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Register a new userEfficiency of surface-driven motion: nano-swimmers beat micro-swimmers
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Surface interactions provide a class of mechanisms which can be employed for propulsion of micro- and nanometer sized particles. We investigate the related efficiency of externally and self-propelled swimmers. A general scaling relation is derived showing that only swimmers whose size is comparable to, or smaller than, the interaction range can have appreciable efficiency. An upper bound for efficiency at maximum power is 1/2. Numerical calculations for the case of diffusiophoresis are found to be in good agreement with analytical expressions for the efficiency.
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A system of ferromagnetic particles trapped at a liquid-liquid interface and subjected to a set of magnetic fields (magnetocapillary swimmers) is studied numerically using a hybrid method combining the pseudopotential lattice Boltzmann method and the discrete element method. After investigating the equilibrium properties of a single, two and three particles at the interface, we demonstrate a controlled motion of the swimmer formed by three particles. It shows a sharp dependence of the average center-of-mass speed on the frequency of the time-dependent external magnetic field. Inspired by experiments on magnetocapillary microswimmers, we interpret the obtained maxima of the swimmer speed by the optimal frequency centered around the characteristic relaxation time of a spherical particle. It is also shown that the frequency corresponding to the maximum speed grows and the maximum average speed decreases with increasing inter-particle distances at moderate swimmer sizes. The findings of our lattice Boltzmann simulations are supported by bead-spring model calculations.
Small objects can swim by generating around them fields or gradients which in turn induce fluid motion past their surface by phoretic surface effects. We quantify for arbitrary swimmer shapes and surface patterns, how efficient swimming requires both surface ``activity to generate the fields, and surface ``phoretic mobility. We show in particular that (i) swimming requires symmetry breaking in either or both of the patterns of activity and ``mobility, and (ii) for a given geometrical shape and surface pattern, the swimming velocity is size-independent. In addition, for given available surface properties, our calculation framework provides a guide for optimizing the design of swimmers.
We investigate the way in which oscillating dumb-bells, a simple microscopic model of apolar swimmers, move at low Reynolds number. In accordance with Purcells Scallop Theorem a single dumb-bell cannot swim because its stroke is reciprocal in time. However the motion of two or more dumb-bells, with mutual phase differences, is not time reversal invariant, and hence swimming is possible. We use analytical and numerical solutions of the Stokes equations to calculate the hydrodynamic interaction between two dumb-bell swimmers and to discuss their relative motion. The cooperative effect of interactions between swimmers is explored by considering first regular, and then random arrays of dumb-bells. We find that a square array acts as a micropump. The long time behaviour of suspensions of dumb-bells is investigated and compared to that of model polar swimmers.
Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the difficulty in modeling the temporally long-lived hydrodynamic interactions between many dynamic bodies. We address this through a novel discrete-time dynamical system (iterated map) that describes the hydrodynamic interactions between flapping swimmers arranged in one- and two-dimensional lattice formations. Our 1D results exhibit good agreement with previously published experimental data, in particular predicting the bistability of schooling states and new instabilities that can be probed in experimental settings. For 2D lattices, we determine the formations for which swimmers optimally benefit from hydrodynamic interactions. We thus obtain the following hierarchy: while a side-by-side single-row phalanx formation offers a small improvement over a solitary swimmer, 1D in-line and 2D rectangular lattice formations exhibit substantial improvements, with the 2D diamond lattice offering the largest hydrodynamic benefit. Generally, our self-consistent modeling framework may be broadly applicable to active systems in which the collective dynamics is primarily driven by a fluid-mediated memory.
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.
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