Electrohydrodynamic stability of a liquid column under cross fields: Application to continuous flow electrophoresis

An infinite, conductive cylindrical column of electrolyte lying inside another electrolyte flattens when it is submitted to a transverse continuous electric field. This "ribbon" effect can be canceled by a second oscillatory field whose direction is perpendicular to both the column axis and to the first electric field. The linear stability of the equilibrium with respect to elliptic perturbations of the cross section is studied, and it is shown that the stability of the circular shape depends on the sign of a discriminating function of the conductivity and permittivity ratios. Possible applications of the results to continuous flow electrophoresis are discussed: Even for unstable situations the growth rate of disturbances is reduced by the application of a second field so that we expect the efficiency of the separation to be improved.