Sensitivity of the spreading rate of a liquid droplet on a surface to the approximation of the contact angle

This paper presents a numerical study of the impaction of a liquid droplet on a flat, solid surface. In particular, the sensitivity of the spreading rate of the droplet to the approximation of the contact angle is investigated. The full Navier-Stokes equations, subject to free surface boundary conditions and a dynamically inactive ambient, are solved using the Galerkin finite element technique. The free surface is determined by the spineflux method. Simulation of the spreading rate requires information on the dynamic contact angle at the solid-liquid-gas interface. A wetting parameter, η, is introduced to determine the contact angle. Results show that the spreading rate is sensitive to η when the Weber number of droplet upon impact is small (We = 1.4 in this study). Here, the inertial forces and surface tension forces are comparable. The sensitivity decreases as the Weber number increases. At large Weber numbers, inertial effects dominate the surface tension forces and, hence, the spreading rate. Thus, the contact angle approximation has little influence. Larger Reynolds numbers also result in greater inertial effects. For such cases, there is also reduced sensitivity to the wetting parameter.