J. CHEM. SOC. FARADAY TRANS., 1994, 90(14), 2043-2046 Water Distillation through Poly(tetrafluoroethy1ene) Hydrophobic Membranes in a Stirred Cell M. 1. Vazquez-Gonzalez and L. Martinez Departamento de Fisica Aplicada , Facultad de Ciencias, Universidad de Malaga, 29011-Malaga , Spain The aim of this paper is the study of the transport of pure water through microporous hydrophobic membranes in a stirred cell containing two phases at different temperatures. The dependence of the phenomena on stirring rate and on the average temperature has been investigated. The influence of these operating conditions on mass-transfer rate is discussed, taking into account mass and heat transfer within the membrane and adjoining liquids. The concept of temperature polarization is introduced into the transport equations and shown to be important in the interpretation of experimental results.If a membrane separates two liquid phases having the same concentration, but at different temperatures, mass transfer through the membrane is observed. In analysing these ther- mally induced processes it is convenient to consider two dif- ferent processes : (1) thermo-osmosis, occurring across dense membranes, by a dissolution-diffusion mechanism ; and (2) distillation, occurring across porous membranes, by an evaporation-diffusion-ondensation mechanism. In the latter case the observed fluxes are usually much higher than in the thermo-osmotic case. We have studied thermo-osmosis pre- viously.' In the present work we focus our attention on the distillation process.In this process the liquids or solutions must not wet the membrane, otherwise the pores will be filled immediately as a result of capillary forces. This implies that non-wettable porous hydrophobic membranes must be used in the case of aqueous solution^.^.^ When the liquid phases contain pure water and there is no temperature difference, the system is in equilibrium and no transport occurs. If the temperature of one of the two liquid phases is higher than that of the other, a temperature differ- ence exists across the membrane, resulting in a vapour pres- sure difference. Thus, water will evaporate on the hot side; the vapour flows from the warm to the cold side where it condenses. In this way water transport takes place across the membrane from the hot to the cold side.The advantages of membrane distillation are that the distil- lation process takes place at moderate temperatures and that a relatively low temperature difference between the two liquids contacting the microporous hydrophobic membrane gives relatively high fluxes. The need to supply heat to the evaporation surface of the membrane means that the temperature gradients must be in the liquid phase adjacent to the membrane. The same occurs in the condensation surface side. Although the bulk phases on the two sides of the membrane are stirred, the effective temperature difference between the two sides of the mem- brane is not the same as the temperature difference between the bulk solutions (Fig.1).This loss of driving force brought about by thermal gradients in the fluids bounding the mem- brane is known as temperature polarization and has been applied to studies of thermo-osmosis, 'v4*' before being used in membrane distillation.6-8 In the present work we have measured the water distilla- tion through three different membranes for different oper- ation conditions and the theories of mass and heat transfer within the membrane and adjoining fluids have been devel- oped with a view to discussing the results obtained and to characterizing the temperature polarization. Experimental Three commercial PTFE membranes were used. These hydrophobic membranes are marketed by Gelman instru- ments Co.as TF-200, TF-450 and TF-1000, with nominal pore sizes of 0.2, 0.45 and 1.0 pm and porosities of 0.80. They have a limited mechanical strength, and in practice must be supported by different nets made generally of polymer fibres. In this way, they are composite membranes formed by an actual porous PTFE layer with a thickness of 60 pm on a polypropylene screen support. Scanning electron micro-graphs show differences between these screen supports for the three membranes. Pure water (doubly distilled and deionized) was used in