Streaming potentials of nonuniformly charged surfaces

Abstract

The general equations for the streaming potential are solved numerically for a system in which the surfaces of a slit are nonuniformly charged. Specifically, patches of varying surface charge are periodic in the direction of the applied pressure drop. Introduction of the nonuniform charge produces distortions in the equilibrium electrostatic field. This distortion in the electrostatic potential can alter the value of the zeta potential from its expected value. In fact, under conditions of moderate surface charge and ionic strength, the value of the zeta potential is over 30% higher than expected. The characteristic symptom of field distortion is the generation of velocities normal to the charged surface. We describe the physics which gives rise to the normal velocities and identify the dimensionless properties of the streaming-potential system which influence the magnitude of these velocities and influence the value of the zeta potential. As the exact solution of the equations for this streaming-potential system is computationally intensive, a regular, first-order-perturbation solution is also developed. The perturbation solution tests the limits of the popular assumption that the total electric potential is simply the sum of the equilibrium potential and the applied potential.