Statistical-mechanical theory of membrane transport

Abstract This paper is concerned with reviewing a statistical-mechanical theory of membrane transport, its range of validity, and its relation to previous membrane transport theories. We begin by addressing the question “what good is a theory?” and providing our answer thereto. The commercial membrane processes are then briefly surveyed. In the main body of the paper, the statistical-mechanical theory is applied to several processes (ultrafiltration, reverse osmosis, gas separations, dialysis, and electrodialysis), and simplified working equations are derived for each process. The central theme is that there is a unified statistical-mechanical theory of membrane transport, from which all previous theories can be derived.

[1]  K. S. Spiegler,et al.  Transport processes in ionic membranes , 1958 .

[2]  Edward A. Mason,et al.  Generalization of membrane reflection coefficients for nonideal, nonisothermal, multicomponent systems with external forces and viscous flow , 1986 .

[3]  A. Katchalsky,et al.  A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability , 1961, The Journal of general physiology.

[4]  Walther Nernst.  Zur Kinetik der in Lösung befindlichen Körper , 1888 .

[5]  E. Hartley.  "Dynamic" Osmotic Pressures , 1909 .

[6]  A. J. Staverman,et al.  Onsager's reciprocal relation. Examination of its application to a simple process. Comments , 1970 .

[7]  Sidney Loeb,et al.  Sea Water Demineralization by Means of an Osmotic Membrane , 1963 .

[8]  R. J. Bearman.  On the Linear Phenomenological Equations. II. The Linear Statistical Mechanical Theory , 1959 .

[9]  Howard Brenner,et al.  The Constrained Brownian Movement of Spherical Particles in Cylindrical Pores of Comparable Radius: Models of the Diffusive and Convective Transport of Solute Molecules in Membranes and Porous Media , 1977 .

[10]  Bean Cp.  The physics of porous membranes--neutral pores. , 1972 .

[11]  Donald G. Miller.  The Onsager Relations; Experimental Evidence , 1973 .

[12]  J. Bitter.  Effect of crystallinity and swelling on the permeability and selectivity of polymer membranes , 1984 .

[13]  T. Morse,et al.  Generalized Nernst–Planck and Stefan–Maxwell equations for membrane transport , 1976 .

[14]  J. Smit,et al.  The influence of membrane heterogeneity on the solute retention , 1985 .

[15]  E. A. Mason,et al.  Statistical–mechanical theory of membrane transport for multicomponent systems: Passive transport through open membranes , 1978 .

[16]  O. Kedem,et al.  Transport coefficients and salt rejection in unchanged hyperfiltration membranes , 1966 .

[17]  S. Sourirajan.  Mechanism of Demineralization of Aqueous Sodium Chloride Solutions by Flow, under Pressure, through Porous Membranes , 1963 .

[18]  J. Danielli.  Cell permeability and diffusion across the oil-water interface , 1941 .

[19]  H. Lonsdale,et al.  Transport in Composite Reverse Osmosis Membranes , 1971 .

[20]  E. A. Mason,et al.  Effect of heteroporosity on flux equations for membranes. , 1976, Biophysical chemistry.

[21]  A. Finkelstein,et al.  Water movement through lipid bilayers, pores, and plasma membranes : theory and reality , 1987 .

[22]  J. A. Quinn,et al.  Diffusion through composite membranes: A two-dimensional analysis , 1986 .

[23]  J. M. Henis,et al.  The Developing Technology of Gas Separating Membranes , 1983, Science.

[24]  W. Gill,et al.  REVIEW OF REVERSE OSMOSIS MEMBRANES AND TRANSPORT MODELS , 1981 .

[25]  M. Planck,et al.  Ueber die Potentialdifferenz zwischen zwei verdünnten Lösungen binärer Electrolyte , 1890 .

[26]  A. Katchalsky,et al.  Thermodynamics of flow processes in biological systems. , 1962, Biophysical journal.

[27]  E. A. Mason,et al.  Statistical-mechanical theory of passive transport through partially sieving or leaky membranes. , 1980, Biophysical chemistry.

