Oscillations of oblate drop between heterogeneous plates under uniform electric field

The deformed oblate drop’s free translational oscillations

“…In the two above-mentioned limiting cases, there will be no energy dissipation, since the contact line is either stationary or does not interact with the substrate. This condition and its modifications were used in the study of surface waves [4,[15][16][17], oscillations of sessile [18][19][20][21][22] and cylindrical [23][24][25][26][27] drops and bubbles. Equilibrium right angle was considered in most of the above works.…”

Influence of substrate properties on a fluid drop’s free translational oscillations

“…If the oscillations phases of the contact angle and the contact line are different, then wetting constant takes a complex value [22]. The Hocking parameter was a spatial function and described the inhomogeneous surface of the substrate [16,23]. There are different mathematical models for realizations of these conditions of the substrate (see e.g.…”

“…Furthermore, we apply the modified condition (1) for the different Hocking parameters [18]. The free axisymmetrical oscillations of this drop are presented in [16,23] for similar physical system. The distance * h between two parallel solid plates is fixed.…”

“…At infinity the liquid moves together with the vessel as a rigid body. The similar geometry was used, for example, in [16,18,23]. * , where  is the boundary-layer thickness.…”