Influence of surface properties on the dynamics of a clamped drop in an inhomogeneous electric field

Abstract

This article investigates the forced oscillations of an incompressible liquid drop under the action of an inhomogeneous alternating electric field. The drop is surrounded by an incompressible fluid of a different density and is clamped between two inhomogeneous parallel plates. In equilibrium, the drop has the shape of a round cylinder bounded in the axial direction by these plates. The external electric field acts as an external force causing the contact line to move. To describe the motion of the contact line, a modified Hocking boundary condition is used: the velocity of the contact line is proportional to the deviation of the contact angle from its equilibrium value and the rate of fast relaxation processes, the frequency of which is proportional to the doubled frequency of the electric field. The use of this equation makes it possible to qualitatively describe the experimental dependence of the contact angle as a function of stress, in contrast to the Young-Lippmann equation. The solution of the problem is represented as a Fourier series in terms of eigenfunctions of the Laplace operator. The resulting system of inhomogeneous equations for unknown amplitudes is solved numerically. Graphs of the amplitude-frequency characteristics and the dynamic shape of the drop are plotted for various values of the problem parameters. The wetting parameter depends on the polar angle , i.e. the coefficient of interaction between the plate and the fluid (contact line) is a function of the coordinates.