Three-dimensional Monte Carlo model of the coffee-ring effect in evaporating colloidal droplets

The residual deposits usually left near the contact line after pinned sessile colloidal droplet evaporation are commonly known as a coffee-ring'' effect. However, there were scarce attempts to simulate the effect, and the realistic fully three-dimensional (3D) model is lacking since the complex drying process seems to limit the further investigation. Here we develop a stochastic method to model the particle deposition in evaporating a pinned sessile colloidal droplet. The 3D Monte Carlo model is developed in the spherical-cap-shaped droplet. In the algorithm, the analytical equations of fluid flow are used to calculate the probability distributions for the biased random walk, associated with the drift-diffusion equations. We obtain the 3D coffee-ring structures as the final results of the simulation and analyze the dependence of the ring profile on the particle volumetric concentration and sticking probability.