Electrostatic Interactions and Electro-osmotic Properties of Semipermeable Surfaces

TL;DR

This paper investigates the electrostatic and electro-osmotic behaviors of charged semipermeable membranes, revealing how effective surface charge influences potential distribution, pressure, and flow in electrolyte systems.

Contribution

It introduces an effective surface charge concept for semipermeable membranes, simplifying analysis and capturing charge effects that differ from the actual membrane charge.

Findings

Effective surface charge can differ from the real charge and even have opposite sign.

Explicit formulas for disjoining pressure and electro-osmotic velocity are derived.

Potential and ion distributions are obtained from exact and asymptotic solutions.

Abstract

We consider two charged semipermeable membranes, which bound bulk electrolyte solutions and are separated by a thin film of salt-free liquid. Small counter-ions permeate into the gap, which leads to a steric charge separation in the system. To quantify the problem, we define an effective surface charge density of imaginary impermeable surface, which mimics an actual semipermeable membrane and greatly simplify analysis. The effective charge depends on separation, generally differ from the real one, and could even be of the opposite sign. From the exact and asymptotic solutions of the nonlinear Poisson-Boltzmann equation, we obtain the distribution of the potential and of counter-ions in the system. We then derive explicit formulae for the disjoining pressure in the gap and electro-osmotic velocity, and show that both are controlled by the effective surface charge.