An Analytical Model on the Instability of Thin Film Flow Dynamics in a Micro-gap Channel

Abstract

In this paper, a mathematical model is developed to investigate the liquid film dynamics in micro-gap channels, in which a liquid film flows along the wall surfaces and gas flows in the channel core. It is assumed that the Reynolds numbers for both gas and liquid flow are very low and there is no mass transfer at the interface. The instability behavior of the interface of two-phase flow is analysed by employing Stoke's equations, which are solved by non-linear boundary conditions. The solution shows that if the perturbations at the interface are small, they do not grow, however, kinematic waves still exist. All perturbations on the film surface are convoyed by gas flow without growing or decreasing. From the analytical results it is also found that in a micro-gap-channel in the case of constant pressure gradient, the perturbations on both sides of the gap interface are strictly interconnected, and their relationship has been obtained.