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Register a new userVortex-Ring-Induced Internal Mixing Upon the Coalescence of Initially Stationary Droplets
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This study employs an improved volume of fluid method and adaptive mesh refinement algorithm to numerically investigate the internal jet-like mixing upon the coalescence of two initially stationary droplets of unequal sizes. The emergence of the internal jet is attributed to the formation of a main vortex ring, as the jet-like structure shows a strong correlation with the main vortex ring inside the merged droplet. By tracking the evolution of the main vortex ring together with its circulation, we identified two mechanisms that are essential to the internal-jet formation: the vortex-ring growth and the vortex-ring detachment. Recognizing that the manifestation of the vortex-ring-induced jet physically relies on the competition between the convection and viscous dissipation of the vortex ring, we further developed and substantiated a vortex-ring-based Reynolds number criterion to interpret the occurrence of the internal jet at various Ohnesorge numbers and size ratios. For the merged droplet with apparent jet formation, the average mixing rate after jet formation increases monotonically with the vortex-ring Reynolds number, which therefore serves as an approximate measure of the jet strength. In this respect, stronger internal jet is responsible for enhanced mixing of the merged droplet.
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The internal dynamics during the coalescence of a sessile droplet and a subsequently deposited impacting droplet, with either identical or distinct surface tension, is studied experimentally in the regime where surface tension is dominant. Two color high-speed cameras are used to capture the rapid internal flows and associated mixing from both side and bottom views simultaneously by adding an inert dye to the impacting droplet. Given sufficient lateral separation between droplets of identical surface tension, a robust surface jet is identified on top of the coalesced droplet. Image processing shows this jet is the result of a surface flow caused by the impact inertia and an immobile contact line. By introducing surface tension differences between the coalescing droplets, the surface jet can be either enhanced or suppressed via a Marangoni flow. The influence of the initial droplet configuration and relative surface tension on the long-term dynamics and mixing efficiency, plus the implications for emerging applications such as reactive inkjet printing, are also considered.
This letter presents a scaling theory of the coalescence of two viscous spherical droplets. An initial value problem was formulated and analytically solved for the evolution of the radius of a liquid neck formed upon droplet coalescence. Two asymptotic solutions of the initial value problem reproduce the well-known scaling relations in the viscous and inertial regimes. The viscous-to-inertial crossover experimentally observed by Paulsen et al. [Phys. Rev. Lett. 106, 114501 (2011)] manifests in the theory, and their fitting relation, which shows collapse of data of different viscosities onto a single curve, is an approximation to the general solution of the initial value problem.
When two sessile drops of the same liquid touch, they merge into one drop, driven by capillarity. However, the coalescence can be delayed, or even completely stalled for a substantial period of time, when the two drops have different surface tensions, despite being perfectly miscible. A temporary state of non-coalescence arises, during which the drops move on their substrate, only connected by a thin neck between them. Existing literature covers pure liquids and mixtures with low surface activities. In this paper, we focus on the case of large surface activities, using aqueous surfactant solutions with varying concentrations. It is shown that the coalescence behavior can be classified into three regimes that occur for different surface tensions and contact angles of the droplets at initial contact. However, not all phenomenology can be predicted from surface tension contrast or contact angles alone, but strongly depends on the surfactant concentrations as well. This reveals that the merging process is not solely governed by hydrodynamics and geometry, but also depends on the molecular physics of surface adsorption.
For a limited set of impact conditions, a drop impacting onto a pool can entrap an air bubble as large as its own size. The subsequent rise and rupture of this large bubble plays an important role in aerosol formation and gas transport at the air-sea interface. The large bubble is formed when the impact crater closes up near the pool surface and is known to occur only for drops which are prolate at impact. Herein we use experiments and numerical simulations to show that a concentrated vortex ring, produced in the neck between the drop and pool, controls the crater deformations and pinch-off. However, it is not the strongest vortex rings which are responsible for the large bubbles, as they interact too strongly with the pool surface and self-destruct. Rather, it is somewhat weaker vortices which can deform the deeper craters, which manage to pinch off the large bubbles. These observations also explain why the strongest and most penetrating vortex rings emerging from drop impacts, are not produced by oblate drops but by more prolate drop shapes, as had been observed in previous experiments.
We consider self-propelled droplets which are driven by internal flow. Tracer particles, which are advected by the flow, in general follow chaotic trajectories, even though the motion of the autonomous swimmer is completely regular. The flow is mixing, and for P{e}clet and Batchelor numbers, which are realized e.g. in eucaryotic cells, advective mixing can substantially accelerate and even dominate transport by diffusion.
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