This thesis presents the research of my PhD, which is the study of two-phase flows by using the phase-field methods. The key point for this work is the thermodynamic con- sistency. We begin by introducing an extension of the Model H to study the two-phase flows with thermocapilliary effects, where we assume that the coefficient of the surface tension is temperature dependent, and the classical energy equation is coupled with the Model H. We then investigate numerically an established phase-field model (Quasi- incompressible NSCH model) for the two-phase flows with varible density. We design a numerical method where the energy law of the model is preserved at the discrete level. Fianlly we develop a new model to study the two-phase flows with thermocapil- liary effects where the model allows the two fluids to have different physical properties meanwhile maintaining the thermodynamic consistency. The pillbox argument is em- ployed to show that our model can reduce to the sharp-interface model where the jump conditions can be recovered.
|Date of Award||2014|
|Sponsors||China Scholarship Council|
|Supervisor||Ping Lin (Supervisor)|