Experimental Verification of the Space‐Charge Model for Electrokinetics in Charged Microporous Membranes

Abstract

A space‐charge model for electrolyte transport in charged capillary pores was examined experimentally with aqueous solutions of alkali chlorides and in track‐etched mica membranes. The model combines the Gouy‐Chapman view of the double layer with the Nernst‐Planck and Navier‐Stokes transport equations. The pores of experimental membranes were uniform capillaries with a well‐characterized cross section. The pore sizes ranged from an order of magnitude smaller to an order of magnitude larger than the Debye screening lengths of solutions. Three independent quantities were measured: streaming potential, for which an applied pressure across the membrane is the driving force for transport; pore conductivity, for which an applied electrical potential is the driving force; and concentration potential, for which an electrolyte concentration difference is the driving force. Data follow the trends of model predictions but indicate that chloride ions affect the pore wall charge. For monovalent cations, the pore wall charge deduced from pore conductivity measurements yielded theoretical predictions for the streaming potential and for the concentration potential that agree quite well with the data. Such agreement was not obtained with Mg2+, probably because these divalent cations adsorbed onto the negative pore wall. We conclude that, in the absence of strong interaction between the charged pore wall and free ions in solution, the model is quantitatively accurate for pores larger than 30Å in radius and for aqueous electrolyte concentrations of 0.1M or lower.