  This paper investigates the problem of electrophoretic motion of a
polyelectrolyte capsule with a porous arbitrary charged conducting shell in an
electrolyte under the action of an external electric field. The corresponding
boundary value problem for the velocity components and pressure in the case of
small electrical potentials is analytically solved in quadratures. The solution
is analyzed numerically for different values of the specific permeability of
the capsule, and the thickness of the porous and the electric double layers.
The minimum of electrophoretic velocity dependence on the inverse permeability
of the porous layer has been found. This means that the capsule can move with
the same velocity at different permeabilities of the porous shell, other
conditions being equal, which is relevant for the practical use of the
discovered effect. It is shown that the electrophoretic mobility decreases upon
decrease in the conductivity of the material of constituting the porous layer.
This means that a dielectric capsule can be used for electrophoresis as well.
Moreover, its velocity will be even greater than that of a conducting capsule,
all other conditions being equal.
