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Register a new userShape transition and propulsive force of an elastic rod rotating in a viscous fluid
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The deformation of thin rods in a viscous liquid is central to the mechanics of motility in cells ranging from textit{Escherichia coli} to sperm. Here we use experiments and theory to study the shape transition of a flexible rod rotating in a viscous fluid driven either by constant torque or at constant speed. The rod is tilted relative to the rotation axis. At low applied torque, the rod bends gently and generates small propulsive force. At a critical torque, the rotation speed increases abruptly and the rod forms a helical shape with much greater propulsive force. We find good agreement between theory and experiment.
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When a rod is vertically withdrawn from a granular layer, oblique force chains can be developed by effective shearing. In this study, the force-chain structure in a rod-withdrawn granular layer was experimentally investigated using a photoelastic technique. The rod is vertically withdrawn from a two-dimensional granular layer consisting of bidisperse photoelastic disks. During the withdrawal, the development process of force chains is visualized by the photoelastic effect. By systematic analysis of photoelastic images, force chain structures newly developed by the rod withdrawing are identified and analyzed. In particular, the relation between the rod-withdrawing force $F_mathrm{w}$, total force-chains force $F_mathrm{t}$, and their average orientation $theta$ are discussed. We find that the oblique force chains are newly developed by withdrawing. The force-chain angle $theta$ is almost constant (approximately $20^{circ}$ from the horizontal), and the total force $F_mathrm{t}$ gradually increases by the withdrawal. In addition, $F_mathrm{t}sintheta$ shows a clear correlation with $F_mathrm{w}$.
We measure the drag encountered by a vertically oriented rod moving across a sedimented granular bed immersed in a fluid under steady-state conditions. At low rod speeds, the presence of the fluid leads to a lower drag because of buoyancy, whereas a significantly higher drag is observed with increasing speeds. The drag as a function of depth is observed to decrease from being quadratic at low speeds to appearing more linear at higher speeds. By scaling the drag with the average weight of the grains acting on the rod, we obtain the effective friction $mu_e$ encountered over six orders of magnitude of speeds. While a constant $mu_e$ is found when the grain size, rod depth and fluid viscosity are varied at low speeds, a systematic increase is observed as the speed is increased. We analyze $mu_e$ in terms of the inertial number $I$ and viscous number $J$ to understand the relative importance of inertia and viscous forces, respectively. For sufficiently large fluid viscosities, we find that the effect of varying the speed, depth, and viscosity can be described by the empirical function $mu_e = mu_o + k J^n$, where $mu_o$ is the effective friction measured in the quasi-static limit, and $k$ and $n$ are material constants. The drag is then analyzed in terms of the effective viscosity $eta_e$ and found to decrease systematically as a function of $J$. We further show that $eta_e$ as a function of $J$ is directly proportional to the fluid viscosity and the $mu_e$ encountered by the rod.
Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance to bending and the self-propulsion strength of the active components in solution. We show how flexible membranes tend to collapse into multi-folded states, whereas stiff membranes oscillates between an extended configuration and a singly folded state. This study provides a simple example of how to exploit the random motion of active particles to perform mechanical work at the micro-scale.
The viscous drag on a slender rod by a wall is important to many biological and industrial systems. This drag critically depends on the separation between the rod and the wall and can be approximated asymptotically in specific regimes, namely far from, or very close to, the wall, but is typically determined numerically for general separations. In this note we determine an asymptotic representation of the local drag for a slender rod parallel to a wall which is valid for all separations. This is possible through matching the behaviour of a rod close to the wall and a rod far from the wall. We show that the leading order drag in both these regimes has been known since 1981 and that they can used to produce a composite representation of the drag which is valid for all separations. This is in contrast to a sphere above a wall, where no simple uniformly valid representation exists. We estimate the error on this composite representation as the separation increases, discuss how the results could be used as resistive-force theory and demonstrate their use on a two-hinged swimmer above a wall.
Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2 or 4 regular horizontal polygons (called `rings) centred above or below each other. Two rings fall together and periodically oscillate. Four rings usually separate from each other with chaotic scattering. For hundreds of thousands of initial configurations, a map of the cluster lifetime is evaluated, where the long-lasting clusters are centred around periodic solutions for the relative motions, and surrounded by regions of the chaotic scattering,in a similar way as it was observed by Janosi et al. (1997) for three particles only. These findings suggest to consider the existence of periodic orbits as a possible physical mechanism of the existence of unstable clusters of particles falling under gravity in a viscous fluid.
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