An energy balance approach of the dynamics of drop impact on a solid surface

The description of physical mechanisms involved in the impact of a drop upon a dry, partially wettable substrate is still a matter of debate. One way to analyze the balance of these mechanisms is the development of an analytical one-dimensional (1D) model based upon the energy equation. The assimilation of the drop to a cylinder allows a reduction of the energy equation to a second-order differential equation. This paper proposes a semi-empirical description of viscous dissipation taking into account the rolling motion near the contact line. The dissipation due to the rolling motion is added to the calculated dissipation in the core of the droplet. We compare our model to previous ones using a large set of literature data covering a wide range of viscosity, velocity impact, and equilibrium contact angle values. The new dissipation description proposed is shown to supersede those described in previous 1D models. Our model closely predicts the maximum spread factor and the time at which it is obtained on the whole range of Ohnesorge and Weber numbers considered. It also distinguishes between deposition with a steady variation in the wetted area from deposition with advancing and receding phases. The main limitations of the model lie in its inability to reproduce the spread factor at the very beginning of the impact and the rebounding observed after a receding phase for very high values of the equilibrium contact angle.