Fathollah Varnik, Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany
The lattice Boltzmann (LB) method has received growing interest both in the scientific and in the engineering community. Significant extensions and ramifications of the LB method have been proposed allowing the study of a rich variety of fluid dynamical problems such as the flow through porous media, two phase flows as well as transitional flows and turbulence, to name just a few. Due to the lack of an underlying free energy functional, however, most of the lattice Boltzmann approaches for multiphase systems presented so far either lead to thermodynamic inconsistencies or do not allow a proper thermodynamic analysis at all. In this talk, we present a free-energy based two-phase LB approach allowing the study of liquid-vapor systems and their dynamic behavior. Using this approach we investigate finite size driven droplet instability (evaporation) and kinetic of droplet coalescence. Simulation results on droplet instability are then compared to analytic solution obtained via an analysis of the underlying free energy functional thus demonstrating the maturity of the LB method in dealing with non-trivial thermodynamic behavior. As to the dynamics of droplet coalescence, scaling arguments are used in order to obtain basic features of the phenomenon. Also in this case, LB results show good agreement with theoretical expectations.