Oscillations of oblate drop between heterogeneous plates under uniform electric field

The forced oscillations of the incompressible fluid drop under the action of the uniform electric field are considered. In equilibrium, the drop has the form of a circular cylinder bounded axially by the parallel solid planes; the contact angle is right. An incompressible fluid of different density surrounds the drop. The external electric field acts as an external force that causes motion of the contact line. In order to describe this contact line motion, the modified Hocking boundary condition is applied: the velocity of the contact line is proportional to the deviation of the contact angle and the speed of the fast relaxation processes, whose frequency is proportional to twice the frequency of the electric field. The case of heterogeneous plates is investigated. We assume that the Hocking parameter depends on the polar angle in this case. The function describing the change in the coefficient of the interaction between the plate and the fluid (the contact line) is expanded in a series of the Laplace operator eigenfunctions. (paper)