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

• Published in: Theoretical and computational fluid dynamics Vol. 34; no. 5-6; pp. 679 - 692
• Main Authors: Yang, Junxiang, Kim, Hyundong, Lee, Chaeyoung, Kim, Sangkwon, Wang, Jian, Yoon, Sungha, Park, Jintae, Kim, Junseok
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020; Springer; Springer Nature B.V
• Subjects: Boundary conditions; Classical and Continuum Physics; Coffee; Computational Science and Engineering; Computer simulation; Computer-generated environments; Droplets; Engineering; Engineering Fluid Dynamics; Fluid dynamics; Force distribution; Gravity; Monte Carlo method; Monte Carlo simulation; Normal distribution; Original Article; Random walk; Simulation; Statistical methods; Stress concentration; Technology application; Coffee-ring effect; 68U20; Brownian dynamics; 65N06; Pinning boundary condition; 65C05; Monte Carlo simulation; 35K55; Allen–Cahn equation
• ISSN: 0935-4964; 1432-2250
• DOI: 10.1007/s00162-020-00544-w

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.