Numerical Analysis of Electrokinetic Flow through a Cylindrical Channel with a Charge Regulation Boundary Condition

Abstract

Electrokinetic flow, i.e. the combined pressure driven and electroosmotic flow, in charged micrometer sized channels is an important aspect of microfluidics. Numerical models describing this flow often employ a constant surface charge or constant electric potential boundary condition at the channel wall. This work proposes a model that uses an alternative boundary condition, based on a single chemical reaction, to describe the channel surface charge. The resulting streaming potential, axial velocity profiles and axial ion concentration profiles of this model are then compared to a constant surface charge model. We conclude that the model with the altered boundary condition produces similar values for the streaming potential and similar electrokinetic flow profiles when the applied electric field is weak. Also, the timescales needed for the electric potential and ion concentration profiles to reach equilibrium are consistent with the constant charge model. When the applied electric field is strong, and dominates the electrokinetic flow, a reduced axial velocity profile is found.