A semi-empirical force balance-based model to capture sessile droplet spread on smooth surfaces: A moving front kinetic Monte Carlo study

Abstract

This study reports the development of a semi-empirical force balance-based moving front kinetic Monte Carlo (FB-MFkMC) model to describe droplet spreading on a smooth surface. The proposed model depicts the state-by-state evolution of a sessile droplet in a stochastic manner that captures the molecular-level events taking place in an accurate yet efficient manner. In the developed model, the movement of the droplet triple contact line is depicted using rate expressions that detail the probability that the contact line will locally advance over a set distance at each time point. These rate expressions are derived based on the force balance acting upon the droplet interface, which is captured using analytical inertial and capillary expressions from the literature. This work furthermore derives a new semi-empirical expression to depict the viscous damping force acting on the droplet. The derived viscous force term depends on a fitted parameter c, whose value was observed to vary solely depending on the droplet liquid as captured predominantly by the droplet Ohnesorge number. The proposed FB-MFkMC approach is subsequently validated using data obtained both from conducted experiments and from the literature to support the robustness of the framework. The predictive capabilities of the developed model are further inspected to provide insights on the sessile droplet system behavior.