(591f) Sagging of Evaporating Droplets of Colloidal Suspensions on Inclined Substrates

A droplet of a colloidal suspension placed on an
inclined substrate may sag under the action of gravity. Solvent
evaporation raises the concentration of the colloidal particles,
and the resulting viscosity changes may influence the sag of the
droplet. To investigate this phenomenon, we have developed a
mathematical model for perfectly wetting droplets based on
lubrication theory and the rapid-vertical-diffusion approximation.
Precursor films are assumed to be present, the colloidal
particles are taken to be hard spheres, and particle and liquid
dynamics are coupled through a concentration-dependent
viscosity and diffusivity. Evaporation is assumed to be limited by how rapidly solvent molecules can transfer from the liquid to the vapor phase. The resulting one-dimensional system of nonlinear partial differential equations describing the evolution of the
droplet height and particle concentration is solved numerically for a range of initial particle concentrations and substrate
temperatures. The solutions reveal that the interaction between evaporation and non-Newtonian suspension rheology gives rise
to several distinct regimes of droplet shapes and particle concentration distributions. The results provide insight into how
evaporation and suspension rheology can be tuned to minimize sagging as well as the well-known coffee-ring effect, an outcome which is important for industrial coating processes.