Phase-field modeling and computer simulation of the coffee-ring effect

In this study, we propose a novel computational model for simulating the coffee-ring phenomenon. The proposed method is based on a phase-field model and Monte Carlo simulation. We use the Allen–Cahn equation with a pinning boundary condition to model a drying droplet. The coffee particles inside the droplet move according to a random walk function with a truncated standard normal distribution under gravitational force. We perform both two-dimensional and three-dimensional computational experiments to demonstrate the accurate simulation of the coffee-ring phenomenon by the proposed model.