Chain formation of spheres in oscillatory fluid flows

Abstract

A collection of spherical particles subjected to horizontal oscillatory fluid flow is known to form chains perpendicular to the direction of the oscillation. We have developed computer simulations to model such a system and have validated them against experiments carried out in a small fluid-filled cell. In both experiment and simulation we find that the particles go through the same stages of evolution from a dispersed initial configuration to an ordered chain structure. We then use our computer simulations to investigate in detail the interactions responsible for chain formation and the interaction between fully formed chains.

Propulsion of a Two-Sphere Swimmer

“…It would be of interest to make a fully self-propelled swimmer based on the relative vibration of two spheres, driven by an internal linear motor, since such swimmers would not be constrained to move along one axis. Collections of such swimmers might be expected to exhibit interesting cooperative behaviour induced by interacting streaming flows [30,32,33,38,39]. …”

“…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.…”

Spontaneous Orbiting of Two Spheres Levitated in a Vibrated Liquid

“…Under vertical vibration the spheres are attracted to each other and align so that the line joining their centers lies perpendicular to the axis of vibration [2][3][4][5]. As the amplitude of vibration is increased beyond a critical value, the spheres orbit each other in the horizontal plane, with no preferred sense of rotation.…”

“…Ordinarily, such experiments are limited to twodimensional ordering due to the presence of gravity, either with the particles on a surface [2][3][4][5][6], confined to the interface between two immiscible liquids [7,8], or suspended in the liquid via a rod [9][10][11][12]. In a zero-gravity environment, such as on the International Space Station, three-dimensional suspensions of particles have been used in crystal growth [13,14].…”

“…In order to more fully understand the streaming flows and the cause of the instability we carried out simulations based on a molecular-dynamics treatment of the particles coupled to a numerical solution of the continuum Navier-Stokes equations for the fluid. Details of the simulation method and its validation can be found in references [3,5,27] and in the supplementary information [19].…”