Mathematical Modeling of the Dependence of the Vapor Permeability Coefficient of a Membrane on Its Pore Structure

Abstract

The dependence of the vapor permeability coefficient of a distillation membrane on its pore structure is analyzed. The pore structure of the membrane is represented as a two- or three-dimensional network of capillaries that have a fixed length and originate at nodes with a constant coordination number. Three pore-size distribution functions are considered, namely, a uniform, a bimodal, and a triangular function. An explicit expression for the vapor permeability coefficient of the membrane is derived using orientation averaging and the smooth-field approximation. The effect of some structural properties (pore-size distribution, porosity, coordination number of a node, etc.) of the porous membrane on the vapor permeability coefficient is studied numerically. Irrespective of the pore-size distribution function, the vapor permeability coefficient decreases with increasing pore radius and grows with increasing coordination number and Knudsen number.