Electrolyte transport through nanofiltration membranes by the space-charge model and the comparison with Teorell-Meyer- Sievers model

The space-charge (SC) model was applied to predict salt rejection with charged capillaries in reverse osmosis as a model system of nanofiltration membranes. Straightforward numerical calculation was carried out using parameters of feed concentration, pore radius and surface charge density. The rejection dependency on Peclet number by the SC model has been compared with that obtained by the Teorell-Meyer-Sievers (TMS) model which does not take into account the radial distributions of electric potential and ion concentration. The two models show good agreement for capillaries having smaller radius and lower surface charge density. Membrane parameters, reflection coefficient σ and solute permeability coefficient ω have been numerically calculated using the SC model as a function of two dimensionless parameters: the ratio of pore radius to Debye length rpλd and the dimensionless potential gradient in the pore surfaces q0, and the comparison of σ and ω calculated by the SC model with those by the Smit method and by the TMS model has been carried out. It is shown that the TMS model shows good agreement with the SC model in the calculation of the membrane parameters when q0 is less than 1.0, while σ and ω by the Smit method show excellent agreement with those by the SC model when rejection is larger than 0.5.

[1]  F. A. Morrison,et al.  Electrokinetic Energy Conversion in Ultrafine Capillaries , 1965 .

[2]  K. Meyer,et al.  La perméabilité des membranes I. Théorie de la perméabilité ionique , 1936 .

[3]  R. Probstein,et al.  Electrokinetic salt rejection in hyperfiltration through porous materials. Theory and experiment , 1972 .

[4]  J. L. Anderson,et al.  The streaming potential and inadequacies of the Helmholtz equation , 1985 .

[5]  O. Kedem,et al.  Hyperfiltration in charged membranes: the fixed charge model , 1967 .

[6]  K. Meyer,et al.  La perméabilité des membranes. II. Essais avec des membranes sélectives artificielles , 1936 .

[7]  Egon Matijević,et al.  Surface and Colloid Science , 1971 .

[8]  J. Anderson,et al.  Experimental Verification of the Space‐Charge Model for Electrokinetics in Charged Microporous Membranes , 1983 .

[9]  R. J. Petersen,et al.  Composite reverse osmosis and nanofiltration membranes , 1993 .

[10]  S. Nakao,et al.  Negative rejection of anions in the loose reverse osmosis separation of mono- and divalent ion mixtures , 1991 .

[11]  K. S. Spiegler,et al.  Thermodynamics of hyperfiltration (reverse osmosis): criteria for efficient membranes , 1966 .

[12]  F. Tejerina,et al.  Study of some electrokinetic phenomena in charged microcapillary porous membranes , 1987 .

[13]  K. Meyer,et al.  La perméabilité des membranes. IV. Analyse de la structure de membranes végétales et animales , 1936 .

[14]  J. F. Osterle,et al.  Membrane transport characteristics of ultrafine capillaries. , 1968, The Journal of chemical physics.

[15]  A. Katchalsky,et al.  Permeability of composite membranes. Part 1.—Electric current, volume flow and flow of solute through membranes , 1963 .

[16]  Shoji Kimura,et al.  Calculation of ion rejection by extended nernst-planck equation with charged reverse osmosis membranes for single and mixed electrolyte solutions , 1991 .

[17]  A. Giménez,et al.  Streaming potential of some polycarbonate microporous membranes when bathed by LiCl, NaCl, MgCl2 and CaCl2 aqueous solutions , 1989 .

[18]  Eli Ruckenstein,et al.  Electrolyte osmosis through capillaries , 1981 .

[19]  F. A. Siddiqi,et al.  Studies of membrane phenomena , 1969 .

[20]  O. Kedem,et al.  Thermodynamics of hyperfiltration (reverse osmosis) , 1966 .

[21]  Shoji Kimura,et al.  Reverse Osmosis of Single and Mixed Electrolytes with Charged Membranes: Experiment and Analysis , 1991 .

[22]  E. Ruckenstein,et al.  Anomalous effects during electrolyte osmosis across charged porous membranes , 1982 .

[23]  Robert Rautenbach,et al.  Separation potential of nanofiltration membranes , 1990 .

[24]  H. Fujita,et al.  Studies of membrane phenomena. VII. Effective charge densities of membrane , 1968 .

[25]  J. Smit,et al.  The application of the space-charge model to the permeability properties of charged microporous membranes , 1985 .

[26]  Norman Epstein,et al.  Theory of electrokinetic flow in fine cylindrical capillaries at high zeta-potentials , 1975 .

[27]  H. Fujita,et al.  Studies of Membrane Phenomena. I. Membrane Potential , 1965 .

[28]  R. Probstein,et al.  Brackish water salt rejection by porous hyperfiltration membranes , 1973 .

[29]  J. Smit.  Reverse osmosis in charged membranes: Analytical predictions from the space-charge model , 1989 .

[30]  I. B. Oldham,et al.  Streaming potential in small capillaries , 1963 .

[31]  J. C. Fair,et al.  Reverse Electrodialysis in Charged Capillary Membranes , 1971 .

[32]  E. Ruckenstein,et al.  Viscoelectric effects in reverse osmosis , 1981 .

[33]  S. Dukhin,et al.  Phenomenological theory of reverse osmosis in macroscopically homogeneous membranes and its specification for the capillary space-charge model , 1993 .