Effect of thermal convection on thermocapillary migration of a surfactant-laden droplet in a microchannel

Abstract

Despite its significance in droplet-based microfluidic technologies with the use of thermal stimuli and surfactants, coupling effects of thermal- and surfactant-induced Marangoni stresses on the transport of droplets in microchannels are not fully uncovered yet. To facilitate studies in this area, we present a three-dimensional numerical study on the thermocapillary migration of an insoluble-surfactant-laden droplet under Poiseuille flow in a microchannel. This work is realized via our own front-tracking finite-difference method with further integration of the energy conservation equation and the surface surfactant transport equation. Our numerical results agree well with the previously reported analytical results for ambient conditions with negligible thermal convection. In this study, we mainly focus on the effects of the thermal convection at high thermal Peclet numbers and find that it induces a significant change in the thermal Marangoni stress. As a consequence, the migration of surfactant-laden droplets in the microchannel is significantly retarded by the thermal convection, which is observed for two different ambient conditions, i.e., the imposed temperature increasing or decreasing along the main flow direction. To understand the mechanism underlying the effects of the thermal convection, we analyze the distributions of the temperature, surfactant concentration, and the thermal- and surfactant-induced surface tension variations over the droplet surface. Notably, the surfactant-induced Marangoni stress always opposes the thermal-induced Marangoni stress for the entire range of thermal Peclet numbers considered in this study, but the competition between them is significantly alternated by the thermal convection in a quantitative manner.