A Volume-of-Fluid discretization method for surface tension driven flows

Abstract: When deriving boundary conditions appropriate for a fluid-fluid interface, surface  tension gives rise to a normal stress across the interface linearly proportional to the local curvature and a tangential stress associated with gradients in the surface tension.  Here I describe a framework for direct numerical simulation of surface tension driven  flows. I will present a numerical scheme we devised to include surface gradients into our  Volume-of-Fluid interface description, to discretize the tangential (Marangoni) stresses.  Numerical validations and convergence of the method are discussed. We also show  numerical examples, motivated by experimental observations, of the effect of the  concentration-dependent surface tension on the flow field and the interface evolution.  Time permitting, I will also discuss a semi-implicit discretization of the surface tension which involves discretizing the Laplace-Beltrami operator, to include surface diffusion,  for improving the numerical stability.   Bio: Ph.D, University of Toronto, 2007. Postdoc and visiting assistant professor, Virginia Tech, 2007-2009 Professor (since 2020) and Associate Chair for Graduate Studies (2020-2022), NJIT. Visiting Scholar, Brown (2022), Princeton (2015), Sorbonne (2017), University of Lausanne (2011). Editorial, Journal of Engineering Mathematics (2016-2021), European Physical Journal ST (since 2021). Affiliated Faculty, Institute for Data Science and Center for AI Research, NJIT. Joint Appointment, Dept. of Data Science (since 2022), NJIT