A quasi-static model for the normal impact of a viscous drop on a non-wetting substrate is developed. The axisymmetric deformation of a sessile drop is described analytically using new asymptotically exact approximations to solutions of the Young-Laplace equation. Viscous dissipation is accounted for in linearized form through a damping coefficient inversely proportional to the relaxation time of small-amplitude oscillations of a viscous sessile drop. This formulation enables evaluation of the key characteristics of Hertz-type impact at low Weber numbers, including the drop spreading factor, restitution coefficient, and characteristic time scale. Comparison with experimental data demonstrates that the model reliably captures the essential features of slow, viscously damped liquid drop impacts on non-wetting surfaces.
Argatov et al. (Tue,) studied this question.