Self-organization of bouncing oil drops: Two-dimensional lattices and spinning clusters

Lieber, Suzanne I.; Hendershott, Melissa C.; Pattanaporkratana, Apichart; Maclennan, Joseph E.

doi:10.1103/physreve.75.056308

Cited by 31 publications

(30 citation statements)

References 22 publications

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“…The dynamics of the bouncing droplets are extraordinarily rich. Feedback between the droplet and its wave field may lead to selfpropulsion [2] and diffraction of these walking droplets as they pass through a slit [3]; moreover, multiple droplets may lock into complex orbital motions [2] or lattices [4]. We here demonstrate that a droplet on a vertically vibrated soap film may similarly avoid coalescence, and that the bouncing droplet represents a textbook example of a chaotic oscillator, with many features common to the bouncing of an inelastic ball on a solid substrate.…”

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confidence: 86%

Chaotic Bouncing of a Droplet on a Soap Film

Gilet

Bush

2009

Phys. Rev. Lett.

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We examine the complex dynamics arising when a water droplet bounces on a horizontal soap film suspended on a vertically oscillating circular frame. A variety of simple and complex periodic bouncing states are observed, in addition to multiperiodicity and period-doubling transitions to chaos. The system is simply and accurately modeled by a single ordinary differential equation, the numerical solution of which captures all the essential features of the observed behavior. Iterative maps and bifurcation diagrams indicate that the system exhibits all the features of a classic low-dimensional chaotic oscillator. We here demonstrate that a droplet on a vertically vibrated soap film may similarly avoid coalescence, and that the bouncing droplet represents a textbook example of a chaotic oscillator, with many features common to the bouncing of an inelastic ball on a solid substrate.Drops of uniform size (R ¼ 0:08 cm) bounce on a horizontal circular soap film of radius A ¼ 1:6 cm vibrated with vertical displacement B cosð2ftÞ (Fig. 1). The droplet and soap film consist of a glycerol-water-soap mixture (80% water, 20% glycerol, <1% soap) with density ¼ 1:05 g cm À3 , viscosity ¼ 2 cS, and surface tension ¼ 22 dyn cm À1 . Drops of uniform size (R ¼ 0:8 mm) and mass (m ¼ 2:25 mg) were extruded from an insulin syringe (needle diameter 0.35 mm). For the bouncing states, the characteristic drop impact speeds (U $ 4-32 cm s À1 ) are much less than the characteristic wave speed on the film (a film thickness of 4 m indicates a wave speed of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=h p $ 330 cm s À1 ). The influence of capillary waves is thus assumed to be negligible, and the film described as quasistatic: it deforms instantaneously in response to the forcing imposed by the droplet. The Weber number We ¼ U 2 R= lies between 0.06 and 3.9. During impact, the droplet remains roughly spherical: maximum center line distortions of 13% were observed (at We ¼ 3:9), so the surface energy of drop distortion is less than 3% that associated with soap film distortion. Beneath the droplet, the soap film lies tangent to the droplet, and so roughly assumes the form of a spherical cap of radius R. Beyond the droplet, the pressure is atmospheric on either side of the soap film, which thus assumes the form of a catenoid as confirmed experimentally [5]. The spherical cap and catenoid match at a point M corresponding to an angle (Fig. 1). The vertical deflection of the soap film Z and the resulting vertical force F on the droplet may be expressed in terms of :where ¼ ðRsin 2 Þ=A. The force-displacement relation FðZÞ is shown in Fig. 2(a). In the range 0 < Z=R < 3, the film responds as a linear spring, F ¼ kZ, where the effective spring constant k ¼ 8 7 . The force then saturates, achieving a maximum at ¼ =2, and decreases thereafter. This quasistatic description of the film was used successfully by the authors [5] to deduce a criterion for breakthrough of a droplet striking a stationary film [6].When the droplet strikes a static soap film at a...

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confidence: 86%

Chaotic Bouncing of a Droplet on a Soap Film

Gilet

Bush

2009

Phys. Rev. Lett.

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“…To better understand and therefore make use of the above described dynamic self-assembly in engineered microfluidic systems it is important to identify the underlying interactions that yield self-assembly (20)(21)(22)(23). We hypothesized that viscous disturbance flows induced by rotating particles under confinement would repel neighboring particles to infinity whereas fluid inertia in the form of lift forces would act to maintain the particles at finite distances.…”

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confidence: 99%

Dynamic self-assembly and control of microfluidic particle crystals

Lee

Amini

Stone

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

203

228

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Engineered two-phase microfluidic systems have recently shown promise for computation, encryption, and biological processing. For many of these systems, complex control of dispersed-phase frequency and switching is enabled by nonlinearities associated with interfacial stresses. Introducing nonlinearity associated with fluid inertia has recently been identified as an easy to implement strategy to control two-phase (solid-liquid) microscale flows. By taking advantage of inertial effects we demonstrate controllable self-assembling particle systems, uncover dynamics suggesting a unique mechanism of dynamic self-assembly, and establish a framework for engineering microfluidic structures with the possibility of spatial frequency filtering. Focusing on the dynamics of the particleparticle interactions reveals a mechanism for the dynamic selfassembly process; inertial lift forces and a parabolic flow field act together to stabilize interparticle spacings that otherwise would diverge to infinity due to viscous disturbance flows. The interplay of the repulsive viscous interaction and inertial lift also allow us to design and implement microfluidic structures that irreversibly change interparticle spacing, similar to a low-pass filter. Although often not considered at the microscale, nonlinearity due to inertia can provide a platform for high-throughput passive control of particle positions in all directions, which will be useful for applications in flow cytometry, tissue engineering, and metamaterial synthesis.inertial ordering | hydrodynamic interaction | particle-laden flow | defocusing | microfluidics

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“…When two or more droplets are placed on a vibrating interface, complex attractions and repulsions are observed [23], leading to ordered structures such as crystal-like rafts [24]. Such structures are illustrated in the Fig.…”

Section: Interacting Dropletsmentioning

confidence: 99%

Antibubbles, liquid onions and bouncing droplets

Vandewalle

Terwagne

Gilet

et al. 2009

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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a b s t r a c tIn this paper, we emphasize our long series of experiments proving that the physical processes along fluid interfaces can be exploited for creating unusual fluidic objects. We report for the first time a couple of new fluidic objects so-called "liquid onions" and "mayonnaise" droplets. The study starts from the observation of antibubbles, exhibiting unstable liquid-air-liquid interfaces. We show that the lifetime of such a system has the same origin as floating/coalescing droplets on liquid surfaces. By analyzing such behaviours, we created droplets bouncing on a liquid bath. The methods and physical phenomena collected in this paper provide a basis for the development of a discrete microfluidics. Open questions are underlined, experimental challenges and future applications are proposed.

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Self-organization of bouncing oil drops: Two-dimensional lattices and spinning clusters

Cited by 31 publications

References 22 publications

Chaotic Bouncing of a Droplet on a Soap Film

Chaotic Bouncing of a Droplet on a Soap Film

Dynamic self-assembly and control of microfluidic particle crystals

Antibubbles, liquid onions and bouncing droplets

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