The Onset of Marangoni Convection for Evaporating Liquids

The stability of evaporating liquids is examined. The geometries investigated are semi-infinite liquid sheets, bounded liquid sheets, sessile droplets, and funnels. Stability parameters are generated to characterize the stability of evaporating semi-infinite liquid sheets, and bounded liquid sheets. The derivation is made possible by introducing evaporation as the specific heat transfer mechanism at the interface, and using the statistical rate theory expression for evaporation flux so there are no fitting parameters. It is demonstrated that a single parameter can be used to predict the onset criterion instead of two parameters. A linear stability analysis is performed for spherical sessile droplets evaporating on substrates constructed of either insulating or conducting materials. A stability parameter is generated to characterize the stability of sessile droplets evaporating on insulating substrates and conducting substrates. The results indicate that spherical sessile droplets evaporating on insulating substrates are predicted to transition to Marangoni convection. Since there are currently no experimental results to compare the theory with, another analysis is performed for liquids evaporating from funnels, which can be compared with existing experimental observations. A linear stability analysis predicts stable evaporation for funnels constructed of insulating materials, in contrast to the sessile droplet case, and generates a new stability parameter for funnels constructed of conducting materials. The stability parameter is free of fitting variables since the statistical rate theory expression for the evaporation flux is used. The theoretical predictions are found to be consistent with experimental observations for water evaporating from a funnel constructed of poly(methyl methacrylate) (PMMA) and for water and heavy water evaporating from a funnel constructed of stainless steel. A parametric analysis is performed on the new stability parameter for liquids evaporating from funnels constructed of conducting materials, indicating that smaller interfacial temperature discontinuities, higher evaporation rates, and smaller radii correspond to less stable systems. It is also illustrated that calculations using statistical rate theory predict an instability, which is consistent with experimental observations, whereas using the Hertz-Knudsen theory does not predict any instability.Ph