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

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.

Numerical simulations and experiments on droplet coalescence dynamics over a liquid–air interface: mechanism and effect of droplet-size/surface-tension

Present study is on partial/complete coalescence dynamics of a droplet (surrounded by air) over a horizontal pool of the same liquid. Experimental and numerical studies are presented for both isopropanol and glycerol droplet of a constant diameter. Numerical study is presented in more detail for the isopropanol droplet to study the effect of diameter ($$D=0.035-6.7 mm$$ D = 0.035 - 6.7 m m ) and surface tension coefficient ($$\gamma =2-200 mN/m$$ γ = 2 - 200 m N / m ) on the coalescence dynamics. For partial coalescence of an isopropanol droplet and complete coalescence of a glycerol droplet, excellent agreement is demonstrated between our numerically and experimentally obtained interface dynamics; and a qualitative discussion on the mechanism of the partial and complete coalescence is presented. Three regimes of partial coalescence − viscous, inertio-capillary and gravity − proposed in the literature for a liquid-liquid system are presented here for the present liquid-air system while studying the effect of diameter of the isopropanol droplet. Probably for the first time in the literature, our numerical study presents a flow and vorticity dynamics based quantitativeevidence of the coalescence-mechanism, analogy with a freely vibrating Spring-Mass-Damper System, the gravity regime for a liquid-gas system, and the effect of surface tension coefficient $$\gamma$$ γ based coalescence dynamics study. The associated novel $$\gamma$$ γ based droplet coalescence regime map presents a critical Ohnesorge number $$Oh_{c}$$ O h c and critical Bond number $$Bo_{c}$$ B o c for a transition from partial to full coalescence; and such critical values are also presented for the transition under effect of the droplet diameter. The critical values based transition boundaries, obtained separately for the varying D and varying $$\gamma$$ γ , are demonstrated to be in excellent agreement with a correlation reported in the literature.

Manipulation of single sub-femtolitre droplets via partial coalescence in a direct-current electric field

It is demonstrated how aqueous droplets with volumes down to the sub-femtolitre range can be manipulated, including the withdrawal of minute samples from the droplets. The underlying principle is that of partial coalescence with a liquid reservoir in an applied electric field. Upon partial coalescence, a droplet merges with a reservoir and reappears with a smaller diameter. The droplets studied here perform a reciprocating motion between two reservoirs during which their volume gets reduced. Manipulation of droplets with diameters down to 400 nm is reported. A similarity relation is derived expressing the ratio of droplet diameters before and after partial coalescence as a function of the ratio between electric and interfacial-tension forces. The presented scheme allows the withdrawal of minute samples from small droplets and could prove helpful in various applications where droplets are used as tiny reaction spaces or when the goal is to tailor the size of individual droplets.