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Register a new userA basic swimmer at low Reynolds number
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Authors
M. Leoni
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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.
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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 design and simulate the motion of a new swimmer, the {it Quadroar}, with three dimensional translation and reorientation capabilities in low Reynolds number conditions. The Quadroar is composed of an $texttt{I}$-shaped frame whose body link is a simple linear actuator, and four disks that can rotate about the axes of flange links. The time symmetry is broken by a combination of disk rotations and the one-dimensional expansion/contraction of the body link. The Quadroar propels on forward and transverse straight lines and performs full three dimensional reorientation maneuvers, which enable it to swim along arbitrary trajectories. We find continuous operation modes that propel the swimmer on planar and three dimensional periodic and quasi-periodic orbits. Precessing quasi-periodic orbits consist of slow lingering phases with cardioid or multiloop turns followed by directional propulsive phases. Quasi-periodic orbits allow the swimmer to access large parts of its neighboring space without using complex control strategies. We also discuss the feasibility of fabricating a nano-scale Quadroar by photoactive molecular rotors.
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.
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.
Inspired by recent experiments using synthetic microswimmers to manipulate droplets, we investigate the low-Reynolds-number locomotion of a model swimmer (a spherical squirmer) encapsulated inside a droplet of comparable size in another viscous fluid. Meditated solely by hydrodynamic interactions, the encaged swimmer is seen to be able to propel the droplet, and in some situations both remain in a stable co-swimming state. The problem is tackled using both an exact analytical theory and a numerical implementation based on boundary element method, with a particular focus on the kinematics of the co-moving swimmer and droplet in a concentric configuration, and we obtain excellent quantitative agreement between the two. The droplet always moves slower than a swimmer which uses purely tangential surface actuation but when it uses a particular combination of tangential and normal actuations, the squirmer and droplet are able to attain a same velocity and stay concentric for all times. We next employ numerical simulations to examine the stability of their concentric co-movement, and highlight several stability scenarios depending on the particular gait adopted by the swimmer. Furthermore, we show that the droplet reverses the nature of the far-field flow induced by the swimmer: a droplet cage turns a pusher swimmer into a puller, and vice versa. Our work sheds light on the potential development of droplets as self-contained carriers of both chemical content and self-propelled devices for controllable and precise drug deliveries.
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