Influence of Surface Properties on Axisymmetric Oscillations of an Oblate Drop in an Alternating Electric Field

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

“…Similarly, the roots of the second equation are Eigenfrequencies of odd harmonics. These equations are analogous to the equations for the problem of the hemispherical bubble on a substrate [14] and coincide with similar equations from [16].…”

“…0 0  = * ) and its modifications have been used in a large number of articles. In particular, standing waves on the interface [12,13], a hemispherical drop (bubble) [14,15], a electrowetting-on-dielectric (EWOD) [16], a cylindrical drop (bubble) [17], different plate surfaces for sample of cylindrical symmetry [18], a contact angle's hysteresis [19][20][21]. If the oscillations phases of the contact angle and the contact line are different, then wetting constant takes a complex value [22].…”

“…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.…”