Nonequilibrium surface tension

A weakly nonlocal phase-field model is used to define surface tension in liquid binary mixtures in terms of the composition gradient in the interfacial region so that, at equilibrium, it depends linearly on the characteristic length that defines the interfacial width. In nonequilibrium conditions, surface tension changes with time: during mixing, it decreases as the inverse square root of time, while during phase separation, when nuclei coagulate, it increases exponentially to its equilibrium value. In addition, since temperature gradients modify the steepness of the concentration profile in the interfacial region, they induce gradients in the nonequilibrium surface tension, leading to the Marangoni thermocapillary migration of an isolated drop. Similarly, Marangoni stresses are induced in a composition gradient, leading to diffusiophoresis.