Pore flow models and their applicability

Abstract

Pore flow models are classified and concisely reviewed, and it is shown that despite their apparent differences, they are equivalent. It is proven that the difference between the classic formula of Guerout-Elford-Ferry and the most recent ones developed by Pappenheimer-Ussing and Kedem-Katchalsky, is due to the introduction of a more proper viscosity coefficient for the water inside the membranes in the newer formulae. Fundamental assumptions involved in the models are restated and criteria for their applicability are mentioned. Arguments regarding the fundamental validity of the pore size formulae when applied to tight membranes, where continum hydrodynamics become questionable, are reviewed. Recent theoretical analysis of the situtation by Mikulecky, where he shows the calculated pore size merely reflects the extent of the membrane-water interaction is briefly presented. It is argued that since his analysis neglects the influence of the membrane-water interaction on the viscosity coefficient, his treatment is far from conclusive. In support of this argument, the results of the Kinetic studies of Levitt based on direct simulation through molecular dynamics is presented where water molecules (considered as non-interacting hard spheres of 1A radius) are observed in a rigid cylindrical pores of 3.2A in radius and 11A long. The pore size, calculated following the procedures of pore flow models, is in good agreement with the physical size of the simulated pore. It is then concluded that the fundamental validity of the pore flow models in the case of tight membranes is yet unsettled, theoretically, but empirically its validity seems confirmed in some instances.