12 Journal of Chemical Engineering, IEB Vol. ChE. 27, No. 1, June 2012

Drying Induced Phase Separation

Raj Kumar Arya Department of Chemical Engineering, Jaypee University of Engineering and Technology, Guna, A.B. Road, Raghogarh, Guna - 473226, M.P., India

Abstract

Polymeric Membrane can be produced by several methods. This paper deals computational study to prepare polymeric membrane using drying. Asymmetric and symmetric membranes can be prepared by changing the drying parameters like air flow rates, drying temperatures, and coating compositions.

Keywords Polymeric Coatings, Asymmetric Membranes, Symmetric Membranes, Drying, Phase Separation

and polymer rich phases. On solidification polymer rich 1. Introduction phase precipitated to form solid matrix that envelops the polymer lean phase that is rich in solvent and Polymeric membranes are used in large scale in nonsolvent fill the pores. This process avoids the membrane filtration and other separation techniques. complication associated with the use of coagulation There are two types of membranes asymmetric and baths as in wet cast process. Polymer concentration is symmetric. Each of them has its own advantages. These increased to reduce the solvation character of polymer membranes are manufactured by phase separation solvent as the solvent is evaporated from the solution processes of homogenous polymer solutions. During (Young et al., 2002). Evaporation step significantly phase separation, macrovoids are formed that are useful influences the final membrane morphology in dry and in drug delivery systems, ultra-filtration, composite wet cast phase inversion process. membrane supports, bioreactors, screen printing media and breathable fabrics (Penky et al., 2003). Macrovoids If the drying rate is high and coating thickness is small, are the pores of having size distribution of 10-50µm. top surface becomes dense in polymer due to high rate Phase inversion can be achieved by wet casting process, of solvent and nonsolvent evaporation which is called dry casting process, vapor induced phase separation, trapping skinning. Once the skin formation takes place, and thermally induced phase separation (Altinkaya and the nonsolvent penetrates the skin at the weak spots and Ozbas, 2004 and Matsuyama et al., 2000). it initiates the macrovoids (Shojaie et al., 1994). Below the skin layer liquid-liquid phase separation takes place In wet cast process, polymer casting solution is (Koenhen et al., 1977). Liquid –liquid phase separation immersed in the nonsolvent bath which results takes place when a homogeneous solution becomes formation of porous membranes due the solvent loss thermodynamically unstable due to introduction of a and counter diffusion of nonsolvent into the casting non solvent. Original solution decreases its free energy solution (Shojaie et al., 1994). of mixing by splitting up into two liquid phases of Thermally induced phase separation process begins by different composition (Broens et al., 1980). Liquid- dissolving the polymer into the diluent at elevated liquid demixing is caused either by nucleation and temperature. After that the solution is to be casted in growth or spinodal decomposition. Nucleation growth desired shape and subjected in cooling to induce phase mechanism occurs in metastable region between separation. By solvent exchange process diluent is spinodal and bimodal however spinodal decomposition extracted and the evaporation of extractant yields a occurs in the unstable region inside the spinodal curve microporous structure (Matsuyama et al., 2004). (Matsuyama et al., 2000).

Dry cast process is one of the process by which Structure is evolved by spinodal decomposition thermodynamic state of polymer solution can be altered mechanism if composition passes through the critical to achieve the phase inversion. It is characterized by point and phase separation occurs in the unstable region. evaporation of nonsolvent and solvent from initially If the composition passes slowly in the metastable homogeneous single phase solution (Shojaie et al., 1994 region, phase separation occurs in nucleation growth and Young et al., 2002). Due to external effects region. This followed by the growth of macrovoids homogenous polymer solution becomes because of diffusion of solvent and nonsolvent from the thermodynamically unstable initially (Altinkaya and surrounding polymer solution and precipitation bath. Ozbas, 2004) and two phase solution is formed due to During dry casting process and precipitation in wet evaporation. Hence phase separates into polymer lean casting process macrovoids are formed.

