Deposition of Brownian particles during evaporation of two-dimensional sessile droplets

Evaporation of sessile droplets gives rise to internal flow that, in turn, affects drastically the deposition of the suspended particles on the substrate. Analytical expressions for the flow field are used to compute the local velocity inside an evaporating two-dimensional droplet as a function of position and time of evaporation. Trajectories of a sample of suspended Brownian particles are computed along the progress of the evaporation process and terminate upon collision with the solid substrate. Traveling particles are allowed to interact with the evaporating free surface and are either rebounced into the main body of the droplet or float on the surface until they are collected on the substrate. The dependence of the diffusion coefficient on the distance from the substrate is taken into account giving rise to anisotropic diffusional effects that, however, are shown to affect slightly the deposition rate profile except in the case of flow-dominated transport. Results for hydrophilic and strongly hydrophobic substrates are presented and the conditions for the development of the two-dimensional variant of the famous “coffee stain phenomenon” are investigated. Comparison of the simulated deposition profiles with the corresponding predictions of a convection-diffusion lattice–Boltzmann model revealed excellent agreement for various Peclet number values. Simulation of stick-slip evaporation leads to well-defined multiple stripes, the density of which depends strongly on the difference between the initial contact angle and the angle at which the slip step is activated.