Startup of electrophoresis in a suspension of colloidal spheres.

The transient electrophoretic response of a homogeneous suspension of spherical particles to the step application of an electric field is analyzed. The electric double layer encompassing each particle is assumed to be thin but finite, and the effect of dynamic electroosmosis within it is incorporated. The momentum equation for the fluid outside the double layers is solved through the use of a unit cell model. Closed-form formulas for the time-evolving electrophoretic and settling velocities of the particles in the Laplace transform are obtained in terms of the electrokinetic radius, relative mass density, and volume fraction of the particles. The time scale for the development of electrophoresis and sedimentation is significantly smaller for a suspension with a higher particle volume fraction or a smaller particle-to-fluid density ratio, and the electrophoretic mobility at any instant increases with an increase in the electrokinetic particle radius. The transient electrophoretic mobility is a decreasing function of the particle volume fraction if the particle-to-fluid density ratio is relatively small, but it may increase with an increase in the particle volume fraction if this density ratio is relatively large. The particle interaction effect in a suspension on the transient electrophoresis is much weaker than that on the transient sedimentation of the particles.