* Corresponding Author: Dr. Raj Kumar Arya Email: [email protected] , Fax: +91-7544-267011,

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GGGG Gas( T,, h P12bb , P )

zLt= ()

Polymer + Solvent (1) + Solvent (2)

z = 0

Impermeable Substrate

zH=− g g Gas T, h ( )

Fig.1. Schematic of a drying coating

Macrovoids formation can be eliminated by decreasing polymer weight fraction, and membrane thickness on the rate of evaporation. Macrovoids appear to occur in membranes structures produced by dry-cast process. the systems that begin phase separation shortly after the They found that as the nonsolvent weight fraction casting (Penky et al., 2003). increases then membrane morphology changes from dense film to asymmetric to porous structure. Sambrailo Macrovoid formation can be explained by several and Kunst (1987) have studied that membrane hypotheses. At some time interfacial tension between performance improves with evaporation and the casting solution and water bath interface becomes reproducibility decreases with the evaporation. zero during mass transfer process. At this time water Evaporation step is not necessary in order to produce intrusion is favored which causes the initiation of skinned membrane. Membranes with evaporation have fingers. Solvent from the casting solution diffuse into numerous small pores hence higher product rate. these intrusions causes further growth resulting in Dickson et al. (1979) has studied that as the surface skin formation of macrovoids (Shojaie et al., 1994). When thickness increases the membrane flux decreases. the difference in chemical potential of the solvent in the polymer solution and nonsolvent is lowered, then Phase inversion can be promoted by evaporating the number of finger like cavities gets diminished. When casting solution by dry-casting process (Young et al., the difference is large then finger like cavities is 2002). By controlling the drying conditions one can occurred (Koenhen et al., 1977). manipulate the membrane porosity, pore size, and Effective number of pores on membrane surface does permeability (Matsuyama et al., 2002). We can also not change significantly with the change of rate of produce asymmetric and symmetric membranes by evaporation. However longer evaporation time results controlling the polymer solution phase separation in bigger and more uniform pores while shorter (Matsuyama et al., 2000). Final structure of membrane evaporation time results in smaller and less uniform is determined by the rate of solvent evaporation (Young pores on the membrane surface layer (Kunst and et al., 2002). Membrane morphology is greatly affected Sourirajan, 1970). Creation of higher effective number by slight change in temperature. of pores is favored by higher casting solution temperature. Lower evaporation rate tends to increase In the literature people have done image analysis study productivity of films at a given level of solute related to phase separating system (Altinkaya and separation. Number of pores, size, and distribution on Ozbas, 2004, Altinkaya et al, 2005 and Broens et al., the membrane surface are controlled by evaporation rate 1980). In all the studied, only final microstructure has only. been discussed. Image is analysis is one way to study the phase separation systems. In the present work Yamamura et al., (2001) has studied that at higher modeling and simulation study is given for the drying rate polymer component do not have enough formation of asymmetric and symmetric membrane by time to phase separate. Hence smaller microstructure is dry-cast process. Time based study along the depth of generated at high drying rate. Matsuyama et al.(1997), coating will be the more rigorous analysis for phase has studied the effect of nonsolvent weight fraction, separating systems. It will provide information about 14 Journal of Chemical Engineering, IEB Vol. ChE. 27, No. 1, June 2012

