A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects

摘要

In this paper, we develop a phase-field model for binary incompressible(quasi-incompressible) fluid with thermocapillary effects, which allows for thedifferent properties (densities, viscosities and heat conductivities) of eachcomponent while maintaining thermodynamic consistency. The governing equationsof the model including the Navier-Stokes equations with additional stress term,Cahn-Hilliard equations and energy balance equation are derived within athermodynamic framework based on entropy generation, which guaranteesthermodynamic consistency. A sharp-interface limit analysis is carried out toshow that the interfacial conditions of the classical sharp-interface modelscan be recovered from our phase-field model. Moreover, some numerical examplesincluding thermocapillary convections in a two-layer fluid system andthermocapillary migration of a drop are computed using a continuous finiteelement method. The results are compared to the corresponding analyticalsolutions and the existing numerical results as validations for our model.