Lattice Boltzmann simulations of forced wetting transitions of drops on superhydrophobic surfaces

The behavior of drops on superhydrophobic surfaces is of interest from an engineering point of view. As it can be difficult to probe some of the more subtle phenomena by experiment, numerical simulations can be illuminating. Many research efforts have utilized the lattice Boltzmann method to glean important conclusions about the nature of this subject, but only few have done so while eliminating the phenomenon of spurious currents and employing drop densities greater than approximately ten times that of the gas density. This paper presents a new implementation of boundary conditions for the complex geometry found in simulations of drops on superhydrophobic surfaces, which extends an existing model that has been shown to eliminate spurious currents. We validate our model by comparison with experiments, and demonstrate that spurious currents are eliminated for the density ratio encountered in a water/air system. We further discuss the issue of numerical resolution for a problem that possesses such a naturally large separation of scales, and we present a comparison between two- and three-dimensional simulations. We find that an adequate resolution, which may be difficult to achieve, must be given to capture the appropriate transition from the Cassie to the Wenzel state for the case of forced wetting under gravity. Furthermore, the form of our boundary condition may be extended to cover other types of complex geometry not included here.