Nonequilibrium interface equations: An application to thermocapillary motion in binary systems

Interface equations are derived for both binary diffusive and binary fluid systems subjected to nonequilibrium conditions, starting from coarse-grained (mesoscopic) models. The equations are used to describe thermocapillary motion of a droplet in both purely diffusive and fluid cases, and the results are compared with numerical simulations. A mesoscopic chemical potential shift owing to the temperature gradient, and associated mesoscopic corrections involved in droplet motion, are elucidated.