Central Moment Lattice Boltzmann Schemes with Fokker-Planck Guided Collision for Simulation of Multiphase Flows with Surfactant Effects and Turbulence*

We present central moment lattice Boltzmann (LB) schemes, whose collision steps are represented by a novel Fokker-Planck (FP) kinetic model, for computations of multiphase hydrodynamics, interface tracking and surfactant evolution. Our approach involves matching the changes in different discrete central moments under collision to those of the continuous central moments as given by the drift-diffusion based FP model of the Boltzmann equation. This effectively results in relaxations to “equilibria”, the Markovian central moment attractors, which depend on the lower order moments. Based on this, a LB scheme for the pressure and velocity fields in multiphase flows at high density ratios is constructed. The interface motions are captured using the Allen-Cahn equation computed by another FP-guided LB scheme. The surfactant concentration is evolved by a model that accounts its preferential adsorption on interfaces, which is solved by a third LB scheme using FP collision. The Langmuir isotherm then parameterizes the effect of surfactant concentration on surface tension and its tangential gradients. Various simulations involving the effect of surfactant concentrations and turbulence on multiphase systems are presented and the advantages of using the FP model are shown.