A new method for modeling variable surface tension flows using Volume-of-Fluid

The flow induced by variable surface tension is encountered in numerous fluid mechanics problems such as Bénard-Marangoni convection, migration of drops/bubbles due to temperature gradients or concentration gradients of surfactants and many more. An accurate numerical modeling of these variable surface tension flows has been a challenging aspect in multiphase flow simulations. A main source of inaccuracies is the arbitrary thickness of the interface imposed by the grid size. Al-Saud and coworkers [1] proposed a sharp interface method based on the continuum surface stress (CSS) model for the level-set method. In this work, we have extended this sharp interface CSS model to a Volume-of-Fluid (VoF) formulation using height functions. Our method is validated with the analytical and numerical solutions of several problems like the motion of bubbles due to varying surface tension, and the two-dimensional thermo-capillary flow between two parallel plates at different temperatures.