A network microcapillary model for electrokinetic phenomena through microporous membranes

Abstract

The streaming potential and the electro-osmotic pressure are calculated through a simulation procedure, for a membrane consisting of a sample of equally charged pores, but are arranged differently to approach the real structure of actual membranes. It is presumed that a microporous membrane consists in an ensemble of cylindrical microcapillaries with the same pore charge density. The pores can have two sizes, which can be interconnected in three main ways: (1) parallel, (2) series, and (3) square network. On the other hand, it is assumed that these two pore sizes are, in fact, the central values of two Gaussian distributions, of equal relative standard deviations. In particular, here, mean diameters 0.2 or 0.1 and 0.02 or 0.01μm, with standard deviations of 0%, 15% and 25%, in parallel, series and network structures, are considered. This is carried out for several charge densities and concentrations of LiCl aqueous solutions. In these conditions, both the studied electro-kinetic parameters are determined by the widest pore in parallel, and its narrowest section. Interconnections of pores are seen to play a significant role, only when narrow and wide pores are almost equally present. Increasing standard deviations affect differently, but only slightly, the overall result for the electro-kinetic parameters, depending on the assumed structure. All these results indicate that high concentration results of streaming potential should be preferred, to obtain the membrane charge versus the concentration profiles.