Single recalcitrant bubble simulation using a hybrid lattice boltzmann finite difference model

Abstract

In this paper, 2D simulations of a single recalcitrant bubble using a hybrid finite difference lattice Boltzmann method are presented. To solve the flow field, the conservative phase field lattice Boltzmann model of Geier et al. (2015) is employed with a multi-relaxation-time (MRT) scheme which makes it capable of handling multiphase flows with high density and viscosity contrasts. A finite difference approach is applied to obtain the temperature field with a second-order spatial discretization (central) which marches in time with the 2nd order Runge-Kutta marching technique. The well-known continuum surface tension force (CSF) is implemented to define the thermocapillary force which depends on the temperature field. Before delving into the main aim of this work, we first assess the accuracy of the present model by verifying the Laplace law for a static bubble with four different values of surface tension. To further validate the model, thermocapillary migration of a deformable drop, and thermocapillary flow with two superimposed planar fluids are studied as our second and third benchmarks. Comparing the analytical solutions for both velocity and temperature fields with the simulation ones, good agreements are found. We then propose a simple theory with some simplification for the study of the migration of a single recalcitrant bubble, and after that weperform a series of 2D simulations to analyze the effects of density ratios, viscosity ratios, entrance average velocities of the flow, and the values of second derivative of surface tension with respect to the temperature.