Evaporation and fluid flow near the boundary of a stationary dry patch

We consider an isolated circular dry patch formed in an evaporating liquid layer and investigate local viscous flows in both liquid and air near the contact line which is the boundary of the dry patch. Flow patterns in the liquid deviate significantly from the predictions of single-phase models even when the air-to-liquid dynamic viscosity ratio is small. In particular, the separatrices in the liquid flow patterns at large contact angles disappear completely for a range of realistic viscosity ratios when the shear stress on the air side of the interface is accounted for. Experimentally observed motion of microdroplets near the contact line under combined action of gravity and moist air flow is described using our local flow model. We demonstrate that analysis of droplet trajectories leads to unambiguous determination of the local evaporative flux profile. A numerical finite-element approach for the steady diffusion equation is then used to extract the same flux profile from the global solution for concentration field in the limiting case of very thin liquid layer and small contact angle. The local evaporation rate is underpredicted by the numerical method, most likely due to the neglect of convective mass transfer in the air.