The lateral electric force on an off-axis sphere in a circular cylinder.

The electrophoretic velocity of a sphere within a liquid-filled circular cylinder in a direction parallel to the cylinder axis has been studied by Yariv and Brenner (Phys. Fluids 2002, 14, 3354-3357; SIAM J. Appl. Math. 2003, 64, 423-441). We use their analyses of the electric field in order to determine the electrical force on the sphere along the cylinder radius (i.e., perpendicular to its axis) when either the radius of the sphere is small compared to that of the cylinder, or when the radius of the sphere is only slightly smaller than that of the cylinder. In both cases the force acts towards the centreline of the cylinder, and hence this force tends to stabilize electrophoresis of the sphere along the cylinder axis.