure of the gas phase) and the capillary pressure,i.e.,

CPPP (6)

Multicomponent Diffusion

The Ficks law of molecular diffusion works well foriffusion of tracer solutes that are present at low

mponent systems mayepend on all concentration variables, leading to non-

dconcentrations in a single-phase aqueous solution.However, many subtleties and complications arisewhen multiple components diffuse in a multiphaseflow system, as in AGMD [7].

Effective diffusivities in multicodlinear behavior especially when some components are

present in significant (non-tracer) concentrations.Additional nonlinear effects arise from the dependenceof tortuosity on phase saturations, and from couplingbetween advective and diffusive transport. For gasesand vapors, the Fickian model has serious limitationseven at low concentrations, which prompted thedevelopment of the dusty gas model [8,9], and

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accounts for molecular streaming effects (Knudsendiffusion) that become very important when the meanfree path of gas molecules is comparable to pore sizes[8,9,10].

We have usefl

d a pragmatic approach in which diffusiveux of component (water or air) in phase (= liquid,

gas) is written as [7]

XDf (7)

where

dD (8)0

Diffusion coefficients d of

follows [11]

gases depend on

pressure and temperature as

80.1

15.273

15.273,, 000

T

T

P

PTPdTPd

0 (9)

, for general two-phase conditions, th

flux for component is written as

Equ ralfinite difference method [7,12]. Time is discretized

NUMERICAL MODEL

In this pap le AGMDmodule, consisting of a feed channel, a condenser

te and at a specified temperature. Cooling water is

F

ngle

flow channels are initiallyturated with water. Initial pressure in the entire flow

iscosity, and saturated vapor pressure) are calculated

=0 C), the diffusion coefficient for air-water vapor

RESULTS AND DISCUSSIONS

Figure 3 shows the temperature profile in the feed andndenser channels. For this simulation, we assumed a

Finally e diffusive

ggglll

kXDXDf (10)

Spatial and Temporal Discretization

ations 2, 3, and 4 are discretized using the integ

using a fully implicit finite difference scheme. Such adiscretization approach yields a set of three couplednonlinear algebraic equations per volume element ofthe overall flow system. These equations are solvedusing a stabilized bi-conjugate gradient solver [7].

er, we consider only a sing

channel, a membrane and an air-gap, of the AGMDdesign (see Figure 2).We assume that flow in both thefeed and condenser channels can be represented byflow between two flat rectangular plates (see Figure2). In other words, it is assumed that flow is one-dimensional. Because the lengths of the feed andcondenser channels (1. 5 m) are significantly largerthan their widths (0.002 m), this is a reasonableassumption. The hydrophobic membrane and the air

gap are 150 m and 0.001 m wide.

Seawater is input into the feed channel at a constantrasent through the condenser channel countercurrent tothe flow in the feed channel. Simulations areperformed for both the scenarios where the flow ratesare same in the two channels or different. Themembrane and the air gap are initially saturated with

chematic representation of one-dimensional,module of AGMD

igure 2. Ssi

air, whereas the twosa

system is assumed to be 0.55105 Pa, and initialtemperature is 30oC.

All water properties (density, specific enthalpy,vfrom the steam table equations as given by theInternational Formulation Committee [13]. Air is

approximated as an ideal gas, and additivity isassumed for air and vapor partial pressures in the gasphase, Pg = Pa + Pv. The viscosity of air-vapormixtures is computed from a formulation given byHirschfelder et al. [14]. The solubility of air in liquidwater is represented by Henry's law.

At standard conditions (P0=1.01325105 Pa and

T o0mixture is 2.3410-5 m2 s-1. Diffusion at any otherpressure or temperature is calculated using Equation 9.Liquid- and gas-phase relative permeabilities areassumed to be linear functions of saturation.

coflow rate of 1.08 lit hr-1 for both the feed andcondenser channels. As indicated earlier, the wholesystem was initially at 30oC. Hot water was fed at85oC at the left hand side of figure 3, and was flowingleft to right (in Figure 3). Cold water at 30 oC wasflowing from right to left (see Figure 3). After 1000

seconds of operation (as shown in Figure 3), themaximum temperature within the feed channel was72oC and declining gradually from left to right alongthe length of the channel. As expected, temperaturewas rising from right to left in the condenser channel,with the temperature being about 65oC at the exit ofthe condenser channel. In other words, a temperaturedifference was created at any location between the

Condenser

Membrane

Air-gapAir-gap

x

y z

Feed

y z

x

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feed and condenser channel. After continuing with theoperation for a significant time, a steady statetemperature profile is achieved as shown in Figure 3.When steady state conditions are reached, feed waterwas entering the system at 85oC and exiting at about35oC, whereas condenser water (that was entering thesystem at 30oC) was leaving the system at about 80oC.A constant temperature difference of about 5oC was

thus established across most of the lengths of the feedand condenser channels.

Figure 3. Simulated temperature profile in the feed andcondenser channels

Fi dlines) and gas (da on profiles in the

gure 4 shows the gradual evolution of liquid (solished lines) saturati

feed channel at different times during operation, andalso at steady state. Note that gas saturation includescontributions from both water vapor and air. Withcontinued operation more and more vapor is generated(gas saturation increases and liquid saturationdecreases) until a steady state is reached, where liquid

saturation varies between 0.4 (at the feed water entryside) to 0.2 (at the feed water exit side).

