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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).
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Inertio-Capillary Impacts
Droplet impacts are of fundamental importance to the natural water cycle as collision and coalescence of droplets are the primary mechanism by which warm rain forms. Additionally, droplet impacts are of paramount significance in a variety of industrial processes, including spray cooling, wet scrubbing, and even play a role in cooling nuclear reactors. Throughout this work, we utilize a combination of theoretical mod- eling and experiments to elucidate the dynamics of these common phenomena. The first problem we analyze is a droplet impacting a deep fluid bath. Millimetric drops are generated using a piezoelectric droplet-on-demand generator and normally impact a bath of the same fluid. The limit where capillarity and fluid inertia dominate the interfacial dynamics is investigated. This so-called inertio-capillary limit is shown to define an upper bound on the possible coefficient of restitution for droplet–bath im- pact. We then consider the scenario where the substrate is no longer deformable, and study the dynamics of non-wetting droplets impacting on stationary and vibrating substrates, with deterministic chaos emerging in the latter case. Extending beyond axisymmetric impacts, we then analyze droplet impact scenarios where there is some relative tangential velocity between the substrate and droplet. We determine the thresholds for coalescence, and our results suggest that substrate deformability plays an important role in transitions between the bouncing and merging regimes. Finally, we consider an analogous solid case to the normal droplet impact studies, where a small rigid sphere impacts and rebounds from a deformable elastic membrane. We perform experiments and identify new previously unreported behaviors in this simple system which are attributed to the non-negligible inertia of the membrane. Overall, the dynamics of these impact scenarios are extremely rich, producing physical phe- nomena that are inherently multi-scale, requiring information and knowledge from micron to centimeter scales. As showcased here, reduced-order modeling and con- trolled experiments are essential in distilling some simplicity out of the complexity.
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- Award ID(s):
- 2123371
- PAR ID:
- 10647139
- Publisher / Repository:
- Brown Digital Repository
- Date Published:
- Format(s):
- Medium: X
- Institution:
- Brown University
- Sponsoring Org:
- National Science Foundation
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