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On the fine structure of osmosis including three-dimensional pore entrance and exit behaviour

Published online by Cambridge University Press:  21 April 2006

Zong-Yi Yan ,
Sheldon Weinbaum  and
Robert Pfeffer
Zong-Yi Yan
Affiliation:
Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031
Sheldon Weinbaum
Affiliation:
Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031
Robert Pfeffer
Affiliation:
Department of Chemical Engineering, The City College of The City University of New York, New York, NY 10031
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Abstract

This paper presents a detailed quantitative model of osmotic fine structure for both permeable and semi-permeable membranes in dilute bathing solutions. The analysis differs from all previous studies in that it treats for the first time, albeit in an approximate manner, the detailed three-dimensional hydrodynamic interaction of the particles in the entrance and exit regions and the coupling of the convective—diffusive effects in these regions with those in the interior of the pore. Reasonable interpolations between various asymptotic formulas are used to derive the tensorial components of the particle diffusivity and the slip between the fluid and particle phases as functions of position throughout the entire flow field. The solutions show that the entrance and exit regions in the case of permeable membranes can have a significant effect on the osmotic solvent flux q for small particles in short pores although changes in the overall reflection coefficient are small. This is due to the nonlinear sweeping effect of convection at the higher osmotic-flow rates. For semi-permeable membranes the predictions of the model support the hypothesis of Mauro (1957) and Ray (1960) that there is a region of near-discontinuity in pressure and concentration at the plane of the pore entrance and the sweeping effects of convection on the concentration profile are very minor for the dilute solutions studied herein. In contrast, the solutions for the permeable membrane clearly show the existence of three-dimensional unstirred regions which extend two-to-three pore radii from the pore openings. These solutions form the ubstructure of the much thicker one-dimensional unstirred layer described by Dainty (1963) and Pedley et al. (1978). It is shown that when the porosity is low (such as in most biological membranes), the wall concentration in Pedley's solution is the far-field concentration for the entrance/exit solutions presented herein.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 162 , January 1986 , pp. 415 - 438
Copyright
© 1986 Cambridge University Press

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