Evaporation Rates and Bénard-Marangoni Supercriticality Levels for Liquid Layers Under an Inert Gas Flow

In this work, we propose an approximate model of evaporation-induced Bénard-Marangoni instabilities in a volatile liquid layer with a free surface along which an inert gas flow is externally imposed. This setting corresponds to the configuration foreseen for the ESA—“EVAPORATION PATTERNS” space experiment, which involves HFE-7100 and nitrogen as working fluids. The approximate model consists in replacing the actual flowing gas layer by an “equivalent” gas at rest, with a thickness that is determined in order to yield comparable global evaporation rates. This allows studying the actual system in terms of an equivalent Pearson’s problem (with a suitably defined wavenumber-dependent Biot number at the free surface), allowing to estimate how far above critical the system is for given control parameters. Among these, a parametric analysis is carried out as a function of the liquid-layer thickness, the flow rate of the gas, its relative humidity at the inlet, and the ambient pressure and temperature.