Contributed Session 3:
Modeling, Math Biology and Math Finance
Variational modeling and numerical simulation of evaporating thin droplets and the coffee-ring effect
Yakun LI
The Hong Kong University of Science and Technology Peoples Rep of China
Co-Author(s):
Abstract:
Evaporating sessile droplets exhibit complex, multiscale dynamics driven by the coupling of interfacial evaporation, contact line motion, internal fluid flow, and vapor diffusion, leading to phenomena such as the coffee-ring effect. We develop a thermodynamically consistent thin-film model using Onsager`s variational principle combined with the lubrication approximation. The framework incorporates viscous momentum transport, contact line motion, evaporation, and vapor diffusion in a unified setting. A characteristic length scale is introduced by considering the competition between the liquid evaporation at the liquid-gas interface and the vapor diffusion in the gas space, yielding a dimensionless parameter that distinguishes diffusion-limited and transition-limited regimes. Numerical simulations reveal distinct evaporation patterns and flow structures across regimes. We further investigate the coffee-ring effect for drying particle-laden droplets across different dynamic regimes with pinned and depinned contact lines.