the experiments. The water was filtered through a Millipore filter of 0.45 pm nominal pore size before being introduced into the measuring apparatus. All the measurements were made with an experimental device similar to that employed in earlier thermo-osmotic studies.' It is a cell formed by two symmetric cylindrical semicells 0.1 m long, separated by the membrane which is placed in a methacrylate holder with two stainless-steel grids between which the membrane was fixed. The membrane surface area exposed to the flow was 4 = 32.2 x m2.The water in the chamber was stirred by a chain-drive magnetic-cell stirrer assembly, both semicells being sur-rounded by concentric thermostatic chambers, through which flows of fluids at different temperatures were maintained. Two thermocouples were sealed in the membrane holder so that the temperature of each half-cell could be recorded and controlled. The cold chamber was connected to a glass tube placed horizontally and inserted in the top of the half-cell. In the present work a series of experiments has been per- formed with distilled water and three microporous hydropho- bic membranes.A temperature difference was maintained between both sides of the membrane and the volume flux was Fig. 1 Schematic representation of the membrane distillation J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 measured by collecting and weighing the water flowing through the glass tube placed horizontally in the cell. The experiments were carried out for different average tem-peratures in the system and different stirring rates of the bulk phases. The purpose of this paper is to study the experimen- tal situation and to evaluate some characteristic parameters of the membrane system from the flux measurements. Theory Simultaneous heat and mass transport characterize the mem- brane distillation process.The mass transport through the membrane is driven by a vapour pressure difference, resulting from the imposed temperature difference. This mass transport may be explained by the following mechanisms.6 (a)When non-condensable gases are contained in the pores of the membrane (e.g. air) as a stagnant film, the molecular diffusion model applies :9 J, = (l/Y,nXD&/XsXn/r/RT)(P,-'2) (1) where D is the water diffusion coefficient, A4 the water molec- ular weight, E the membrane porosity, x the tortuosity factor, 6 the membrane thickness, Y,,the mole fraction of air (log- mean), T the temperature, and P, and P, the pressures of water vapour corresponding to the T,, and Tm2 tem-peratures, respectively, and R the gas constant. (b) In most cases, when the pore sizes and the mean free molecular paths in the membrane distillation process are of the same order of magnitude, the Knudsen diffusion model applies : O -P,).I, = (~/~H~&/X~X~M/?~RT)''~(P,(2) where r is the membrane pore radius.The two models mentioned suggest the following equation by which the transfer may be described: J = C(P1 -P2) (3) where C can be considered a combined mass-transfer coeffi- cient through the membrane, accounting for the mass-transfer resistances of both molecular and Knudsen diffusion. Inspection of both models suggests that C will be slightly temperature dependent, decreasing < 3% with a 10"C increase in mean temperature.As vapour pressures within the membrane are not directly measurable, it is convenient to express eqn. (3) in terms of temperatures : J = C I dP/dT IT,,,(Tml -(4) This equation is a good approximation for values of T,, -Tm2< 10°C. In eqn. (4) dP/dT can be evaluated from the Clausius-Clapeyron equation at the average membrane temperature T,. Since, as opposed to the temperatures Tbl and G2,temperatures T,, and Tm2are difficult to measure, Tbl -Tb2 is, as a rule, inserted in the above equation. In order to do this, we must introduce the heat-transfer coeffi- cients (hl, h2) in the liquid films near the membrane, the latent heat transfer (A) accompanying vapour flux and the heat transfer by conduction (k,) across the membrane.In this way, for the stationary thermal flux across the membrane system in Fig. 1 we can write: hl(Tbl -'ml) = (km/SXTml -Tm2) + JA = h2(T,2 -q2) (5) From eqn. (4) and (5): -T,,)/JA = [CA(dP/dT)]-'[1 + (k,,,/6h)]+ (l/h) (6) where h = l/(l/h, + 1/h2) is the overall film