Electrohydrodynamic instability of a charged membrane

The stability of shape fluctuations of a flat charged membrane immersed in a fluid is analyzed using a linear stability analysis. A displacement of the membrane surface causes a fluctuation in the conterion density at the surface. This in turn causes an additional contribution to the force density in the momentum equation for the fluid, which results in a normal stress at the surface which is opposite in direction to the stress caused by surface tension. This electrohydrodynamic effect destabilizes fluctuations when the surface potential exceeds a critical value.