Roughness-gradient–induced spontaneous motion of droplets on hydrophobic surfaces: A lattice Boltzmann study

N. Moradi¹, F. Varnik^1,2 and I. Steinbach¹

¹  ICAMS, Ruhr-Universität Bochum - Stiepeler Strasse 129, 44801 Bochum, Germany, EU
²  Max-Planck Institut für Eisenforschung - Max-Planck Str. 1, 40237 Düsseldorf, Germany, EU

Corresponding author: nasrollah.moradi@rub.de

Received: 16 October 2009
Accepted: 11 January 2010

Abstract

The effect of a step-wise change in the pillar density on the dynamics of droplets is investigated via three-dimensional lattice Boltzmann simulations. For the same pillar density gradient but different pillar arrangements, both motion over the gradient zone as well as complete arrest are observed. In the moving case, the droplet velocity scales approximately linearly with the texture gradient. A simple model is provided reproducing the observed linear behavior. The model also predicts a linear dependence of droplet velocity on surface tension. This prediction is clearly confirmed via our computer simulations for a wide range of surface tensions.