Does Maxwell's hypothesis of air saturation near the surface of evaporating liquid hold at all spatial scales?

Abstract

The classical model of evaporation of liquids hinges on Maxwell's assumption that the air near the liquid's surface is saturated. It allows one to find the evaporative flux without considering the interface separating liquid and air. Maxwell's hypothesis is based on an implicit assumption that the vapour-emission capacity of the interface exceeds the throughput of air (i.e. its ability to pass the vapour on to infinity). If this is indeed so, then the air adjacent to the liquid would get quickly saturated, justifying Maxwell's hypothesis. In the present paper, the so-called diffuse-interface model is used to account for the interfacial physics and thus derive a generalised version of Maxwell's boundary condition for the near-interface vapour density. It is then applied to a spherical drop floating in air. It turns out that the vapour-emission capacity of the interface exceeds the throughput of air only if the drop's radius is $r_{d}\gtrsim 10\ \mathrm {\mu } \mathrm {m}$ , but for $r_{d}\approx 2\ \mathrm {\mu } {\rm m}$ , the two are comparable. For $r_{d} \lesssim 1\ \mathrm {\mu } {\rm m}$ , evaporation is interface-driven, and the resulting evaporation rate is noticeably smaller than that predicted by the classical model.