Spontaneous Orbiting of Two Spheres Levitated in a Vibrated Liquid

Pacheco-Martinez, H. A.; Liao, Liam; Hill, R.; Swift, Michael; Bowley, R. M.

doi:10.1103/physrevlett.110.154501

Cited by 19 publications

(13 citation statements)

References 28 publications

(37 reference statements)

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“…The steady streaming structures around a square cylinder (Bearman et al 1984;Zheng & Dalton 1999), two square cylinders (Chern et al 2010), a sphere (Riley 1966;Zhao, Sadhal & Trinh 1999) and a spheroid (Rednikov & Sadhal 2004) have also been investigated. The formation of chains of spherical particles, aligned perpendicular to the direction of oscillation, was observed in the oscillating flow, and the reason was attributed to the steady streaming flow induced by the vibration (Wunenburger, Carrier & Garrabos 2002;Klotsa et al 2009;Pacheco-Martinez et al 2013). Wright, Swift & King (2008) investigated the motion of a dimer consisting of a pair of spheres of unequal size and observed that the dimer migrated in the direction perpendicular to the oscillation direction, with the small sphere as a leading one.…”

Section: Introductionmentioning

confidence: 94%

“…The period-averaged velocity fields at stable state for Re = 50, θ = 90 • and T * = 4 are plotted in figure 5(b), which shows that the steady streaming structure for the ∧-shaped body is mainly composed of 4 circulations (or 4 vortices) near the body. The steady streaming structure for a cylinder (Wang 1968;Van Dyke 1982) or a sphere (Rednikov & Sadhal 2004;Pacheco-Martinez et al 2013) consists of four small circulating cells attached on the body surface and four large outer ones further away from the body, when T * is small. For our case with T * = 4, the size of the inner circulations is comparable to the body size, since the fluid can travel a distance more than a in one oscillation period for T * = 4, according to (2.15).…”

Section: Stable Flow Regimementioning

confidence: 99%

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Numerical studies on the dynamics of an open triangle in a vertically oscillatory flow

Shao

Zhang

et al. 2016

J. Fluid Mech.

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A direct-forcing fictitious domain method is employed to study the dynamics of an open triangle in a vertically oscillatory flow. The flow structures, the vertical force and the torque on the fixed body are analysed for the stable flow regime in which the flow structures form and evolve exactly in the same way in each period and the unstable regime, respectively. Our results indicate that in the stable flow regime for the body with upright orientation, the steady streaming structure mainly comprises two vortex pairs located respectively above and below the body. Due to up-down asymmetry of the body, the pair below the body produces a larger vertical force on the body than the upper pair, which is mainly responsible for the non-zero average force at relatively high Reynolds numbers. The average force increases with increasing Reynolds number or increasing dimensionless period for the parameter range studied, due to the vortex effects. In the unstable regime, a vortex pair is ejected downward from each body edge. The irregular motion of the emitted vortices below the body leads to the irregular fluctuation of the vertical force. Regarding the torque on a tilted body, in the stable regime, the body experiences a restoring torque when its vertex angle is larger than a critical value being close to (and smaller than) 60 • , and otherwise a destructive torque, irrespective of the value of tilt angle. For a fixed vertex angle, the torque magnitude is largest when the tilt angle is around 45 • . In the unstable regime, the persistent ejection of the vortex pair during upward flow and corresponding restoring torque are observed for a large tilt angle with one edge aligned close to the horizontal direction, as in the experiment of Liu et al. (Phys. Rev. Lett., vol. 108, 2012, 068103). For a relatively small tilt angle, the emission direction of the vortex pair has intermittency, leading to the intermittency in the direction of torque. The reasons for the above observations are discussed. The predictions on the stable orientation for a hovering body in the stable flow regime and the irregular orientation in the unstable regime are confirmed in the dynamic simulation of a freely moving body. The body with the stable horizontal orientation in case of small vertex angle migrates along the body-shape-diverging direction.

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Section: Introductionmentioning

confidence: 94%

Section: Stable Flow Regimementioning

confidence: 99%

Numerical studies on the dynamics of an open triangle in a vertically oscillatory flow

Shao

Zhang

et al. 2016

J. Fluid Mech.

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“…In order to investigate the motion of the spheres and the fluid in detail we used simulations which were based on an embedded boundary method described previously [30][31][32][33][34]. The fluid was assumed to obey the NavierStokes equations which were discretised on a staggered mesh [35] and solved using the projection method [36] to ensure incompressibility of the fluid.…”

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confidence: 99%

Propulsion of a Two-Sphere Swimmer

et al. 2015

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We describe experiments and simulations demonstrating the propulsion of a neutrally-buoyant swimmer that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There appears to be a critical onset value of the streaming Reynolds number for swimming to occur. We observe a change in the streaming flows as the Reynolds number increases, from that generated by two independent oscillating spheres to a collective flow pattern around the swimmer as a whole. The mechanism for swimming is traced to a strengthening of a jet of fluid in the wake of the swimmer.

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“…As a further more recent example, by investigating experimentally the behaviour of two identical spheres suspended magnetically in a fluid to mimic weightless conditions, Pacheco-Martinez et al (2013) observed the spheres to spontaneously orbit each other under the influence of mutual attraction for sufficiently large vibration amplitudes.…”

Section: The Role Of Hydrodynamic and Electrostatic Interactionsmentioning

confidence: 97%

On the nature, formation and diversity of particulate coherent structures in microgravity conditions and their relevance to materials science and problems of astrophysical interest

Lappa

2016

Geophysical & Astrophysical Fluid Dynamics

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Different phenomena related to the spontaneous accumulation of solid particles dispersed in a fluid medium in microgravity conditions are discussed, with an emphasis on recent discoveries and potential links with the general field of astrophysical fluid-dynamics on the one hand, and with terrestrial applications in the field of materials science on the other hand. With special attention to the typical physical forces at play in such an environment, namely, surface-tension gradients, oscillatory residual gravity components, inertial disturbances and forces of an electrostatic nature, specific experimental and numerical examples are presented to provide inputs for an increased understanding of the underlying cause-and-effect relationships. Studying these systems can be seen as a matter of understanding how macroscopic scenarios arise from the cooperative behaviour of sub-parts or competing mechanisms (nonlinearities and interdependencies on various spatial and temporal scales). Through a critical assessment of the properties displayed by the resulting structures (which appear in the form of one-dimensional circuits formed by aligned particles, planar accumulation surfaces, three-dimensional compact structures resembling “quadrics”, micro-crystallites or fractal aggregates), we discuss a possible classification of the related particle attractors in the space of parameters according to the prevailing effect

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Spontaneous Orbiting of Two Spheres Levitated in a Vibrated Liquid

Cited by 19 publications

References 28 publications

Numerical studies on the dynamics of an open triangle in a vertically oscillatory flow

Numerical studies on the dynamics of an open triangle in a vertically oscillatory flow

Propulsion of a Two-Sphere Swimmer

On the nature, formation and diversity of particulate coherent structures in microgravity conditions and their relevance to materials science and problems of astrophysical interest

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