Computational modeling of three-dimensional thermocapillary flow of recalcitrant bubbles using a coupled lattice Boltzmann-finite difference method

Abstract

This study analyzes the thermocapillary flow of recalcitrant bubbles within thin channels using a hybrid finite difference lattice Boltzmann method (LBM). It extends a recently developed phase-field LBM to account for temperature effects by coupling the scheme with a fourth-order Runge–Kutta algorithm to solve the governing energy equation. The LBM makes use of a weighted-multiple relaxation-time collision scheme, which has been previously shown to capture high density and viscosity contrasts. This paper makes contributions in two fundamental areas relating to thermocapillary flow. First, it presents and verifies a novel, three-dimensional model to resolve thermocapillary dynamics for practical applications. The verification was undertaken via comparison with analytical solutions for the flow of immiscible fluids in a heated microchannel and for the migration of a droplet in a temperature field. Second, it provides new insight into the inherently three-dimensional nature of recalcitrant bubbles. It was found that the competing inertial and thermal effects allow these bubbles to propagate against the bulk motion of the liquid toward regions of low surface tension.