The dynamics of bouncing, partially coalescing, liquid metal droplets in a viscous medium

Abstract

Planar partial coalescence is a phenomenon in which a droplet at a free surface or interface between two fluids coalesces into the plane surface producing a smaller droplet rather than coalescing completely. This smaller, ‘daughter’ droplet will be driven towards the interface by gravity and capillary forces resulting in a cascade effect of progressively small daughter droplets until the Ohnesorge Number approaches $\sim$ 1 and the cascade terminates with a full coalescence event. This paper utilizes a room temperature liquid metal alloy composed of gallium, indium and tin to study partial coalescence in a viscous quiescent medium and observed bouncing of the coalescing droplets on the interface. We observed the event using high speed videography measuring effects such as the droplet to daughter droplet ratio, droplet velocities, droplet bounce heights and coefficients of restitution for the bouncing event. An existing model (Honey & Kavehpour, Phys. Rev. E, vol. 73, 2006) from our group was used, validated and expanded upon to include buoyancy effects to estimate the initial velocity of the droplet and we developed two new models for the droplet travel and maximum bounce height. The first utilizes the Stokes model for drag to moderate success while the second utilizes a model from Beard & Pruppacher (J. Atmos. Sci., vol. 26, 1969, pp. 1066–1072) and a fourth-order Runge–Kutta numerical integration scheme to predict the droplet velocity and position as functions of time. Additionally the coefficient of restitution was determined from the model using a shooting method technique in tandem with measured data to find a coefficient of restitution value of $A = 0.27 \pm 0.06$ . This ‘bouncing drop’ phenomenon continues in a quiescent viscous fluid to the sub-micron scale and was facilitated by the material properties of the liquid metal including the high density, moderate viscosity and particularly high interfacial tension.

Inertio-capillary rebound of a droplet impacting a fluid bath

“…The exact value of the saturation restitution coefficient does seem to vary, however, from 0.2 in Moláček & Bush (2012) for more viscous drops, to 0.3 in Bach et al (2004) and Zhao et al (2011), to as low as 0.1 (Zou et al 2011) for large Bo impact scenarios. Remarkably, recent experiments on rebound of liquid metal droplets in viscous media also showed similar values of the coefficient of restitution with α = 0.27 (McGuan, Candler & Kavehpour 2022). A similar saturation is also observed in our experimental results presented herein, with water droplets generally bouncing higher that the 5 cSt silicone oil droplets.…”

“…2011) for large impact scenarios. Remarkably, recent experiments on rebound of liquid metal droplets in viscous media also showed similar values of the coefficient of restitution with (McGuan, Candler & Kavehpour 2022). A similar saturation is also observed in our experimental results presented herein, with water droplets generally bouncing higher that the 5 cSt silicone oil droplets.…”

New insights into suspended drops: When soft matter meets acoustic levitation

“…The Rayleigh equation, which forms the cornerstone of the drop oscillation theory, asserts that surface tension acts as a restoring force to keep the drop surface in its equilibrium position. Moreover, it is crucial to the understanding of drop stability, rupture mechanisms, and surface tension 20–22 . More focus has been placed on the equilibrium shape and oscillation dynamics of the acoustically levitated drop as a result of the technology's ongoing use in the study of drop dynamics.…”

“…Moreover, it is crucial to the understanding of drop stability, rupture mechanisms, and surface tension. [20][21][22] More focus has been placed on the equilibrium shape and oscillation dynamics of the acoustically levitated drop as a result of the technology's ongoing use in the study of drop dynamics.…”