how the microstructure is changing with time as the ci, is the concentration of solvent i, t is the time, z, is the drying proceeds. thickness of the coatings at anytime, D and D , are 11 22 Various diffusion models (Alsoy and Duda, 1999, main diffusion coefficients that characterize transport Zielinski and Hanley, 1998 and Price and Romdhane, due to solvents own concentration gradient, D12 and 2003) have been developed for continuous polymer D , are cross diffusion coefficients that characterize film. As the polymer-solvent-nonsolvent system phase 21 separates, all these diffusion models may or may not be transport due to other solvents concentration gradient. valid. The concentration of polymer, balancing component, Hence, a study is needed to check the validity of various can be obtained by equating sum of mass fraction to available diffusion models and time based study for one. Several models for predicting diffusion coefficients phase separating systems. Cellulose acetate(3)– have been proposed in the literature. All these models water(1)–acetone(2) is selected for the study because all are derived from Bearman’s friction factor theory by the free volume parameters are available for this system. making certain assumptions. Alsoy and Duda (1999) Water works as the nonsolvent due to low diffusion and assumed that the ratio of self diffusion coefficients of mass transfer coefficient compared to acetone. solvent to polymer is equal to inverse ratio of molecular Experimental study will performed using Confocal weights. Zielisnki and Hanley (1999) assumed that the Raman Microscopy. It enables to catch the Raman ratio is equal to inverse ratio of specific volumes. spectra and image analysis with time within the coating. Dabral et al. (2002) neglected friction between solvents That can be convoluted to get the concentration within when compared to friction between solvents and the coating with time. polymers. Price and Romdhane (2003), Nauman and Savoca (2001) reported that whenever the ratio of diffusion coefficients is a constant, the models predict 2. Model and Simulation of Drying negative concentration for the balancing component. Coating All the models are given in Table 1. D1 , and D2 Fig. 1 shows the schematic of a drying coating, which appearing in Table 1 are the self diffusion coefficients, has been cast on impermeable substrate. As the solvent which can be calculated using Vrentas and Duda reaches at the surface, it evaporates into the air on the (1977a, b) free volume theory top side of the coating. As mass of solvents decreasing ⎛ ⎛ N ξ ⎞ ⎞ with time, hence coating – gas interface is moving ⎜ ⎜ ω Vˆ * iN ⎟ ⎟ closer to the substrate opposite to diffusion. There is no ⎜ ⎜∑ j j ⎟ ⎟ ⎝ j=1 ξ jN ⎠ mass transfer from the substrate side; hence, fluxes will D = D exp⎜− ⎟ i 0i ˆ be zero at the substrate. ⎜ VFH ⎟ ⎜ γ ⎟ Mass Transport: ⎝ ⎠ critical molar volume of a jumping unit of component i ξ = Both the solvents are diffusing with the coating from i3 critical molar volume of the jumping unit of the polymer substrate side to coating side. At anytime total mass ˆ * transfer of any diffusing species is the sum of the mass Vi M ji ξ = (Vrentas et al., 1984), and transfer due to its own concentration gradient and mass i3 ˆ * transfer due to concentration gradient of second solvent. V3 M j3 ˆ N Mass balance for solvent 1 VFH K1i = ωi ()K 2i+T − Tgi ∑ γ i=1 γ ∂c1 ∂ ⎛ ∂c1 ⎞ ∂ ⎛ ∂c2 ⎞ D , is the pre-exponential factor for component i, ω = ⎜ D11 ⎟ + ⎜ D12 ⎟ 0i (1) i ∂t ∂z ⎝ ∂z ⎠ ∂z ⎝ ∂z ⎠ * , is the mass fraction of the component i, ˆ , is the Vi Mass Balance for Solvent 2 specific critical hole free volume of component i ˆ required for a jump, VFH , is the average hole free ∂∂cc21∂∂⎛⎞⎛⎞ ∂ c 2 volume per gram of mixture, γ , is an overlap factor =+⎜⎟⎜⎟DD21 22 (2) ∂∂tz⎝⎠⎝⎠ ∂ z ∂ z ∂ z which is introduced because the same free volume is available to more than one molecule, M ji , is the The reference velocity is chosen to be volume average velocity because it is shown to be equal to zero if there molecular weight of a jumping unit of component i. is no change in volume on mixing (Cairncross, 1994). 15 Journal of Chemical Engineering, IEB Vol. ChE. 27, No. 1, June 2012

Activity for the ternary polymer – solvent – solvent Activity coefficient of solvent 1, system can be calculated using Flory Huggins theory lna = lnγ + lnφ (Favre et al., 1996). 111 ⎛⎞VV ⎛ V ⎞ 1122 1 =+−−−lnφ1⎜⎟ 1 φφ 1 2 φχφχφφφχχχ 3 + 13 3 + 12 2 + 2 3 ⎜ 13 +− 12 23 ⎟ ⎝⎠VV23 ⎝ V 2 ⎠

