Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and Its Numerical Simulations with Mixed Finite Element Method (Communications in Computational Physics, 2020)
In this paper, we study the Marangoni effects in the mixture of two Newtonianfluids due to the thermo-induced surface tension heterogeneity on the interface.We employ an energetic variational phase field model to describe its physicalphenomena, and obtain the corresponding governing equations defined by a modified Navier-Stokes equations coupled with phase field and energy transport. A mixedTaylor-Hood finite element discretization together with full Newton's method are appliedto this strongly nonlinear phase field model on a specific domain. Under differentboundary conditions of temperature, the resulting numerical solutions illustrate thatthe thermal energy plays a fundamental role in the interfacial dynamics of two-phaseflows. In particular, it gives rise to a dynamic interfacial tension that depends on thedirection of temperature gradient, determining the movement of the interface along asine/cosine-like curve.