Inertio-capillary rebound of a droplet impacting a fluid bath

Abstract

The rebound of droplets impacting a deep fluid bath is studied both experimentally and theoretically. Millimetric drops are generated using a piezoelectric droplet-on-demand generator and normally impact a bath of the same fluid. Measurements of the droplet trajectory and other rebound metrics are compared directly with the predictions of a linear quasipotential model, as well as fully resolved direct numerical simulations of the unsteady Navier–Stokes equations. Both models resolve the time-dependent bath and droplet shapes in addition to the droplet trajectory. In the quasipotential model, the droplet and bath shape are decomposed using orthogonal function decompositions leading to two sets of coupled damped linear harmonic oscillator equations solved using an implicit numerical method. The underdamped dynamics of the drop are directly coupled to the response of the bath through a single-point kinematic match condition which we demonstrate to be an effective and efficient model in our parameter regime of interest. Starting from the inertio-capillary limit in which both gravitational and viscous effects are negligible, increases in gravity or viscosity lead to a decrease in the coefficient of restitution and an increase in the contact time. The inertio-capillary limit defines an upper bound on the possible coefficient of restitution for droplet–bath impact, depending only on the Weber number. The quasipotential model is able to rationalize historical experimental measurements for the coefficient of restitution, first presented by Jayaratne & Mason (Proc. R. Soc. Lond. A, vol. 280, issue 1383, 1964, pp. 545–565).

New insights into head-on bouncing of unequal-size droplets on a wetting surface

“…This significantly increases computational costs, and the effects of rarefied gas dynamics become significant. To overcome these difficulties, a 2-VOF approach has been proposed and used by several researchers (Ramírez-Soto et al 2020;Alventosa, Cimpeanu & Harris 2023) to study droplet bouncing. By avoiding overlap between the two-volume fraction fields, a situation similar to an incompletely drained air film with a large air film gap can be simulated, ensuring the occurrence of bouncing (see Appendix).…”

“…It is well known that bouncing is observed for a certain range of We for equal-size droplet collision in air (Qian & Law 1997). In this study, the ranges of parameters leading to bouncing are selected based on experimental data from studies by Ramírez-Soto et al (2020), Abouelsoud & Bai (2021) and Ray et al (2023a), as well as observations from similar phenomena reported by Qian & Law (1997) and Alventosa et al (2023). The ranges of parameters used in DNS are summarized in table 1.…”

Calculation of internal-wave-driven instability and vortex shedding along a flat bottom

“…The Basilisk multi-phase flow library has been validated by several recent papers in Journal of Fluid Mechanics , e.g. Mostert, Popinet & Deike (2022) (breaking waves), Alventosa, Cimpeanu & Harris (2023) (droplet impact), Riviére et al. (2021) (turbulent bubble break-up), Mostert & Deike (2020) (dissipation in waves) and Innocenti et al.…”

Analysis of high-speed drop impact onto deep liquid pool

“…2015; Ray, Biswas & Sharma 2015; Deka et al. 2017; Fudge, Cimpeanu & Castrejón-Pita 2021; Alventosa, Cimpeanu & Harris 2023; Fudge et al. 2023) can be found in the literature, focusing on those phenomena that are assumed axisymmetric.…”

“…Recent simulations of liquid drops impinging onto liquid surfaces are mostly based on the latter category of models. Substantial axisymmetric simulations of the problem (Morton et al 2000;Josserand & Zaleski 2003;Berberović et al 2009;Thoraval et al 2012;Ervik et al 2014;Agbaglah et al 2015;Ray, Biswas & Sharma 2015;Deka et al 2017;Fudge, Cimpeanu & Castrejón-Pita 2021;Alventosa, Cimpeanu & Harris 2023;Fudge et al 2023) can be found in the literature, focusing on those phenomena that are assumed axisymmetric. For three-dimensional (3-D) calculations, whose primary objective is to capture the non-axisymmetric mechanisms involved in the splashing process, efforts were focused on dynamic refinement techniques (Popinet 2003;Nikolopoulos, Theodorakakos & Bergeles 2007), in order to resolve multiple interfaces resulting from the splash, while ensuring a reasonable grid size.…”