The evaporation of droplets has been a much-studied problem in recent years, finding applications everywhere from the spraying of pesticides on leaves to diagnostic applications of bloody drying. Unfortunately, many of the most critical industrial applications, such as the printing of OLED screens, involve arrays of droplets with polygonal footprints in close enough proximity to one another that the evaporative behaviours interfere with one another via the vapour phase. This is in stark contrast to the state of the theoretical literature in which we have only had techniques for dealing with droplets with circular or elliptic footprints, and even then, only for such droplets in isolation.

We discuss recent advancements in this area relaxing both of these constraints, demonstrating how arbitrary arrays of non-circular droplets may be analysed theoretically. We examine a variety of industrially relevant problems, including the evaporative behaviours of rectangular droplets (used for OLED screens), as well as a continuum formulation designed to cope with the extremely large arrays observed in 8K screens (O(10^8) droplets). We briefly discuss the uses of these solutions in other physical contexts.