A front-tracking method for computational modeling of impact and spreading of viscous droplets on solid walls

A finite-difference/front-tracking method is developed for computational modeling of impact and spreading of a viscous droplet on dry solid walls. The contact angle is specified dynamically using the empirical correlation given by Kistler (1993). The numerical method is general and can treat non-wetting, partially wetting and fully wetting cases but the focus here is placed on the partially wetting substrates. Here the method is implemented for axisymmetric problems but it is straightforward to extend it to three dimensional cases. Grid convergence of the method is demonstrated and the validity of the dynamic contact angle method is examined. The method is first tested for the spreading and relaxation of a droplet from the initial spherical shape to its final equilibrium conditions for various values of Eotvos number. Then it is applied to impact and spreading of glycerin droplets on wax and glass substrates and, the results are compared with experimental data of Sikalo et al. (2005). The numerical results are found in a good agreement with the experimental data. Finally the effects of governing non-dimensional numbers on the spreading rate, apparent contact angle and deformation of the droplet are investigated.