Jayant Pande

All good things come in threes—Three beads learn to swim with lattice Boltzmann and a rigid body solver

We simulate the self-propulsion of devices in a fluid in the regime of low Reynolds numbers. Each device consists of three bodies (spheres or capsules) connected with two damped harmonic springs. Sinusoidal driving forces compress the springs which are resolved within a rigid body physics engine. The latter is consistently coupled to a 3D lattice Boltzmann framework for the fluid dynamics. In simulations of three-sphere devices, we find that the propulsion velocity agrees well with theoretical predictions. In simulations where some or all spheres are replaced by capsules, we find that the asymmetry of the design strongly affects the propelling efficiency.

Lattice Boltzmann simulations of the bead- spring microswimmer with a responsive stroke— from an individual to swarms

Propulsion at low Reynolds numbers is often studied by defining artificial microswimmers which exhibit a particular stroke. The disadvantage of such an approach is that the stroke does not adjust to the environment, in particular the fluid flow, which can diminish the effect of hydrodynamic interactions. To overcome this limitation, we simulate a microswimmer consisting of three beads connected by springs and dampers, using the self-developed waLBerla and [Formula: see text] framework based on the lattice Boltzmann method and the discrete element method. In our approach, the swimming stroke of a swimmer emerges as a balance of the drag, the driving and the elastic internal forces. We validate the simulations by comparing the obtained swimming velocity to the velocity found analytically using a perturbative method where the bead oscillations are taken to be small. Including higher-order terms in the hydrodynamic interactions between the beads improves the agreement to the simulations in parts of the parameter space. Encouraged by the agreement between the theory and the simulations and aided by the massively parallel capabilities of the waLBerla-[Formula: see text] framework, we simulate more than ten thousand such swimmers together, thus presenting the first fully resolved simulations of large swarms with active responsive components.

Asymptotic expansions of the hypergeometric function with two large parameters—application to the partition function of a lattice gas in a field of traps

The canonical partition function of a two-dimensional lattice gas in a field of randomly placed traps, like many other problems in physics, evaluates to the Gauss hypergeometric function

Forces and shapes as determinants of micro-swimming: effect on synchronisation and the utilisation of drag

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Setting the pace of microswimmers: when increasing viscosity speeds up self-propulsion

in the limit when one or more of its parameters become large. This limit is difficult to compute from first principles, and finding the asymptotic expansions of the hypergeometric function is therefore an important task. While some possible cases of the asymptotic expansions of

Effect of body deformability on microswimming

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General asymptotic expansions of the hypergeometric function with two large parameters

have been provided in the literature, they are all limited by a narrow domain of validity, either in the complex plane of the variable or in the parameter space. Overcoming this restriction, we provide new asymptotic expansions for the hypergeometric function with two large parameters, which are valid for the entire complex plane of

When micro-swimmers get a spring in their stroke

z

Dynamics of magnetocapillary microswimmers: Lattice Boltzmann simulations

except for a few specific points. We show that these expansions work well even when we approach the possible singularity of

Microswimming with inertia

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