The Hydrodynamic Stability of Rapidly Evaporating Liquids With Time Dependent Base States

Abstract

The hydrodynamic stability of a rapidly evaporating liquid surface is examined. The problem is modeled to mimic the case of a superheated liquid in equilibrium with its vapor in which, the pressure above the liquid surface is dropped suddenly. Both the liquid and its vapor are assumed to be inviscid, incompressible and semi-infinite in extent. In addition, the temperature dependence of fluid properties is neglected. A linear stability analysis is applied to this model. This study differs from previous work in that time dependent base states are used. As a result, a system of linear homogeneous differential equations must be integrated in time. This system consists of a partial differential equation for the liquid temperature field and two other linked ordinary differential equations in time. Various types of thermal boundary conditions yielding different base state temperature profiles are considered. The results of this experimentation are contrasted. An attempt is made to compare results of the transient method to experimental data.