When does an impacting drop stop bouncing? (2208.05935v2)

Abstract: Non-wetting substrates allow impacting liquid drops to spread, recoil, and takeoff, provided they are not too heavy (Biance et al. 2006) or too viscous (Jha et al. 2020). In this article, using direct numerical simulations with the volume of fluid method, we investigate how viscous stresses and gravity conspire against 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 takeoff, allowing 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 drops limiting regimes by calculating the energy budgets and relating them to the drop's shape and internal flow.

• The paper defines the transition from bouncing to non-bouncing behavior for droplets impacting non-wetting surfaces.
• The study uses numerical simulations and experimental data to show the transition occurs when viscous and gravitational forces dominate, approximated by the condition Oh + Bo ~ 1.
• This work highlights the critical influence of viscosity and gravity for applications like inkjet printing and pesticide delivery, suggesting re-evaluation of existing theoretical frameworks.

Analyzing the Non-Bouncing Transition of Droplets on Non-Wetting Surfaces

The paper "When does an impacting drop stop bouncing?" by Vatsal Sanjay, Pierre Chantelot, and Detlef Lohse explores the dynamics of droplet impact on non-wetting substrates, focusing on the conditions under which a droplet ceases to rebound. Using direct numerical simulations, the authors delve into the interplay between viscous stresses and gravitational effects that inhibit bouncing, comparing these factors against capillarity.

The paper examines droplet behavior through variables such as the Weber number (We), Ohnesorge number (Oh), and Bond number (Bo), offering a comprehensive regime map that delineates bouncing from non-bouncing regimes. This map shows that droplet dynamics are primarily influenced by viscous and gravitational forces when Oh and Bo are both below unity, drawing the boundary for when a droplet transitions into non-bouncing behavior.

The authors present a primary finding that the transition from bouncing to non-bouncing occurs under the condition $Oh + Bo \sim 1$. This criterion is supported by both simulations and experimental data from previous studies, confirming the notion that non-bouncing is linked to either high viscosity or gravity, depending on droplet size in relation to the capillary lengths.

In scenarios where either the Ohnesorge number or Bond number approaches unity, viscous dissipation and gravitational potential energy, respectively, play pivotal roles in preventing a rebound. For high-Oh drops, dissipation throughout the liquid becomes significant, impeding the restitution of kinetic energy. In contrast, for heavy drops, gravitational energy hinders the vertical motion necessary for a bounce, resulting in successive oscillations without rebound.

Notably, the work challenges existing models which often neglect certain energy losses. The authors highlight the inadequacies of traditional models that do not account for viscous dissipation in thin layers or the energy stored in drop deformation at take-off, effectively advocating for a re-evaluation of these theoretical frameworks.

This paper not only provides insights into the boundary conditions of droplet bouncing but also highlights the critical influence of viscosity and gravity in practical applications such as inkjet printing, cooling technologies, and pesticide delivery. Future research could expand these findings to incorporate the role of different surface textures and material compositions, which might further refine the predictive models for droplet behavior on complex surfaces. As the field progresses, such work will be instrumental in optimizing processes that rely on precise manipulation of liquid drops.