A wetting force-based model for contact line dynamics in droplet impact on curved substrates

Purpose Numerical simulations of moving three-phase contact line on curved substrates are performed in scenarios without any splashing or rebounding after liquid impact. While velocity-based dynamic contact angle models have been used previously, a force-based approach that closely relates dynamic contact angle to underlying flow physics has not been implemented for curved surfaces. The purpose of this study is to develop and implement a force-based model for curved substrates where dynamic contact angle is adjusted by wetting force at contact line. Design/methodology/approach The magnitude and direction of wetting force are calculated for different geometries after computing dynamic contact angle with respect to equilibrium contact angle while considering the effect of curvature of substrate during contact line motion. The resolved components of wetting force are included as source terms in radial and axial momentum equations, for which a sign convention is derived for different configurations. The overall algorithm for wetting force is implemented using user-defined routines within the framework of an existing CFD solver using volume of fluid method. Adaptive mesh refinement is also used near the interface because of intensive nature of the computations. The model is used to simulate droplet impact on convex and concave spherical surfaces, and conical surface along with water entry of a spherical ball. The effect of curvature and impact velocity on contact line motion over convex spherical surface is studied, while the role of contact angle for different surfaces is also examined. Findings The results from the simulations show that the present force-based methodology is able to capture the temporal evolution of dynamic contact angle closely based on the underlying physical mechanisms, without resorting to any empiricism or approximations. The simulations also bring forth the deviations of the dynamic contact angle from the specified equilibrium contact angle values during contact line motion on different curved geometries, the reasons for which are adequately discussed. A validation with existing numerical and experimental results shows the effectiveness of the proposed methodology in accurately capturing contact line motion. Originality/value The results showcase several new and important findings as no prior investigation has been done with regard to implementation of such a force-based approach to study moving contact lines on curved surfaces, to the best of the authors’ knowledge. This study comprehensively outlines and presents all the steps involved in implementing the force-based model while considering the effect of curvature on different geometries under various conditions, and establishes it as an effective and accurate approach to capture contact line dynamics. This study can definitely be helpful to the modelling community towards accurate, physics-based modelling of moving contact lines.