heat-transfer coeficien t . On the other hand, from eqn. (4) and (5) Tml -Tm2 = + (H/hl) + (H/h2)1-'(Tb1 -Tb2) (7) where H = CA(dP/dT) + k,/6 (8) and z = [l + (H/h,) + (H/h2)]-l = [l + (H/h)]-l (9) is the temperature polarization coefficient. Eqn. (6) may be used for the analysis of experimental results for which Kl, &, and J are reported, as dP/dT is a function of T, = + Tb,)/2 assuming the temperature polarization is similar on either side of the membrane. Spe- cifically, a fit to a linear function of the values of (Tbl -T,,)/JA opposite to those of l/(dP/dT)A should yield an intercept of l/h and a slope of (l/C)[l + (kddh)],from which C may be obtained.Results and Discussion Experiments were carried out for a fixed temperature differ- ence Tbl -Tbz = 10°C between the bulk phases 1 and 2 (Fig. 1). The stirring rate used varied from 150 to 350 rpm in steps of 50 rpm, and the average temperature from 25 to 55"C, in steps of 5 "C. The flux results so obtained are shown in Table 1. The distillate flux increases monotonically with stirring rate, corresponding"*" to a decrease of the heat resistance in the boundary layers of the membrane.On the other hand, the distillate flux increases when the absolute temperature level in the membrane increases, corresponding to an increase of dP/dT with temperature. Eqn. (6) of the transport model shows how J increases when h and dP/dT augment each other. Plots of eqn. (6) for the experimental water flux corre- sponding to the same stirring rate and different average tem- peratures have been carried out in order to evaluate h and C, resulting in plots having a correlation coefficient > 0.98. Three representative plots are shown in Fig. 2. The h values obtained from the intercept of plots of eqn. (6) are shown in Table 2 for the different stirring rates and mem- branes, the h error being ca. 10%. The differences between the h values for the same stirring rate and different membranes Table 1 Mass fluxes per unit area (/lo-' kg m-' s-l ) for the three membranes at various stirring rates and average temperatures, T, membrane stirringrate T,/"C type (rpm) 25 30 35 40 45 50 55 TF 200 150 1.23 1.51 1.63 2.00 1.89 2.27 2.41 200 1.35 1.68 1.82 2.23 2.20 2.84 2.78 250 1.43 1.81 1.96 2.39 2.45 2.84 3.05 300 1.49 1.90 2.07 2.52 2.64 3.03 3.27 350 1.53 1.98 2.15 2.61 2.80 3.19 4.44 TF 450 150 0.91 1.21 1.36 1.59 1.74 2.08 2.08 200 1.00 1.35 1.52 1.79 1.96 2.34 2.36 250 1.06 1.46 1.64 1.94 2.12 2.53 2.57 300 1.10 1.55 1.73 2.06 2.25 2.67 2.72 350 1.14 1.61 1.80 2.15 2.35 2.78 2.85 TF lo00 150 1.27 1.58 1.86 2.27 2.45 2.51 3.12 200 1.41 1.82 2.14 2.27 2.78 2.85 3.46 250 1.52 1.99 2.35 2.79 3.03 3.11 3.70 300 1.59 2.13 2.52 2.96 3.22 3.31 3.88 350 1.66 2.24 2.65 3.09 3.37 3.46 4.01 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 0.5 4 1 I 0 1 2 [l/,?($)]/10-9 kg K J-' Pa-' Fig. 2 AT/JA us. l/rZ(dP/dT) corresponding to the results obtained for the TF 200 (+), TF 450 (A) and TF lo00 (+) membrane when the stirring rate was 250 rpm are attributed to the differences in the membrane screen sup- ports. On the other hand, for the same membrane the h values increase with the stirring rate as suggested by the heat transfer theory for stirred cells.' '9'' In order to evaluate the C coefficients from the slope of plots of eqn.(6),the thermal conductivity of the porous mem- branes, k, ,was calculated as k, = Ek, + (1 -&)k, where k, and k, are the thermal conductivities of the gas phase and the PTFE phase, re~pectively:'~ k, = 0.027 W m-' IC',k, = 0.22 W m-' K-'. In this way, the following Table 2 Overall film heat-transfer coefficient (/W rnW2K-') for the different membranes at different stirring rates stirring rate (rpm) TF 200 TF 450 TF loo0 150 952 938 1311 200 1102 1127 1500 250 1216 1282 1643 300 1307 1410 1754 350 1570 1518 1843 0.5 I \ 1 0.4 0.3 0.5 0.4 T 0.3 0.2 I 11 I 200 300 4 0 stirring rate (rpm) Fig.4 Temperature polarization coefficient for the different mem- branes us. stirring rate. Average temperature 318 K. +, TF 200;A, TF 450;+,TF 1OOO. C values are obtained: C(TF 200) = (22 & 2) x kg m-'s-' Pa-' C(TF 450) = (14 f2) x lo-' kg m-' s-' Pa-' C(TF 1000)= (18 & 2) x lop7kg m-' s-' Pa-' results which are independent of the stirring rate in the system. On the other hand, values of the mass-transfer coefficients predicted from the molecular diffusion theory, C,, and the Knudsen diffusion theory, CK , have been evaluated for 40 "C, which is intermediate in the experimental range studied. The calculations have been performed by using the numerical values for the relevant geometric parameters reported here- after. The tortuosity factor is typi~ally'~ = 2, the diffusivity x of water vapour in air at 40 "C and at normal pressure is13 2.88 x m2 s-' and Xn in eqn.