Calculation of ac electric field effects on the average height of a charged colloid: Effects of electrophoretic and Brownian motions

Numerical solutions are presented for the time-dependent probability density of a charged colloidal particle near a planar wall, subjected to an alternating electric field, Brownian motion, and DLVO forces. These are the first time-dependent probability distribution solutions for a driven particle in a mobility gradient. The effects of electrophoretic particle motion on the probability distribution for finding a single, 6 mum diameter, polystyrene particle at a given height above an indium-tin oxide surface were studied via numerical solution of the complete convective-diffusion equation, ignoring inertia, in one dimension. Application of an ac electric field monotonically increased the average particle height over a complete cycle of the electric field; the strongest increase was at low frequency and large electric field strengths. These results agreed with observed behavior in potassium hydroxide solutions at high voltages but did not capture the depression of the average height at low voltages. The calculations agreed with the monotonic increase of average height observed in sodium bicarbonate solutions, but the slope of the increase was far less than experimentally observed. The calculated effects are present in the experimental results but do not encompass all the observations.