Eur. Phys. J. E (2006) 21: 231-242
https://doi.org/10.1140/epje/i2006-10063-7

Regular Article

Lateral vibration of a water drop and its motion on a vibrating surface

¹ Department of Chemical Engineering, Lehigh University, 18015, Bethlehem, PA, USA
² Cornell University, Ithaca, NY, USA

^* e-mail: mkc4@lehigh.edu

Received: 5 September 2006
Accepted: 4 December 2006
Published online: 5 January 2007

Abstract

The resonant modes of sessile water drops on a hydrophobic substrate subjected to a small-amplitude lateral vibration are investigated using computational fluid dynamic (CFD) modeling. As the substrate is vibrated laterally, its momentum diffuses within the Stokes layer of the drop. Above the Stokes layer, the competition between the inertial and Laplace forces causes the formation of capillary waves on the surface of the drop. In the first part of this paper, the resonant states of water drops are illustrated by investigating the velocity profile and the hydrostatic force using a 3d simulation of the Navier-Stokes equation. The simulation also allows an estimation of the contact angle variation on both sides of the drop. In the second part of the paper, we investigate the effect of vibration on a water drop in contact with a vertical plate. Here, as the plate vibrates parallel to gravity, the contact line oscillates. Each oscillation is, however, rectified by hysteresis, thus inducing a ratcheting motion to the water droplet vertically downward. Maximum rectification occurs at the resonant states of the drop. A comparison between the frequency-dependent motion of these drops and the variation of contact angles on their both sides is made. The paper ends with a discussion on the movements of the drops on a horizontal hydrophobic surface subjected to an asymmetric vibration.