(109d) Surfactant-Enhanced Thermocapillary Flows

Nguyen and Stebe [PRL, 2002] report Marangoni-Benard flow in a water drop covered with a surfactant monolayer in LE-LC coexistence, characterized by strong reduction in surface tension with temperature, and no dependence on composition for mean surface concentrations between the two binodals. In Marangoni-Benard flow, evaporative cooling establishes a vertical temperature gradient. Surface temperature perturbations create surface tension gradients (Marangoni stresses) that pull from warm toward cool regions. Outward flow from the warm regions draws warmer liquid up from below, reinforcing the temperature perturbation, and establishing the flow. Typically, this flow does not occur in water because of surfactant adsorption; surfactants swept toward the cool regions decrease the surface tension there, eliminating the driving force for the flow. In contrast, for monolayers in coexistence, surface tension is decoupled from surface concentration, and thus the surfactant-related surface tension gradients are absent.

However, open questions remain. Specifically, can a thermocapillary flow persist in an insoluble monolayer? Or, will surface convection cause surfactant to accumulate sufficiently at cool regions and deplete at warm regions to drive the interface out of coexistence and into single phase regions with strong surfactant-induced Marangoni stress that oppose the motion? We consider this question numerically in two model systems, (i) a liquid film in a 2-D cavity with an imposed horizontal temperature gradient, and (ii) a thin film with an imposed vertical temperature gradient subjected to a surface temperature perturbation. Dynamic and steady-state flow patterns are presented for both cases.