 Solution

In electrophoresis, an applied electric field drives a charged particle and its associated diffuse ionic atmosphere relative to the liquid. Electric forcing is balanced by viscous stresses, giving a steady velocity $\mathbf{v}={\mu }_e\mathbf{E}$ in the linear regime. The relevant electrokinetic potential is the zeta potential at the slipping plane, rather than necessarily the solid surface potential.

For a thin electric double layer, the surrounding layer develops an electro-osmotic flow and the Smoluchowski electrophoretic mobility is ${\mu }_e=ϵ\zeta /\eta$. The sign of $\zeta$ fixes the direction. This transport is different from dielectrophoresis, which can move a neutral polarizable particle in a nonuniform field.