Flow and stability of a gravity-driven thin film over a locally heated porous wall

Abstract

Stability analysis is performed for a gravity-driven thin liquid film flowing down a locally heated porous substrate. Using the lubrication approximation, the governing equations are simplified to derive the evolution equation for the free surface of the liquid film. The Beaver-Joseph condition is employed at the interface of the porous layer and the liquid film. The base profiles are mainly influenced by parameters that appear due to non-uniform heating. Linear stability analysis is performed and reported that both thermocapillary and rivulet instabilities are enhanced with increasing values of the Marangoni number, Biot number, and Beavers–Joseph coefficient and decreasing values of the Darcy number. Dependence of critical Darcy number on the porous layer thickness and the Beavers–Joseph coefficient is presented. It is also shown that the full Darcy model can be replaced with an approximated slip model. The growth rate from nonlinear computations is consistent with the linear stability analysis.