Vapor Diffusion and Moist AIr Flow Near a Dry Patch in Evaporating Liquid Layer

We consider a circular dry patch formed in an evaporating liquid layer on a flat heated substrate. Moist air flow is induced by evaporation and thus depends on the distribution of vapor concentration. We solve a steady diffusion equation for vapor concentration above the dry patch formed in a liquid layer of infinite extent using integral transforms and validate our approach by comparing the analytical solution for vapor concentration profile along the patch surface with the previously reported numerical results. For the case when the extent of the liquid layer is finite, we develop a numerical solution using finite-element method with adaptive mesh and derive an approximate analytical solution which is shown to be in good agreement with the numerical results. Local evaporation-induced air flow structure is investigated using the approximate analytical solution for steady diffusion and then used to conduct parametric studies of trajectories of microdroplets flying towards the dry patch. Droplet dynamics is sensitive to changes in the layer-surface temperature and droplet size, but has only weak dependence on the air humidity.