Transient Thermo-Diffuso-Capillary Convection Around a Bubble in a Surfactant Solution: A Numerical Investigation Using the Volume-of-Fluid Technique

Marangoni Convection occurs when a surface tension gradient is established at a liquid-gas interface. The variation in surface tension could be driven by an interface temperature gradient, resulting in Thermocapillary Convection, or by an interface concentration gradient, giving rise to Diffuso-Capillary Convection, or a combination of both. Such flows are found to be of interest in microgravity (and otherwise), as they are known to significantly contribute to heat and mass transfer enhancement at the interface. This paper deals with the computational study of bubble induced thermo-diffuso capillary convection in the presence of surfactants and a stratified thermal field. Bubble induced thermo-capillary convection in a pure liquid has been substantially studied and the effects of various parameters like liquid properties, wettability, bubble size, channel depth, and temperature gradients on the strength of thermo-capillary currents and the associated heat transfer enhancement at the bubble interface are well established. In this study the physico-chemical properties of an aqueous solution of Sodium-Dodecyl-Sulphate (SDS), a surfactant, were used to introduce the effects of surfactant concentration-induced surface-tension gradients in addition to the temperature induced gradients. Unlike in purely thermo-capillary flows, where the interface sees a near-constant surface-tension gradient from base to apex, the presence of surfactant molecules at the interface results in gradients that vary significantly along the interface with maximum gradients at the bubble base and the apex, resulting in a pair opposing vortices anchored to the bubble interface. The presence of the opposing vortices, results in weaker capillary-flows at higher thermal Marangoni numbers. This is in contrast with purely thermal Marangoni convection, where a larger Marangoni number yields a stronger capillary flow. It was also observed that while the Marangoni number may provide an accurate estimation of heat-transfer enhancement under steady-state conditions, it may not be possible in the case of a transiently developing Marangoni-flow. The heat transfer enhancement is maximum near the time of bubble introduction and then diminishes to a lower, stable value. Also, the capillary flows and the associated heat transfer is found to significantly vary with the wetting behavior at the liquid-solid-vapor interface, even for the same set of Marangoni numbers.