[28]  Gunnar Eigil Jonsson,et al.  Water and solute transport through cellulose acetate reverse osmosis membranes , 1975 .

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

[30]  R. J. Bearman.  On the Linear Phenomenological Equations , 1958 .

[31]  M. Planck,et al.  Ueber die Erregung von Electricität und Wärme in Electrolyten , 1890 .

[32]  E. A. Mason,et al.  The role of viscous flow in theories of membrane transport , 1985 .

[33]  J. Lorimer.  Phenomenological coefficients and frames of reference for transport processes in liquids and membranes Part 3—theory of convective contributions to isothermal and non-isothermal transport in ionic membranes , 1983 .

[34]  William A. Wakeham,et al.  Diffusion through Multiperforate Laminae , 1979 .

[35]  E. Bresler,et al.  Irreversible Thermodynamics and Flow across Membranes. , 1969, Science.

[36]  E. A. Mason,et al.  Effect of heteroporosity on membrane rejection coefficients , 1981 .

[37]  W. S. Lazarus-Barlow.  Observations upon the Initial Rates of Osmosis of certain Substances in Water and in Fluids containing Albumen , 1895, The Journal of physiology.

[38]  R. L. Riley,et al.  Transport properties of cellulose acetate osmotic membranes , 1965 .

[39]  E. A. Mason,et al.  Test of the Onsager relation for ideal gas transport in membranes , 1972 .

[40]  E. A. Mason,et al.  Energy-barrier models for membrane transport. , 1979, Biophysical chemistry.

[41]  E. A. Mason,et al.  Similarity relations (dimensional analysis) for membrane transport , 1980 .

[42]  J. A. Quinn,et al.  Separation of gases with synthetic membranes , 1983 .

[43]  J. M. Henis,et al.  Composite Hollow Fiber Membranes for Gas Separation: The Resistance Model Approach , 1981 .

[44]  E. Lightfoot,et al.  Diffusional interaction in an ion-exchange membrane , 1968 .

[45]  K. Spiegler.  Diffusion of Gases across Porous Media , 1966 .

[46]  D. R. Lloyd,et al.  Application of the stefan-maxwell equations to the pressure-driven membrane separation of dilute multicomponent solutions of nonelectrolytes , 1988 .

[47]  E. Bresler,et al.  Diffusive and Convective Flow Across Membranes: Irreversible Thermodynamic Approach , 1969, Science.

[48]  E. Bresler,et al.  Onsager's reciprocal relation. Examination of its application to a simple membrane transport process , 1969 .

[49]  W. Henkens,et al.  Salt rejection and flux in reverse osmosis with compactible membranes , 1979 .

[50]  W. Deen.  Hindered transport of large molecules in liquid‐filled pores , 1987 .

[51]  Thomas K. Sherwood,et al.  Desalination by Reverse Osmosis , 1967 .

[52]  E. A. Mason,et al.  Equations for membrane transport. Experimental and theoretical tests of the frictional model. , 1975, Biophysical journal.

[53]  E. A. Mason,et al.  Statistical-mechanical theory of passive transport through semipermeable membranes. , 1979, Biophysical chemistry.

[54]  E. A. Mason,et al.  Steady-State Sieving across Membranes , 1971, Science.

[55]  Muriel Rukeyser.  Josiah Willard Gibbs , 1949 .

[56]  A. Katchalsky,et al.  Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. , 1958, Biochimica et biophysica acta.

[57]  H. Brown,et al.  Static Diffusion of Gases and Liquids in Relation to the Assimilation of Carbon and Translocation in Plants , 1900 .

[58]  J. A. Quinn,et al.  Restricted transport in small pores. A model for steric exclusion and hindered particle motion. , 1974, Biophysical journal.

[59]  E. Bresler,et al.  Onsager's reciprocal relation. Examination of its application to a simple process. Reply , 1970 .

[60]  J. Kirkwood,et al.  Statistical Mechanics of Transport Processes. XI. Equations of Transport in Multicomponent Systems , 1958 .