Electrophoretic mobility of charged porous shells or microcapsules and electric conductivity of their dilute suspensions

[Display omitted] •The electrophoretic mobility of a charged porous shell is analytically obtained.•The electric conductivity of a suspension of charged porous shells is analytically obtained.•The mobility of the shell and conductivity of the suspension increase with the shell thickness.•The effect of shell thickness on the mobility of a shell with low permeability is significant.•The effect of shell thickness on the mobility of a shell with thick double layer is significant. An analysis is presented for the electrophoresis and electric conduction in a dilute suspension of charged spherical porous shells or permeable microcapsules with electric double layers of arbitrary thickness in an electrolyte solution. With the assumption that the system is slightly perturbed from equilibrium, the linearized electrokinetic equations governing the ionic electrochemical potential energy and fluid velocity distributions are solved as series expansions in the small fixed charge density of the porous shells. Explicit formulas for the electrophoretic mobility of the porous shells and effective electric conductivity of the suspension are derived. Both the electrophoretic mobility and the effective conductivity decrease monotonically with a decrease in the relative thickness of the porous shells, but these decreases are not conspicuous until the porous shells are quite thin. When the fluid permeability of the porous shells is smaller or the electric double layers are thicker, the effect of this relative thickness on the electrophoretic mobility and effective conductivity becomes more significant. In the limiting case of zero inner radius of the porous shells, our formulas reduce to the corresponding results obtained for the electrophoresis and electric conduction in a suspension of charged porous spheres.