https://doi.org/10.1140/epjst/e2016-60202-6
Regular Article
Dancing drops over vibrating substrates
1 Lehrstuhl Statistische Physik/ Nichtlineare Dynamik, Brandenburgische Technische Universität, Erich–Weinert–Strasse 1, 03046 Cottbus, Germany
2 Lehrstuhl Aerodynamik und Strömungslehre, Brandenburgische Technische Universität, Siemens–Halske–Ring 14, 03046 Cottbus, Germany
a e-mail: borciar@b-tu.de
Received: 30 June 2016
Revised: 5 August 2016
Published online: 2 May 2017
We study the motion of a liquid drop on a solid plate simultaneously submitted to horizontal and vertical harmonic vibrations. The investigation is done via a phase field model earlier developed for describing static and dynamic contact angles. The density field is nearly constant in every bulk region (ρ = 1 in the liquid phase, ρ ≈ 0 in the vapor phase) and varies continuously from one phase to the other with a rapid but smooth variation across the interfaces. Complicated explicit boundary conditions along the interface are avoided and captured implicitly by gradient terms of ρ in the hydrodynamic basic equations. The contact angle θ is controlled through the density at the solid substrate ρS, a free parameter varying between 0 and 1 [R. Borcia, I.D. Borcia, M. Bestehorn, Phys. Rev. E 78, 066307 (2008)]. We emphasize the swaying and the spreading modes, earlier theoretically identified by Benilov and Billingham via a shallow-water model for drops climbing uphill along an inclined plane oscillating vertically [E.S. Benilov, J. Billingham, J. Fluid Mech. 674, 93 (2011)]. The numerical phase field simulations will be completed by experiments. Some ways to prevent the release of the dancing drops along a hydrophobic surface into the gas atmosphere are also discussed in this paper.
© EDP Sciences, Springer-Verlag, 2017
