Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-18T23:22:21.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Molecular models for permeation through thin membranes: the effect of hydrodynamic interaction on permeability

Published online by Cambridge University Press:  29 March 2006

George H. Malone ,
Thomas E. Hutchinson  and
Stephen Prager
George H. Malone
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis
Thomas E. Hutchinson
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis
Stephen Prager
Affiliation:
Department of Chemistry, University of Minnesota, Minneapolis
Get access Rights & Permissions [Opens in a new window]

Abstract

A variational method involving minimization of the energy dissipation rate which was previously developed for transport in polymer systems is applied here to flow of a continuum solvent through a thin membrane. The membrane is represented by an array of spherical particles undergoing Brownian motion, subject to various interactions with one another and with the motion of the solvent. General upper bounds on the solvent permeability of the membrane are obtained in terms of equilibrium distribution functions, and applications of the method are illustrated for the case where membrane elements are confined to a plane. Calculations which treat all beads equivalently give permeability estimates whose dependence on the number n of beads per unit area of membrane has the form, at low n, \[ \kappa = (6\pi\eta n)^{-1}(1-\alpha n+\ldots), \] where η is the solvent viscosity and α is a constant. More-elaborate trials which allow the drag on a bead to be influenced by the distribution of other beads in the vicinity give the stronger bounding estimate \[ \kappa = (6\pi\eta n)^{-1}(1+\alpha^{\prime}n\ln n+\ldots). \] Comparison with a self-consistent field approach suggests that this logarithmic behaviour is the true first-order correction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 4 , 2 October 1974 , pp. 753 - 767
Copyright
© 1974 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1972 Sedimentation in a dilute dispersion of spheres J. Fluid Mech. 52, 245.Google Scholar
Batchelor, G. K. & Green, J. T. 1972 The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech. 56, 401.Google Scholar
Blank, M. 1962 Monolayer permeability and the properties of natural membranes J. Phys. Chem. 66, 1911.Google Scholar
Blank, M. 1964 An approach to a theory of monolayer permeation by gases J. Phys. Chem. 68, 2793.Google Scholar
Brinkman, H. C. 1948 On the permeability of media consisting of closely packed porous particles. Appl. Sci. Res., Hague, A1, 81.Google Scholar
Childress, S. 1972 Viscous flow past a random array of spheres J. Chem. Phys. 56, 2527.Google Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres J. Fluid Mech. 5, 317.Google Scholar
Hill, T. 1956 Statistical Mechanics. McGraw-Hill.
Kedem, O. & Katchalsky, A. 1958 Thermodynamic analysis of the permeability of biological membranes to non-electrolytes Biochim. Biophys. Acta, 27, 229.Google Scholar
Keller, J. B., Rubenfeld, L. A. & Molyneux, J. E. 1967 Extremum principles for slow viscous flows with applications to suspensions J. Fluid Mech. 30, 97.Google Scholar
Kirkwood, J. G. & Riseman, J. 1948 The intrinsic viscosities and diffusion constants of flexible macromolecules in solution J. Chem. Phys. 16, 565.Google Scholar
Luzatti, V., Reiss-Husson, F., Rivas, E. & Gulik Krzywicki, T. 1966 Structure and polymorphism in lipid-water systems, and their possible biological implications Ann. N.Y. Acad. Sci. 137, 409.Google Scholar
Rotne, J. & Prager, S. 1969 Variational treatment of hydrodynamic interaction in polymers J. Chem. Phys. 50, 4831.Google Scholar
Rouse, P. E. 1953 A theory of the linear viscoelastic properties of dilute solutions of coiling polymers J. Chem. Phys. 21, 1272.Google Scholar
Solomon, A. K. 1960 Red cell membrane structure and ion transport. J. Gen. Physiol. 43 (suppl. 1), 1.Google Scholar
Woodbury, G. W. & Prager, S. 1964 Brownian motion in many-particle systems. I. Forced interdiffusion of two species J. Am. Chem. Soc. 86, 3417.Google Scholar
Yamakawa, H. 1970 Transport of polymer chains in dilute solution: hydrodynamic interaction. J. Chem. Phys. 53, 436.Google Scholar
Yasuda, H., Lamaze, G. E. & Peterlin, A. 1971 Diffusive and hydraulic permeabilities of water in water-swollen polymer membranes. J. Polymer Sci. A2, 1117.Google Scholar
Zimm, B. H. 1956 Dynamics of polymer molecules in dilute solution: viscoelasticity, flow birefringence and dielectric loss. J. Chem. Phys. 24, 269.Google Scholar