Marangoni Convection With a Curved and Deforming Free Surface in a Cavity

A finite-volume based computational model is developed to predict Marangoni convection in a cavity with a curved and deforming free surface. The two-dimensional incompressible continuity, momentum, and energy equations are solved on a staggered Cartesian grid. The free surface location is computed using the volume-of-fluid transport equation. Normal and tangential boundary conditions at the free surface are modeled using respectively a surface pressure and a continuum surface force technique. Computational predictions of thermocapillary flow in a shallow cavity are shown to be in good agreement with previously published asymptotic results. The new transient model is then used to study the influence of Marangoni number and Capillary number on thermocapillary flows in a cavity for different static contact angles. The flows are characterized by streamline and isotherm patterns. The influence of the dimensionless parameters on heat transfer rate at the cavity walls is exposed by examination of local Nusselt number profiles.