When does an impacting drop stop bouncing?

Abstract

Non-wetting substrates allow impacting liquid drops to spread, recoil and take-off, provided they are not too heavy (Bianceet al.,J. Fluid Mech., vol. 554, 2006, pp. 47–66) or too viscous (Jhaet al.,Soft Matt., vol. 16, no. 31, 2020, pp. 7270–7273). In this article, using direct numerical simulations with the volume of fluid method, we investigate how viscous stresses and gravity oppose capillarity to inhibit drop rebound. Close to the bouncing to non-bouncing transition, we evidence that the initial spreading stage can be decoupled from the later retraction and take-off, allowing us to understand the rebound as a process converting the surface energy of the spread liquid into kinetic energy. Drawing an analogy with coalescence-induced jumping, we propose a criterion for the transition from the bouncing to the non-bouncing regime, namely by the condition${Oh}_{c} + {Bo}_{c} \sim 1$, where${Oh}_{c}$and${Bo}_{c}$are the Ohnesorge number and Bond number at the transition, respectively. This criterion is in excellent agreement with the numerical results. We also elucidate the mechanisms of bouncing inhibition in the heavy and viscous drop limiting regimes by calculating the energy budgets and relating them to the drop's shape and internal flow.