Simulations of droplets impacting orthogonally over dry surfaces at low Reynolds numbers

A numerical study on contact angle dynamics during spreading and recoil of droplets impacting orthogonally on different dry surfaces is presented by using a finite element variational approach. The contact motion is computed by solving single-fluid formulation of the Navier-Stokes equations for two immiscible and incompressible fluids. The evolution of the interface is solved over axisymmetric domains by using a new numerical surface tension representation and an original tracking technique. Surfaces markers are first advected along streamlines and then the interface is reconstructed with a mass conserving technique. The surface tension term is computed by using the finite element variational formulation and therefore only the first derivative is required. The contact angle hysteresis phenomenon is taken into account by using a consistent mathematical approach which is based on a finite element variational formulation of the problem and, since the problem is singular, a physical regularization is discussed. The boundary singular condition at the contact point is imposed as a penalty term. In particular, the equation that relates the apparent contact angle and the contact line velocity is imposed as an external constraint. This mathematical and numerical modeling of the wetting phenomena circumvents numerous difficulties due to the representation of the surface tension, the non-integrable stress singularity at the moving contact line and the inability to describe in closed form the velocity dependence of the dynamic contact line. A simple model for the apparent contact angle is used in order to provide an insight to the dynamic behavior of the apparent contact angle and its dependence on contact line velocity. The numerical model is tested in different situations with the wetting properties of the target surfaces ranging from wettable to non-wettable and several impact parameters leading to partial and complete rebound.