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arXiv · 1908.10631

Percolation transition of pusher-type microswimmers

Fabian Jan Schwarzendahl·Marco G. Mazza
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Abstract

We identify the presence of a continuum percolation transition in model suspensions of pusher-type microswimmers. The clusters dynamically aggregate and disaggregate resulting from a competition of attractive and repulsive hydrodynamic and steric interactions. As the microswimmers' filling fraction increases, the cluster size distribution approaches a scale-free form and there emerge large clusters spanning the entire system. We characterize this microswimmer percolation transition via the critical exponents associated to cluster size distribution $\tau$, correlation length $\nu$, mean cluster size $\gamma$, and clusters' fractal dimension $d_f$. We are able to show that two scaling relations, known from percolation theory, also hold for our microswimmers. A real-space renormalization group transformation can approximately predict the value of the exponent $\nu$. This finding opens new vistas on microswimmers' congregative processes.

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Fabian Jan Schwarzendahl, Marco G. Mazza. 2019-08-28. Percolation transition of pusher-type microswimmers. https://arxiv.org/abs/1908.10631

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