Long-wave dynamics of an inextensible planar membrane in an electric field

In this paper the dynamics of an inextensible capacitive elastic membrane under an electric field is investigated in the long-wave (lubrication) leaky dielectric framework, where a sixth-order nonlinear differential equation with an integral constraint is derived. Steady equilibrium profiles for a non-conducting membrane in a direct current (DC) field are found to depend only on the membrane excess area and the volume under the membrane. Linear stability analysis on a tensionless flat membrane in a DC field gives the growth rate in terms of membrane conductance and electric properties in the bulk. Numerical simulations of a capacitive conducting membrane under an alternating current (AC) field elucidate how variation of the membrane tension correlates with the nonlinear membrane dynamics. Different membrane dynamics, such as undulation and flip-flop, are found at different electric field strength and membrane area. In particular a travelling wave on the membrane is found as a response to a periodic AC field in the perpendicular direction.