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Register a new userPeriodic motion of sedimenting flexible knots
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We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwined loops, oscillating periodically around each other. We then recover this motion numerically and find out that it is accompanied by a very slow rotation around the vertical symmetry axis. We analyze the dependence of the characteristic time scales on the chain flexibility and aspect ratio. It is observed in the experiments that this oscillating mode of the dynamics can spontaneously form even when starting from a qualitatively different initial configuration. In numerical simulations, the oscillating modes are usually present as transients or final stages of the evolution, depending on chain aspect ratio and flexibility, and the number of loops.
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An array of spheres descending slowly through a viscous fluid always clumps [J.M. Crowley, J. Fluid Mech. {bf 45}, 151 (1971)]. We show that anisotropic particle shape qualitatively transforms this iconic instability of collective sedimentation. In experiment and theory on disks, aligned facing their neighbours in a horizontal one-dimensional lattice and settling at Reynolds number $sim 10^{-4}$ in a quasi-two-dimensional slab geometry, we find that for large enough lattice spacing the coupling of disk orientation and translation rescues the array from the clumping instability. Despite the absence of inertia the resulting dynamics displays the wavelike excitations of a mass-and-spring array, with a conserved momentum in the form of the collective tilt of the disks and an emergent spring stiffness from the viscous hydrodynamic interaction. However, the non-normal character of the dynamical matrix leads to algebraic growth of perturbations even in the linearly stable regime. Stability analysis demarcates a phase boundary in the plane of wavenumber and lattice spacing, separating the regimes of algebraically growing waves and clumping, in quantitative agreement with our experiments. Anisotropic shape thus suppresses the classic linear instability of sedimenting sphere arrays, introduces a new conserved variable, and opens a window to the physics of transient growth of linearly stable modes.
Surface bound catalytic chemical reactions self-propel chemically active Janus particles. In the vicinity of boundaries, these particles exhibit rich behavior, such as the occurrence of wall-bound steady states of sliding. Most active particles tend to sediment as they are density mismatched with the solution. Moreover Janus spheres, which consist of an inert core material decorated with a cap-like, thin layer of a catalyst, are gyrotactic (bottom-heavy). Occurrence of sliding states near the horizontal walls depends on the interplay between the active motion and the gravity-driven sedimentation and alignment. It is thus important to understand and quantify the influence of these gravity-induced effects on the behavior of model chemically active particles moving near walls. For model gyrotactic, self-phoretic Janus particles, here we study theoretically the occurrence of sliding states at horizontal planar walls that are either below (floor) or above (ceiling) the particle. We construct state diagrams characterizing the occurrence of such states as a function of the sedimentation velocity and of the gyrotactic response of the particle, as well as of the phoretic mobility of the particle. We show that in certain cases sliding states may emerge simultaneously at both the ceiling and the floor, while the larger part of the experimentally relevant parameter space corresponds to particles that would exhibit sliding states only either at the floor or at the ceiling or there are no sliding states at all. These predictions are critically compared with the results of previous experimental studies and our experiments conducted on Pt-coated polystyrene and silica-core particles suspended in aqueous hydrogen peroxide solutions.
The interaction between swimming microorganisms or artificial self-propelled colloids and passive (tracer) particles in a fluid leads to enhanced diffusion of the tracers. This enhancement has attracted strong interest, as it could lead to new strategies to tackle the difficult problem of mixing on a microfluidic scale. Most of the theoretical work on this topic has focused on hydrodynamic interactions between the tracers and swimmers in a bulk fluid. However, in simulations, periodic boundary conditions (PBCs) are often imposed on the sample and the fluid. Here, we theoretically analyze the effect of PBCs on the hydrodynamic interactions between tracer particles and microswimmers. We formulate an Ewald sum for the leading-order stresslet singularity produced by a swimmer to probe the effect of PBCs on tracer trajectories. We find that introducing periodicity into the system has a surprisingly significant effect, even for relatively small swimmer-tracer separations. We also find that the bulk limit is only reached for very large system sizes, which are challenging to simulate with most hydrodynamic solvers.
The dynamics of a triangular magnetocapillary swimmer is studied using the lattice Boltzmann method. Performing extensive numerical simulations taking into account the coupled dynamics of the fluid-fluid interface and of magnetic particles floating on it and driven by external magnetic fields we identify several regimes of the swimmer motion. In the regime of high frequencies the swimmers maximum velocity is centered around the particles inverse coasting time. Modifying the ratio of surface tension and magnetic forces allows to study the swimmer propagation in the regime of significantly lower frequencies mainly defined by the strength of the magnetocapillary potential. Finally, introducing a constant magnetic contribution in each of the particles in addition to their magnetic moment induced by external fields leads to another regime characterised by strong in-plane swimmer reorientations that resemble experimental observations.
Terrestrial experiments on active particles, such as Volvox, involve gravitational forces, torques and accompanying monopolar fluid flows. Taking these into account, we analyse the dynamics of a pair of self-propelling, self-spinning active particles between widely separated parallel planes. Neglecting flow reflected by the planes, the dynamics of orientation and horizontal separation is symplectic, with a Hamiltonian exactly determining limit cycle oscillations. Near the bottom plane, gravitational torque damps and reflected flow excites this oscillator, sustaining a second limit cycle that can be perturbatively related to the first. Our work provides a theory for dancing Volvox and highlights the importance of monopolar flow in active matter.
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