= 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 $\mu_e=\epsilon\zeta/\eta$. The sign of $\zeta$ fixes the direction. This transport is different from <dielectrophoresis>, which can move a neutral polarizable particle in a nonuniform field.
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