Journal of Membrane Science, Vol.163, No.2, 239-255, 1999
Streaming potential and surface charge density of microporous membranes with pore diameter in the range of thickness
A system formed by two phases bathing a microporous membrane is studied considering its behavior as a dynamic system. So, the natural frequencies for each used membrane is determined and then, applying a flow ramp with a rate sufficiently small, the streaming potential can be obtained from the slope of the pressure values versus electrical potential. The determination of the electric potential inside the pores, phi, requires to solve the Poisson-Boltzmann equation in the case of membranes with pore diameter in the range of thickness, for which the radial components of velocity of the fluid must be considered. Since there is no analytical solution, a numerical method was used to obtain phi. The electrical potential value at a distance equal to hydrodynamic radius from pore axis (zeta potential) is used to evaluate the streaming potential by the Helmholtz-Smoluchowsky relation. These values were compared with the experimental data accomplishing the suitable iterations over the surface charge density until coincidence. The values of the surface charge density for the studied membranes show a concentration dependence described by Langmuir's model for the greatest pore diameters and Freundlich's model for the smallest pore diameters.