Electrohydrodynamic Flow induced by the Onsager Effect

We analyze the electrohydrodynamic flow around a cylindrical/spherical particle in a leaky dielectric medium induced by the Onsager effect, which describes the electric-field-dependent ion dissociation rate of weak electrolytes. From the Onsager effect, the conductivity is shown to increase linearly with respect to the electric field strength and the Coulombic force by the Maxwell-Wagner polarization can be induced in non-uniform electric field. In this paper, the time-averaged Stokes flow around a cylindrical/spherical particle by the Onsager effect is solved analytically using the perturbation expansion to the 1^st order accuracy. The flow field solutions are expressed with a finite set of eigenfunctions in cylindrical and spherical coordinates. The flow velocity is proportional to the cubic of the electric field strength. It is also shown that the flow patterns can be classified by a simple straining, intermediate and eight-folded octagonal flow according to the Clausius-Mossoti factor, which is a function of complex conductivities of liquid and particle. The results are compared with full numerical simulations and experiments to discuss the detailed mechanism of flow structures.