(1) is taken to be 0.9. The results obtained are: CK(TF 200) = 18 x lop7kg m-' s-' Pa-' CK(TF 450) = 41 x kg m-' s-' Pa-' CK(TF 1OOO)= 90 x kg m-'s-' Pa-' CD = 14 x lop7kg m-* s-l Pa-' Considering the differences in their pore sizes, the three membranes perform in a similar way, as evidenced by the experimental mass-transfer coefficients. This suggests a mechanism based largely on molecular diffusion, which is independent of pore size. In fact, the C, value predicted by the molecular diffusion theory is very similar to those obtained for the TF 450 and TF lo00 membranes. Only for the TF 200 membrane does the C value obtained indicate that the combined molecular/Knudsen diffusion coefficient best describes the mass fluxes observed.This interpretation is coherent with the fact that for this membrane the pore size is more similar to the mean-free molecular path of water vapour than that for the other membranes. The experimental C and h values allow us to quantify the z temperature polarization coefficient. Fig. 3 shows the results obtained for the three membranes (at a representative stirring rate) as a function of the average temperature in the system, 0.2 I I 1 1 294 304 314 324 '+,j calculated according to eqn. (8) and (9). This behaviour is T/K different from that obtained in thermo-osmosis, where the zFig. 3 Temperature polarization coefficient for the different mem- branes us.average temperature in the system. Stirring rate 300 rpm. polarization coefficient is independent of the temperature. ' +, TF 200;A, TF 450;+,TF 1OOO. This is because in membrane distillation the H coefficient for 2046 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the membrane, as shown in the expression (8), accounts for the energy fluxes due to the convective transport of the evaporating vapour occurring simultaneously with the heat conduction across the membrane. It is the first contribution, increasing with the temperature, that is not present in the 2 3 4 5 A. C. M. Franken, J. A. M. Nolten, M. H. V. Mulder, D. Barge- man and C. A. Smolders, J. Membr. Sci., 1987,33, 315. G.C. Sarti and C. Gostoli, Membranes and Membrane Processes, ed. E. Drioli and M. Nakagaki, Plenum Press, New York, 1986. H. Vink and S. A. A. Chisthi, J. Membr. Sci., 1976, 1, 149. F. Bellucci, J. Membr. Sci., 1981,9, 285. thermo-osmosis process. 6 R. W. Schofield, A. G. Fane and C. J. D. Fell, J. Membr. Sci., Finally, Fig. 4 shows the z values obtained for the three membranes as a function of the stirring rate, also calculated according to eqn. (8) and (9). In this case the z variations are due to the h variation with the stirring rate, this behaviour being similar to that obtained in thermo-osmosis. All these results highlight the fact that any attempt to compare a membrane distillation transport model with mea- sured data must take into account the significant influence of temperature polarization, which depends on the heat-transfer coefficient of the membrane and of the liquid layers. 7 8 9 10 11 12 13 1987,33, 299. J. M. Ortiz de Zarate, F. Garcia-Lopez and J. I. Mengual, J. Chem. SOC., Faraday Trans., 1990,86,2891. S. Bandini, C. Gostoli and G. C. Sarti, Desalination, 1991,81,91. R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Pheno- menu, John Wiley, New York, 1960. M. Mulder, Basic Principles of Membrane Technology, Kluwer, Dordrecht, 1992. T. G. Kaufmann and E. F. Leonard, AZChE J., 1968,14,421. H. Hikita and Y. Konishi, AZChE J., 1984,30,945. J. H. Perry, Chemical Engineers Handbook, McGraw-Hill, New York,4th edn., 1963. 14 M. Imai, S. Furusaki and T. Miyauchi, I. E. C. Proc. Des. Den, References 1982,21, 421. 1 C. Fernandez-Pineda and M. I. Vhzquez-Gonzalez, J. Chem. SOC., Faraday Trans. I, 1988,84,647. Paper 4/00520A; Received 27th January, 1994