SURFACTANT-INDUCED RETARDATION OF THE THERMOCAPILLARY MIGRATION OF A DROPLET

A neutrally buoyant droplet in a fluid possessing a temperature gradie nt migrates under the action of thermocapillarity. The drop pole in th e high-temperature region has a reduced surface tension. The surface p ulls away from this low-tension region, establishing a Marangoni stres s which propels the droplet into the warmer fluid. Thermocapillary mig ration is retarded by the adsorption of surfactant: surfactant is swep t to the trailing pole by surface convection, establishing a surfactan t-induced Marangoni stress resisting the flow (Barton & Subramanian 19 90). The impact of surfactant adsorption on drop thermocapillary motio n is studied for two nonlinear adsorption frameworks in the sorption-c ontrolled limit. The Langmuir adsorption framework accounts for the ma ximum surface concentration Gamma(infinity)', that can be attained for monolayer adsorption; the Frumkin adsorption framework accounts for G amma(infinity)' and for non-ideal surfactant interactions. The composi tional dependence of the surface tension alters both the thermocapilla ry stress which drives the flow and the surfactant-induced Marangoni s tress which retards it. The competition between these stresses determi nes the terminal velocity U', which is given by Young's velocity U-0' in the absence of surfactant adsorption. In the regime where: adsorpti on-desorption and surface convection are of the same order, U' initial ly decreases with surfactant concentration for the Langmuir model. A m inimum is then attained, and U' subsequently increases slightly with b ulk concentration, but remains significantly less than U-0'. For cohes ive interactions in the Frumkin model, U' decreases monotonically with surfactant concentration, asymptoting to a value less than the Langmu ir velocity. For repulsive interactions, U' is non-monotonic, initiall y decreasing with concentration, subsequently increasing for elevated concentrations. The implications of these results for using surfactant s to control surface mobilities in thermocapillary migration are discu ssed.