Dynamics of clean and particle-laden drying droplets on soft viscoelastic substrates

A fundamental question arises about the way that the substrate elasticity affects droplet evaporation in the presence of non-interacting particles in the bulk, to be able to control the deposition patterns. In this work, we investigate the dynamics of a pair of both clean and particle-laden volatile droplets residing on a compliant substrate described by the Kelvin-Voigt model. The presence of neighbouring droplets necessitates to fully account for the diffusion of vapor in the atmosphere; the effects of evaporative cooling, thermocapillarity and the effect of particles on rheology are also considered. We propose a lubrication theory based model to derive evolution equations for the droplet profile, the displacement of the elastic solid and the profile of particle concentration in the bulk; these evolution equations are coupled with the Laplace’s equation for the vapor concentration in the gas phase solved in 2D. We perform a thorough parametric analysis to investigate the complex flow dynamics ranging from droplet attraction and repulsion, to symmetry breaking and to sustained droplet oscillations. We show that these phenomena are determined by a delicate interplay between the substrate softness, the capillary and Marangoni forces, particle transport in the bulk and rheology.