Evaporation of multiple drops

In recent years there has been considerable interest in the diffusion-limited evaporation of sessile drops, mainly because of its importance in a variety of industrial processes such as printing, patterning, DNA-microarray production, and the manufacture of OLED devices. The available analytical solutions are for a solitary drop, whereas in industrial processes there are usually multiple drops in proximity to each other, and the evaporation of each of them would be highly sensitive to the presence of the others. Fabrikant [1] showed, in a different physical context, that the evaporative fluxes from multiple drops satisfy a system of Fredholm integral equations. We extend his methodology to derive explicit asymptotic expressions for the spatially varying fluxes of the drops. These are compared with direct numerical calculations and are found to be in good agreement. Also we give an indication of the effect that the reduced evaporation rates would have on coffee-stain formation.

[1] Fabrikant, V. I. "On the potential flow through membranes." Zeitschrift für angewandte Mathematik und Physik ZAMP 36.4 (1985): 616-623.