Three-dimensional simulation of instabilities and rivulet formation in heated falling films

A thin heated film draining on an inclined plate has been studied by integrating the three-dimensional conservation equations for mass, momentum, and energy in an arbitrary Lagrangian Eulerian frame of reference. The kinematic equation is solved to precisely update the interface location. The temporal discretization is done using a projection scheme and the spatial discretization is done using a finite element method. Detailed analysis of nonlinear dynamics associated with the rivulet formation is performed for layers subjected to both thermocapillary and surface-wave instabilities. Comparisons with long-wave theory are made to validate the numerical scheme. (C) 1997 Academic Press.