The Dynamics of Oblate Drop Between Heterogeneous Plates Under Alternating Electric FieldNon-uniform Field

The dynamics of the incompressible fluid drop under the non-uniform electric field are considered. The drop is bounded axially by two parallel solid planes and the case of heterogeneous plates is investigated. The external electric field acts as an external force that causes motion of the contact line. We assume that the electric current is alternative current and the AC filed amplitude is a spatially non-uniform function. In equilibrium, the drop has the form of a circular cylinder. The equilibrium contact angle is 0.5π. 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, which frequency is proportional to twice the frequency of the electric field. The Hocking parameter depends on the polar angle, i.e. the coefficient of the interaction between the plate and the fluid (the contact line) is a function of the plane coordinates. This function is expanded in a series of the Laplace operator eigenfunctions.