A transport model of electrolyte convection through a charged membrane predicts generation of net charge at membrane/electrolyte interfaces

Recent measurements of electrical potentials on cartilage undergoing compression revealed the expected negative streaming potentials due to the presence of fixed negative charge in the cartilage matrix. However, these measurements also detected positive electric potentials extending into the external saline bath. We hypothesized that these positive potentials arise from convective displacement of mobile ions through an extended non-equilibrium double layer at the cartilage/bath interface. To examine this possibility, we developed a model of electrolyte transport across a charged membrane and examined the distribution of electric potential and mobile ion concentrations in response to forced convection. The extended Nernst-Planck and Poisson equations were solved numerically assuming the membrane to be infinitely permeable and infinitely stiff so that neither a streaming potential nor a deformation-induced diffusion potential could occur. First order solutions for forced convection of a mono-monovalent electrolyte through the membrane depicted an altered structure of the extended double layer and the creation of net interfacial electric charge densities with opposing polarity on opposite sides of the membrane. The model predicted an increase of the electric and concentration polarizations with increasing ratio of membrane fixed charge to bath ionic strength, but only up to a point of saturation. In this regime, the non-linear behavior of the equation system reveals modifications of the extended double layers inducing localized electric fields and ion concentration gradients in addition with those induced in the bulk of the membrane. This convection-induced interfacial polarization has not been previously studied in detail and could be an important controlling factor in several situations involving transport and electrokinetic phenomena through charged media.