Dynamics of a drop floating in vapor of the same fluid

Abstract

Evaporation of a liquid drop surrounded by either vapor of the same fluid, or vapor and air, is usually attributed to vapor diffusion -- which, however, does not apply to the former setting, as pure fluids do not diffuse. The present paper puts forward an additional mechanism, one that applies to both settings. It is shown that disparities between the drop and vapor in terms of their pressure and chemical potential give rise to a flow. Its direction depends on the vapor density and the drop's size. In undersaturated or saturated vapor, all drops evaporate -- but in oversaturated (yet thermodynamically stable) vapor, there exists a critical radius: smaller drops evaporate, larger drops act as centers of condensation and grow. The developed model is used to estimate the evaporation time of a drop floating in saturated vapor. It is shown that, if the vapor-to-liquid density ratio is small, so is the evaporative flux -- as a result, millimeter-sized water drops at temperatures lower than $70^{\circ}\mathrm{C}$ survive for days. If, however, the temperature is comparable (but not necessarily close) to its critical value, such drops evaporate within minutes. Micron-sized drops, in turn, evaporate within seconds for all temperatures between the triple and critical points.