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Mechanism of osmotic flow in a periodic fiber array

¹Departments of Biomedical and Mechanical Engineering, The City College of The City University of New York, New York, New York; and ²Department of Physiology and Membrane Biology, University of California, Davis, California

Submitted 26 June 2005 ; accepted in final form 19 September 2005

The classic analysis by Anderson and Malone (Biophys J 14: 957–982, 1974) of the osmotic flow across membranes with long circular cylindrical pores is extended to a fiber matrix layer wherein the confining boundaries are the fibers themselves. The equivalent of the well-known result for the reflection coefficient ₀ = (1 – )², where is the partition coefficient, is derived for a periodic fiber array of hexagonally ordered core proteins. The boundary value problem for the potential energy function describing the solute distribution surrounding each fiber is solved by defining an equivalent fluid annulus in which the pressures and osmotic forces are determined. This model is of special interest in the osmotic flow of water across a capillary wall, where recent experimental studies suggest that the endothelial glycocalyx is a quasiperiodic fiber array that serves as the primary molecular sieve for plasma proteins. Results for the reflection coefficient are presented in terms of two dimensionless numbers, = a/R and = b/R, where a and b are the solute and fiber radii, respectively, and R is the outer radius of the fluid annulus. In general, the results differ substantially from the classic expression for a circular pore because of the large difference in the shape of the boundary along which the osmotic force is generated. However, as in circular pore theory, one finds that the reflection coefficients for osmosis and filtration are the same.

endothelial glycocalyx layer; reflection coefficient

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