The onset of Marangoni convection for evaporating liquids with spherical interfaces and finite boundaries

We examine the stability of evaporating liquids with spherical interfaces bounded at one value of the polar angle for all azimuthal angles. A linear stability analysis is performed and the results are used to explain why a system with water evaporating from a funnel constructed of PMMA undergoes stable quiescent evaporation but a system with a funnel constructed of stainless steel experiences a transition from a quiescent state to a state with Marangoni convection. We develop the expression for a new stability parameter that provides a quantitative prediction of the transition to Marangoni convection, and find the predictions to be consistent with experiments.