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.