Figure 4. Liquid and gas saturation profiles in the feedchannel.

Ini nof air is one and the tion of air in the gas

tially, the air-gap contained only air (gas saturatiomass frac

phase is one). However, vapor generated in the feedchannel diffused through the membrane and enteredthe air-gap, where it condensed, and the condensedwater drained out into a collection bucket(conceptually). Consequently, the liquid and gas phasesaturation (plus the mass fraction of air and water

vapor) changed with time in the air-gap duringoperation. This is illustrated in Figure 5, which showsthe transient change in saturation and mass fractionprofiles in the air-gap.

Figure 5. Temperature, liquid and gas saturation, and airmass fraction profiles in the air-gap.

rate as anction of time. This figure shows results from three

Figure 6 sfu

hows the freshwater collection

operation modes. For these three operations, all thephysical and operational parameters are identicalexcept the flow rates in the feed and condenser

channels. For Case 1, the flow rate in both thechannels is 1.08 lit hr-1. However, these flow rates are2.16 lit hr-1 and 3.24 lit hr-1 for Case 2 and Case 3,respectively. From Figure 6, it is clear that increasingthe flow rate increases the freshwater collection rates.However, the freshwater collection rate as a percent offeed water flow rate remains more or less similar(because this is governed by thermodynamicequilibrium between the liquid and vapor phases).

0.00

0.05

0.10

0.15

0.20

0.25

0.30

ate

0 200 400 600 800

Time (hour)

CondensateFlow

R

(lit/hour) Case 1

Case 2

Case 3

Figure 6. Freshwater collection rates as a function of time

for three different feed water flow rates

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Aflow rate , and by

ults s in thi er are all based etion t diffusi efficie of ai r

apor mixture is only a function of temperature and

ARY AND CONCLUSIONS

Mem ledesa essof memstill as an energy-efficient water purification

The author houghtfultechnical d ChrisDotremont about membrane distillation.

1. C. Charcosset,D 1 (2009).2. G. W. Meindersma, C. M. Guijt, and A. B. de Haan,

Environmental Progress2 441 (2005).emical

6.

roperties

13. International Form

Them

Feed Condenser

e (lit

Conde

Temp.

Collection

hr )

dditional simulations were performed varying thes in the feed and condenser channels

changing the temperature of the water into thecondenser channel. These simulation scenarios and thefreshwater collection rates from them additional areshown in Table 1.

TABLE 1. Different Simulation Scenarios and FreshwaterCollection Rates From

The res hown s pap on thassump hat on co nt r-watevpressure and not of saturation. Diffusion coefficienthas a strong influence on diffusive flux of vapor and

freshwater collection rates. Additionally, weconsidered operations only for one fixed pressure.Changing the operational pressure will also change thefreshwater collection rates. Changing other parameters(such as porosity and tortuosity, which are functions ofspacer geometries) will also change the diffusive fluxand hence freshwater collection rates. Finally, thepresence of dissolved solid will also influence theextent of vaporization and the amount of freshwaterthat can be collected. These different operationalscenarios will be investigated in a future paper with anobjective to optimize the performance of memstilloperations.

SUMM

brane distillation is emerging as a viablination technology. To establish the effectiven

technology and to help optimize the design andoperation of a memstill facility, there is a definite needfor developing a better understanding of theunderlying physical processes associated withmemstill and building a robust mathematical model forit. The conceptual and mathematical models of fluid

flow and heat and mass transport for memstill to datehave been based on the assumption of steady-stateconditions and/or utilizing some empirical relationshipfor heat and mass transport coefficients. Theseprevious modeling approaches do not aim for actuallysolving the temperature and the saturation fields in thevarious subcomponents of the overall system. In thispaper, we present an alternative modeling approach,

where the transient temperature and liquid and gassaturation fields in the subdomains are actuallydetermined by solving the coupled mass and energybalance equations. The rate at which freshwater can becollected is determined from these transienttemperature and saturation fields. Freshwatercollection rates under different operational conditionswere determined in this paper. In future papers, we

intend to investigate further operational and designissues associated with memstill using the approachdescribed in this first paper. While this present paper isconcerned about a single AGMD module, we plan toextend the mathematical model to a system involvingmultiple AGMD modules.

ACKNOWLEDGMENTS

Scenario Water

Rate (lit

Water

Rat

nser Rate (lit-1

hr-1

) hr-1

) (oC)

Case 3 3.24 3.24 30 0.22

Case 4Case 5 0.31

3.243.24

3.246.48

2020

0.26

wish to acknowledges the many tdiscussions with Lou Jing an

REFERENCES

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4, 434-3. A.Criscuoli, M.C. Carnevale, and E. Drioli, Ch

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Separation and Purification Technology 43, 233-244(2005).

5. L.-H. Cheng, P.-C. Wu, and J. Chen, Ind. Eng. Chem.

Res. 48, 4948-4959 (2009).J.H. Hanemaaijer et al., Desalination 199, 175-176(2006).

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12. T.N. Narasimhan and P.A. Witherspoon, Water Resour.Res.12, 57 64 (1976).

ulation Committee, A Formulation ofthe Thermodynamic Properties of Ordinary Water

Substance, Dsseldorf:IFC Secretariat, 1967.14. J.O.Hirschfelder, C.F. Curtiss and R.B. Bird, Molecular

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Multiphase flow membrane distillation