Evaporation and the coffee-ring effect for non-circular droplets

Diffusion-limited evaporation of liquid droplets has received significant research interest due to its fundamental significance in a variety of industrial and engineering applications such as inkjet printing, microscale and colloidal patterning, DNA microarray technologies and the manufacture of Q/OLEDs. However, beyond circular and elliptical droplets, there are very few existing analytical solutions, despite a number of these applications exhibiting droplets of a more complex geometry. Here, we address this deficiency by deriving asymptotic results for the evaporative flux of a weakly non-circular droplet. We show how these results may be used to find the ‘coffee ring’ profiles for large droplets, with excellent agreement to numerical simulations. We then demonstrate how the mathematical framework may be extended to consider polygonal drops and arrays of droplets, with an eye to industrial applications.