We developed a phase field model for Marangoni convection in compressible fluids of van der Waals type far from criticality. The theoretical description is based on the Navier-Stokes equation with extra terms responsible for describing the Marangoni effect, the classical heat equation, and the continuity equation. The model previously developed for a two-layer geometry is now extended to drops and bubbles. Finally, we report on 2D numerical simulations for drop Marangoni migration in a vertical temperature gradient.
Borcia, R., Bestehorn, M. (2007). Phase field models and Marangoni flows. FDMP-Fluid Dynamics & Materials Processing, 3(4), 287–294. https://doi.org/10.3970/fdmp.2007.003.287
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