Calculation of Electrohydrodynamic Flow around a Single Particle on an Electrode

A numerical solution of the equations describing electrohydrodynamic flow around a single particle next to an electrode during passage of alternating current is presented. The Stokes equations, the diffusion equation, and Laplace's equation are solved simultaneously. The results confirm earlier approximate calculations showing that electrohydrodynamic flow is a significant factor in aggregative and deaggregative behavior of colloidal particles near electrodes. Both electrode kinetics and the ratio of particle size to diffusion layer thickness affect not only the strength of the flow around the particle but also its direction. Sluggish electrode kinetics causes the lateral flow around a particle in KOH solution to move away from it at 100 Hz, but fast electrode kinetics causes the flow to reverse at the same frequency. Increasing the frequency can cause flow reversal, which might explain experimental observations of the existence of a critical frequency above which particles separate and below which they aggregate in alkaline solution. The critical frequency is inversely proportional to the square of the particle radius.