Activity coefficient of solvent 2,

lna222= lnγ + lnφ =

⎛⎞VV2222 V 2 ⎛ VV 22 ⎞ lnφφφφχφχφφφχχχ2+−⎜⎟ 1 1 − 2 − 3 + 23 3 + 12 2 + 1 3 ⎜ 12 + 23 − 13 ⎟ ⎝⎠VV13 V 1 ⎝ VV 11 ⎠

Where, χ , is the Flory – Huggins binary interaction parameter can be determined from the Bristow and Watson (1958) semi-empirical equation given below,

V i 2 χij=+0.35 ()δδ i − j RT V i , is the partial molar volume of solvent i, δi , is the solubility parameter of solvent i, δ j , is the solubility parameter of polymer j, and volume fraction is given by ˆ φi = ciVi ,where ci , is the concentration of species i, ˆ Vi , is the specific volume of species i.

Boundary conditions at the free surface:

At the surface both the solvents are evaporating into the gas. The solvent rate of evaporation per unit area is a product of the difference in the partial pressure of the solvent at the surface of coating and in the bulk of the nearby gas and mass transfer coefficient, which is the combined action of convection and diffusion. The rate of evaporation is equal to sum of diffusive flux and convective flux at the surface of the coating. Since, volume average velocity is zero for this case. Hence, for only flux is the diffusive flux.

Flux of solvent 1 at free surface ⎛ ∂c1 ∂c2 ⎞ ⎜− D11 − D12 ⎟ z =L(t) = ⎝ ∂z ∂z ⎠ 1−−−−cV kGG pGG p cV k p GG p ( 1111) 12( ib) 1222() ib Flux of solvent 2 at free surface ⎛ ∂c2 ∂c1 ⎞ ⎜− D22 − D21 ⎟ z = L(t) = ⎝ ∂z ∂z ⎠ 1−−−−cV kGG pGG p cVk p GG p ( 22) 22( 2ib 2) 21() 1 ib 1

Boundary conditions at the base:

Since, base is impermeable. Hence, there is no mass transfer through the base to the gas.

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Flux of solvent 1 at the base Heat taken away from the coating by the solvents vapors per unit area ⎛ ∂c1 ∂c2 ⎞ ⎜− D11 − D12 ⎟ z =0 =0 N −1 (10) ∂z ∂z = GGGˆ ⎝ ⎠ ∑ kHpgi∆− vi() ii p ib i=1 Flux of solvent 2 at the base Heat accumulation within the coating per unit area = ppˆ ⎛ ∂c2 ∂c1 ⎞ ρ CXtdTp ( ) ⎜− D22 − D21 ⎟ z =0 =0 (11) ⎝ ∂z ∂z ⎠ Heat accumulation within the substrate per unit area = ssˆ ρ CHdTp Change in coating thickness: Heat taken by the coating + substrate = Heat supplied by the gas – Heat taken by the solvents vapors Since both the solvents are evaporating from the surface By arranging all the terms, we will get following of coating to the gas flowing parallel to the coating equation for change in coating temperature. surface. Rate of change of mass per unit area per unit dT time will give the change in coating thickness. = dt dL GG G GG G =−Vk p − p − Vk p − p N − 1 11() 1ib 1 2 2() 2 ib 2 ⎡ GG Gˆ GGgg⎤ dt ⎢ hTT()−+∑ kgi ∆ H vi ( p ii −+ p ib )() hTT −⎥ (12) − ⎢ i=1 ⎥ ppˆˆ ss G G ⎢ ρρCXt()+ CH ⎥ Where ,L is the thickness of coating, k and k , are pp 1 2 ⎣⎢ ⎦⎥ the convective mass transfer coefficient of solvent 1 and hG and hg , are the heat transfer coefficients at the solvent 2 respectively,V 1 and V 2 , are the partial molar surface of the coating and the base side respectively, G G volume of solvent 1 and 2 respectively, p1b and p2b , ˆ ∆Hvi , is the enthalpy of evaporation of solvent i, ρ , is are the partial pressure of solvent 1 and 2 in bulk gas the density, G G respectively, p1i , p2i is equilibrium partial pressure of ˆ Cp , is the specific heat, superscripts, p, polymer, s, solvent 1 and solvent 2 respectively, and can be calculated by substrate.

