Pinning, retraction, and terracing of evaporating droplets containing nanoparticles

We consider the dynamics of a slender, evaporating droplet containing nanoparticles. We use lubrication theory to derive a coupled system of equations that govern the film thickness and the concentration of nanoparticles. These equations account for capillarity, Marangoni stresses, evaporation, and disjoining pressure; the nanoparticle-induced structural component of the disjoining pressure is also considered. Contact line singularities are avoided through the adsorption of ultrathin films wherein evaporation is suppressed by the disjoining pressure; a similar approach has recently been used by Ajaev [J. Fluid Mech. 2005, 528, 279-296] who has built on the previous work of Moosman and Homsy [J. Colloid Interface Sci. 1980, 73, 212-223]. The results of our numerical simulations indicate that, depending on the value of system parameters, the droplet exhibits a variety of different behaviours, which include spreading, evaporation-driven retraction, contact line pinning, and "terrace" formation.