Modelling the Evaporation of a Binary Droplet in
a Well

Abstract

While the drying behaviour of sessile droplets has been extensively studied over
the last 25 years, the evaporation of droplets from wells (DiWs) has largely been
neglected, especially from a mathematical modelling standpoint. Understanding a
drying DiW is both important for industrial processes (such as inkjet printing and,
increasingly, the manufacture of organic displays) and an interesting problem in its
own right as a natural progression from sessile droplets, and we still do not have a
thorough theoretical description of their evaporation.
The main aim of this project was to build an understanding of pure and binary DiWs
under the lubrication approximation by constructing a simple mathematical model
for the evolution of their shape. We solved the resulting partial differential equations
for droplet height and composition profile numerically using the Method of Lines. In
the case of a pure droplet, we found that we could control the interface shape using a
single parameter (C) based on the capillary number; the more complex binary system
required two new parameters governing evaporation and surface tension differences.
Comparison to experimental data was improved with the inclusion of a dynamic
evaporative flux for each component that depended on the their volume fraction
distribution.
These simulations offer insight into the deposit that evaporating DiWs leave behind.
We have shown that the smaller C, the more likely the DiW will cause an undesirable
ring stain, but this is suppressed in binary droplets in which the more volatile
component has the lower surface tension.