Aggregation dynamics for two particles during electrophoretic deposition under steady fields

The motion of particles deposited on an electrode by electrophoresis is governed by electrokinetics, electrohydrodynamics, and Brownian diffusion. Under a de electric field, the particles attract each other through their electroosmotic flows, but Brownian diffusion tends to randomize the distribution. Here, we develop a mathematical model for the time evolution of the probability of separation between two deposited particles. Predictions from the model for the mean separation versus time and the standard deviation about the mean separation are compared with experimental data for pairs of polystyrene latex particles deposited on thin-film metallic electrodes. The good agreement in the absence of adjustable parameters indicates that the convective - diffusion analysis based on electrokinetics is the mechanism behind particle aggregation during electrophoretic deposition under de field conditions, that is electroosmotic convection drives the particles together and the Brownian motion of the particles tends to separate them.