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Register a new userScattering of low Reynolds number swimmers
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We describe the consequences of time reversal invariance of the Stokes equations for the hydrodynamic scattering of two low Reynolds number swimmers. For swimmers that are related to each other by a time reversal transformation this leads to the striking result that the angle between the two swimmers is preserved by the scattering. The result is illustrated for the particular case of a linked-sphere model swimmer. For more general pairs of swimmers, not related to each other by time reversal, we find hydrodynamic scattering can alter the angle between their trajectories by several tens of degrees. For two identical contractile swimmers this can lead to the formation of a bound state.
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In their search for metabolic resources microbes swim through viscous environments that present physical anisotropies, including steric obstacles across a wide range of sizes. Hydrodynamic forces are known to significantly alter swimmer trajectories near flat and low-curvature surfaces. In this work, we imaged hundreds-of-thousands of high-curvature scattering interactions between swimming bacteria and micro-fabricated pillars with radii from ~1 to ~10 cell lengths. As a function of impact parameter, cell-pillar interactions produced distinct chiral distributions for scattering angle -- including unexpected counter-rotator trajectories -- well-described by a sterics-only model. Our data and model suggest that alteration of swimmer trajectories is subject to distinct mechanisms when interacting with objects of different size; primarily steric for objects below ~10 cell lengths and requiring incorporation of hydrodynamics at larger scales. These alterations in trajectory impact swim dynamics and may affect microbial populations in ways that depend on the shape and placement of obstacles within an environment.
In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of non-reciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a bi-flagellated sphere at low Re via Quincke rotation. These Quincke swimmers exhibit three different forms of motion, including a self-oscillatory state due to elasto-electro-hydrodynamic interactions. Each form of motion follows a distinct trajectory in space. Our experiments and numerical results demonstrate a new method to generate, and potentially control, the locomotion of artificial flagellated swimmers.
Swimming and pumping at low Reynolds numbers are subject to the Scallop theorem, which states that there will be no net fluid flow for time reversible motions. Living organisms such as bacteria and cells are subject to this constraint, and so are existing and future artificial nano-bots or microfluidic pumps. We study a very simple mechanism to induce fluid pumping, based on the forced motion of three colloidal beads through a cycle that breaks time-reversal symmetry. Optical tweezers are used to vary the inter-bead distance. This model is inspired by a strut-based theoretical swimmer proposed by Najafi and Golestanian [Phys.Rev. E, 69, 062901, 2004], but in this work the relative softness of the optical trapping potential introduces a new control parameter. We show that this system is able to generate flow in a controlled fashion, characterizing the model experimentally and numerically.
We investigate the hydrodynamic interactions between microorganisms swimming at low Reynolds number. By considering simple model swimmers, and combining analytic and numerical approaches, we investigate the time-averaged flow field around a swimmer. At short distances the swimmer behaves like a pump. At large distances the velocity field depends on whether the swimming stroke is invariant under a combined time-reversal and parity transformation. We then consider two swimmers and find that the interaction between them consists of two parts; a dead term, independent of the motion of the second swimmer, which takes the expected dipolar form and a live term resulting from the simultaneous swimming action of both swimmers which does not. We argue that, in general, the latter dominates. The swimmer--swimmer interaction is a complicated function of their relative displacement, orientation and phase, leading to motion that can be attractive, repulsive or oscillatory.
We introduce a generic model of weakly non-linear self-sustained oscillator as a simplified tool to study synchronisation in a fluid at low Reynolds number. By averaging over the fast degrees of freedom, we examine the effect of hydrodynamic interactions on the slow dynamics of two oscillators and show that they can lead to synchronisation. Furthermore, we find that synchronisation is strongly enhanced when the oscillators are non-isochronous, which on the limit cycle means the oscillations have an amplitude-dependent frequency. Non-isochronity is determined by a nonlinear coupling $alpha$ being non-zero. We find that its ($alpha$) sign determines if they synchronise in- or anti-phase. We then study an infinite array of oscillators in the long wavelength limit, in presence of noise. For $alpha > 0$, hydrodynamic interactions can lead to a homogeneous synchronised state. Numerical simulations for a finite number of oscillators confirm this and, when $alpha <0$, show the propagation of waves, reminiscent of metachronal coordination.
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