Electrophoresis of a small sphere in a cylinder of finite length.

The pressure due to electrophoretic motion of a charged colloidal sphere in a fluid-filled circular cylinder is determined in the limit in which the sphere radius is small compared with that of the cylinder. If the ends of the cylinder are open, pressure-driven Poiseuille flow occurs, but the magnitude of this flow is shown to be small when the cylinder is long compared to its radius. It is concluded that the flow has little effect upon electrophoretic velocities, unlike when the diameter of the sphere is comparable to that of the cylinder in which case the Poiseuille flow increases electrophoretic velocities and creates long-range interactions between spheres.