vap p1i = P1 ()T .φ1.γ1 Numerical Analysis vap p2i = P2 ()T .φ2.γ 2 Discretization of nonlinear ordinary and coupled differential equations (1) and (2) is done using γ andγ , are the activity constants for the solvent 1 1 2 Galerkin’s finite element formulation using quadratic and 2 respectively. basis functions. Galerkin’s method transforms partial differential equations into ordinary differential Energy Transport equations, which were integrated with ode15s of Matlab. The size of the elements increased The coating is heated by hot air blown on top and progressively from the surface to the substrate. The bottom. Because coating is very thin, the conductive 2 ⎛⎞i −1 resistance of the coating is negligible compared to position p, of ith node is given by p = ⎜⎟where convective resistance in the air. Hence, the coating ⎝⎠ne temperature is assumed to be uniform through the i=1 to ne+1, and ne, is the total number of the elements. thickness (Alsoy and Duda, 1999). Detailed heat This is done to capture steep concentration gradients transport model of Price and Cairncross (2000) showed 0 near the surface. Total number of nodes equal to 2ne+1, a temperature variation of about 0.1 C. Temperature of hence total numbers of unknown for each species are coating and the substrate is assumed to be same. equal to 2n +1, and total unknowns are 2n +3 because at Radiation heat transfer is also neglected because e e 0 each time there are two other variables are temperature temperatures are usually less than about 150 C. and the thickness of the coating. The coating was divided into 20 elements of unequal size. The time Heat supplied by the hot from the top side per unit area taken for the solution is around 15 to 30 min CPU time. = hTGG( − T) How many elements one should will be decided based on the error analysis between two different elements. If Heat supplied by the hot from the bottom side per unit the cumulative absolute error associated between gg area = hT()− T different elements are less than or equal to 0.5%.

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Generally we double the elements for the elemental thickness decreases and voids volume increases. Water analysis, 10, 20, and 40 and so on. works as the controlling factor because of low diffusion and mass transfer coefficient. As the drying takes place 3. Results and Discussion the acetone evaporated faster from the top surface and surface beneath have high amount of water. Due to this All the free volume parameters and experimental initially homogenous solution becomes thermo- conditions for cellulose acetate (3)-water (1)-acetone(2) dynamically unstable hence phase separates. system are given in Table 2 and Table 3 respectively, Table 3. Experimental parameters for Cellulose Table 2. Free volume parameters (Altinkaya and Ozbas, acetate/water/acetone System (Altinkaya and Ozbas, 2004) 2004) Initial Conditions Temperature 296 K Cellulose Cellulose J Parameter Unit Acetate Acetate / Heat capacity 0.75 / acetone water g.K Substrate 3 2 cm cm -4 -4 parameters Density 2.5 D0 3.6×10 8.55×10 s g Base thickness 0.0508 cm K cm3 11 0.000186 0.00218 J Heat Capacity 2.5 γ g.K g.K 3 K cm 3 12 cm 0.000364 0.000364 Density of polymer 1.31 γ g.K g K K -53.33 -152.29 J 21 Heat of evaporation of 2444 solvent 1 g K22 K -240 -240 Coating Heat of evaporation of J T K 0 0 552 g1 parameters solvent 2 g

Tg 2 K 0 0 Bottom air supply g 297 K 3 temperature, T * cm Top air supply Vˆ 0.943 1.071 297 K 1 g temperature, T G Mole fraction of the cm3 0 Vˆ * 1.0 1.0 solvent 1 in the air 2 Mole fraction of the g 0 solvent 2 in the air ξ 0.715 0.252 χ 0.5 1.4

χ12 1.3

Effect of Nonsolvent Concentration

In the Cellulose acetate-water-acetone system, water works as the nonsolvent. From the Fig. 2, we can say that if the initial nonsolvent concentration is very low, phase separation may not take place and dense polymer film may be obtained rather than a porous membrane.

