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Register a new userFeeling, following, feeding, fleeing: a copepods life at low Reynolds number
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In this fluid dynamics video, we present various aspects of copepod behavior at low Re.
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It has been known for some time that some microorganisms can swim faster in high-viscosity gel-forming polymer solutions. These gel-like media come to mimic highly viscous heterogeneous environment that these microorganisms encounter in-vivo. The qualitative explanation of this phenomena first offered by Berg and Turner [Nature (London) 278, 349 (1979)], suggests that propulsion enhancement is a result of flagellum pushing on quasi-rigid loose polymer network formed in some polymer solutions. Inspired by these observations, inertia-less propulsion in a heterogeneous viscous medium composed of sparse array of stationary obstacles embedded into incompressible Newtonian liquid is considered. It is demonstrated that for prescribed propulsion gaits, including propagating surface distortions and rotating helical filament, the propulsion speed is enhanced when compared to swimming in purely viscous solvent. It is also shown that the locomotion in heterogenous viscous media is characterized by improved hydrodynamic efficiency. The results of the rigorous numerical simulation of the rotating helical filament propelled through a random sparse array of stationary obstructions are in close agreement with predictions of the proposed resistive force theory based on effective media approximation.
Recent experiments have demonstrated that small-scale rotary devices installed in a microfluidic channel can be driven passively by the underlying flow alone without resorting to conventionally applied magnetic or electric fields. In this work, we conduct a theoretical and numerical study on such a flow-driven watermill at low Reynolds number, focusing on its hydrodynamic features. We model the watermill by a collection of equally-spaced rigid rods. Based on the classical resistive force (RF) theory and direct numerical simulations, we compute the watermills instantaneous rotational velocity as a function of its rod number $N$, position and orientation. When $N geq 4$, the RF theory predicts that the watermills rotational velocity is independent of $N$ and its orientation, implying the full rotational symmetry (of infinity order), even though the geometrical configuration exhibits a lower-fold rotational symmetry; the numerical solutions including hydrodynamic interactions show a weak dependence on $N$ and the orientation. In addition, we adopt a dynamical system approach to identify the equilibrium positions of the watermill and analyse their stability. We further compare the theoretically and numerically derived rotational velocities, which agree with each other in general, while considerable discrepancy arises in certain configurations owing to the hydrodynamic interactions neglected by the RF theory. We confirm this conclusion by employing the RF-based asymptotic framework incorporating hydrodynamic interactions for a simpler watermill consisting of two or three rods and we show that accounting for hydrodynamic interactions can significantly enhance the accuracy of the theoretical predictions.
In this study, we use numerical simulations to investigate the flow field induced by a single magnetic microrobot rotating with a constant angular speed about an axis perpendicular to an underlying surface. A parallel solver for steady Stokes flow equations based on the boundary-element method is used for simulating these flows. A simple transformation is introduced to extend the predictive capability of the solver to cases with small unsteadiness. Flows induced by four simple robot shapes are investigated: sphere, upright cylinder, horizontally-laid cylinder, and five-pointed star-shaped prism. Shapes with cross-sections that are axisymmetric about the rotation axis (sphere and upright cylinder) generate time-invariant flow fields, which could be useful for applications such as micromanipulation. Non-axisymmetric shapes (horizontally-laid cylinder and the star-shaped prism) induce significant unsteadiness inside the flow field, which could be desirable for applications such as micromixing. Furthermore, a slender horizontally-laid cylinder generates substantially three-dimensional flows, an added benefit for micromixing applications. The presence of nearby walls such as a bottom substrate or sidewalls has a retarding effect on the induced flows, which is quantified. Finally, we present the driving torque and power-consumption of these microrobots rotating in viscous liquids. The numerical modeling platform used in this work can enable future optimal microrobot designs for a given application requirement.
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 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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