Thermocapillary effects in foams: Thermal diffusion through a bubble staircase and impact on shear modulus

A temperature gradient is applied to a single layer of bubbles in a regular two-dimensional foam (a ‘bubble staircase’), allowing a thermocapillary effect to occur and alter the structure and, thus, the shear modulus. In this model, local surface tension is a function of local surfactant concentration and local temperature. As thermal energy diffuses through the structure from an elevated (or lowered) temperature at a wall, the surface tension changes; in turn, surface tensions inequities result in a Marangoni flux of surfactant along the interface, re-adjusting surface tension inequities. An additional physicochemical equilibration of the film with a nearby bulk reservoir of surfactant (e.g., liquid-containing Plateau borders) allows for interaction of the films with their environment. As the temperature at the wall is increased, surface tension difference between the liquid on the hotter side and that on the cooler side also increases, causing migration of the vertices separating films towards the cooler side. This change in structure affects also the elastic modulus of the foam. In both simulation results and theoretical predictions, temperature variations on the order of tens of degrees are significant.