At higher nonsolvent concentration the rate of shrinkage is decreased, due to lower polymer concentration the formation of more graded pore sub-layer structure Fig.2. Concentration paths for cellulose acetate –water – having higher porosity is favored. If we further increase acetone systems (case 1. volume fraction of cellulose the water content then we will get symmetric acetate, water, and acetone is 10, 10 and 80 membrane. As the water content increases the skin

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respectively, surface-air interface - ○, solution – thickness increases, then delay in phase transition is substrate interface- □. Case.2. Volume fraction of expected due to increase in the total mass of acetone. It cellulose acetate, water, and acetone is 10, 20 and 70 causes greater asymmetry in final structure with thicker respectively, surface-air interface -●, solution – densified layer near free surface. substrate interface- ■ , for the same thickness: 0.01cm W and hear transfer coefficient: 2.2x10-4 ). cm2 . K

Fig.4. Concentration paths for cellulose acetate –water- acetone system. ( Case 1. thickness: 0.01cm, surface-air

interface-●, solution–substrate interface- ■. Case.2. Thickness: 0.05cm, surface-air interface-▲, solution– Fig. 3. Concentration paths for cellulose acetate –water- substrate interface-▼. For the same volume fraction of acetone system. (Case 1. volume fraction of cellulose cellulose acetate, water and acetone is 10, 20 and 70 acetate, water, and acetone is 5, 20 and 75 respectively, respectively and hear transfer coefficient: 2.2x10-4 surface-air interface - ○, solution –substrate interface- W □. Case 2. Volume fraction of cellulose acetate, water, 2 ). and acetone is 10, 20 and 70 respectively, surface-air cm. K interface -●, solution –substrate interface- ■ for the same thickness: 0.01cm and hear transfer coefficient: W 2.2x10-4 ). cm2 . K

Effect of Polymer Concentration

From Fig. 3, it can be concluded that at low polymer concentration we will get dense polymer film and at higher polymer concentration asymmetric polymer membrane. Since only substrate side evade the two phase region and surface side is out of two phase region. At low polymer concentration, solvent and nonslovent can diffuse easily within the film due to which skin formation does not take place. Hence no phase separation takes place. By increasing the polymer Fig.5. Concentration paths for cellulose acetate –water- content we are increasing more resistance to solvent and acetone system (Case 1. heat transfer coefficient: non solvent diffusion hence probability to phase W separation at substrate side is higher. 2.2x10-4 , surface-air interface-●, solution – cm2 . K

substrate interface- ■. Case 2. Heat transfer coefficient: Effect of Coating thickness W 8.4x10-4 , surface-air interface-▲, solution – cm2 . K From Fig. 4, we can say that faster phase separation is substrate interface-▼. For the same volume fraction of achieved by decreasing the initial film thickness due to cellulose acetate, water and acetone is 10, 20 and 70 decrease in resistance of diffusion controlled mass respectively and thickness: 0.01cm). transfer. It favors less asymmetric membranes because top and bottom polymer concentrations are same. As the

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Effect of Air Velocity 4. Broens, L., Altena, F.W. Smolders, C.A. and Koenhen, D.M., 1980, “Asymmetric Membrane From Fig. 5, we can say that as we increase the air Structures as a Result of phase separation velocity the phase separation is completely suppressed phenomena”, Desalination, 32, 33 – 45. and uniformly dense coating devoid of substantial 5. Dickson, J.M., Lloyd, D.R. and Huang, R.Y.M., microstructure will result. 1979, “Ionically crosslinked Poly (acrylic acid)

