Numerical simulation of spreading drops

We consider a liquid drop that spreads on a wettable surface. Different time evolutions have been observed for the base radius r depending of the relative role played by inertia, viscosity, surface tension and the wetting condition. Numerical simulations were performed to discuss the relative effect of these parameters on the spreading described by the evolution of the base radius r(t) and the spreading time tS. Different power law evolutions r(t) ∝ tn have been observed when varying the parameters. At the early stage of the spreading, the power law t1/2 (n = 1/2) is observed as long as capillarity is balanced by inertia at the contact line. When increasing the viscosity contribution, the exponent n is found to increase despite the increase of the spreading time. The effect of the surface wettability is observed for liquids more viscous than water. For a small contact angle, the power law t1/2 is then followed by the famous Tanner law t1/10 once the drop shape has reached a spherical cap.