Micro-swimmer collective dynamics in Brinkman flows
arxiv(2024)
摘要
Suspensions of swimming micro-organisms are known to undergo intricate
collective dynamics as a result of hydrodynamic and collision interactions.
Micro-swimmers, such as bacteria and micro-algae, naturally live and have
evolved in complex habitats that include impurities, obstacles and interfaces.
To elucidate their dynamics in a heterogeneous environment, we consider a
continuum theory where the the micro-swimmers are embedded in a Brinkman wet
porous medium, which models viscous flow with an additional resistance or
friction due to the presence of smaller stationary obstacles. The conservation
equation for the swimmer configurations includes advection and rotation by the
immersing fluid, and is coupled to the viscous Brinkman fluid flow with an
active stress due to the swimmers' motion in it. Resistance alters individual
swimmer locomotion and the way it disturbs the surrounding fluid, and thus it
alters its hydrodynamic interactions with others and and such affects
collective dynamics.The entropy analysis and the linear stability analysis of
the system of equations both reveal that resistance delays and hinders the
onset and development of the collective swimming instabilities, and can
completely suppress it if sufficiently large. Simulations of the full nonlinear
system confirm these. We contrast the results with previous theoretical studies
on micro-swimmers in homogeneous viscous flow, and discuss relevant
experimental realizations.
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