At higher air flow rate of evaporation will be higher Membranes. III. Reverse Osmosis Results for Dry than the diffusion mass transfer. Top surface becomes Cast Membranes” Journal of Applied Polymer dried very soon however beneath we have much amount Science, 24, 1341 – 1351. of water and acetone which favor the phase separation. 6. Koenhen, D. M., Mulder, M.H.V. and Smolders, Hence, we are likely to get the asymmetric membranes. C.A., 1977, “Phase separation Phenomena during At low air flow rate external mass transfer is less the Formation of Asymmetric Membranes”, Journal compared to diffusion controlled mass transfer rate. Drying takes place slowly and have high acetone of Applied Polymer Science, 21, 199-215. content. Higher amount of acetone favor homogeneous 7. Krantz, W.B., Ray, R.J., Sani, R.L. and Gleason, polymer film. K.J., 1986, “Theoretical Study of the Transport Processes Occurring During the Evaporation Step 4. Conclusion in Asymmetric Membrane Casting”, 29, 11 – 36. 8. Kunst, B. and Sourirajan, S., 1970, “Effect of Based on the simulation results we can conclude the Casting Conditions on the Performance of Porous following; Cellulose Acetate Membranes in Reverse Osmosis”, Journal of Applied Polymer Science, 14, 1. We can produce asymmetric and symmetric 723-733. membrane by dry casting method by changing 9. Matsuyama, H., Kim, M. and Lloyd, D. R., 2002, the drying conditions. 2. Low water content give dense polymer film “Effect of extraction and drying on the structure of however high water content gives asymmetric microporous polyethylene membranes prepared via and then symmetric membranes without thermally induced phase separation”, Journal of changing the polymer content. Membrane Science, 2004, 413-419. 3. Above certain amount of polymer we will get 10. Matsuyama, H., Nishiguchi, M. and Kitamura, Y., membrane for the same amount of water. 2000, “Phase Separation Mechanism during 4. Phase separation totally is suppressed at high Membrane Formation by Dry-Cast Process”, air velocity. Journal of Applied Polymer Science, 77, 776-782. Acknowledgements 11. Matsuyama, H., Teramoto, M. and Uesaka, T., 1997, “Membrane Formation and Structure This work was funded by King Abdul Aziz City for Development by dry-cast Process”, Journal of Science and Technology (KACST) (Grant Number: 79- Membrane Science, 135, 271-288. 25). 12. Penky, M.R., Zartman, J., Krantz, W.B., Greenberg, A.R. and Todd, P., 2003, “Flow- References Visualization during macrovoids pore formation in dry-cast cellulose acetate membranes”, Journal of 1. Alsoy, S. and Duda, J.L., 1999, “Modeling of Membrane Science, 211, 71-90. Multicomponent Drying of Polymer Films”, 13. Price, P.E. and Romdhane, I.H., 2003, AICHE Journal, 45, 4, 896-905. “Multicomponent Diffusion Theory and Its 2. Altinkaya, Sacide Alsoy and Ozbas, Bulent, 2004, Application to Polymer-Solvent Systems”, AICHE “Modeling of asymmetric membrane formation by Journal, 49, 2, 309-322. dry – casting method”, Journal of Membrane Science, 230, 71–89. 14. Sambrailo, D. and Kunst, B., 1987, “Asymmetric 3. Altinkaya, Sacide Alsoy, Yenal, Hacer and Ozbas, Membrane Formation. Is the Evaporation Step Bulent, 2005, “Membrane Formation by dry-cast Necessary?” Desalination, 64, 321-328. process model validation through morphological 15. Shojaie, S. S., Krantz, W. B. and Greenberg, A. R., studies”, Journal of Membrane Science, 249, 163 – 1994, “Dense Polymer Film and Membrane 172. Formation via the dry-cast process Part II. Model

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validation and morphological studies”, Journal of 18. Young, T.H., Huang, J.H. and Chuang, W.Y., 2002, Membrane Science, 94, 281 – 298. “Effect of evaporation temperature on the 16. Shojaie, Saeed S., Krantz, William B. and formation of particulate membranes from Greenberg, Alan R., 1994, “Dense polymer film crystalline polymers by dry-cast process”, and membrane formation via the dry-cast process European Polymer Journal, 38, 63-72. Part I.Model development”, Journal of 19. Zielinski, J.M. and Hanley, B., 1999, “Practical Membrane Science, 94, 255 – 280. Friction-Based Approach to Modeling 17. Yamamura, M., Nishio, T., Kajiwara, T. and Multicomponent Diffusion”, AICHE Adachi, K., 2001, “Effect of stepwise change of drying rate on microstructure evolution in polymer films”, Drying Technology, 19, 7, 1397-1410.