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How hydrodynamics influences the collective motion of microswimmers: A particle-based simulation study

Subject Area Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Term from 2014 to 2023
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 254465319
 
Final Report Year 2021

Final Report Abstract

Microswimmers such as bacteria move in a fluid environment, where they generate flow fields with which they interact with bounding surfaces and neighboring microswimmers. Within the six-years period of the SPP: Microswimmers - From Single Particle Motion to Collective Behavior, our goal was to perform full hydrodynamic simulations of a collection of model microswimmers called squirmers to explore their emergent collective dynamics in different settings due to their hydrodynamic interactions. For solving the Navier-Stokes equations that govern fluid flow also in the relevant limit of small Reynolds numbers, where inertia is negligible, we used the mesoscopic method called multi-particle collision dynamics. During the six-years period of the SPP we published a total of 13 publications on topics connected to the project including the Topical Review. The model microswimmer squirmer is a spherical particle with a prescribed velocity field on its surface, which propels the squirmer through the fluid. With the two leading velocity modes, one can adjust the squirmer to assume one of the relevant microswimmer types: neutral or pusher/puller. The squirmer was introduced by Lighthill in 1952 and later by Blake to model ciliated microswimmers. In our project, we first studied the landmark of activity, the motility-induced phase separation, where self-propelled particles at sufficiently high density and swimming velocity phase separate into a dilute gas and a dense cluster phase. In our work we saw clear indications for the importance of fluid flow since the binodal to the gas phase depends on mean density. Furthermore, we could clarify the difference of swim pressure between the two phases. It is due to squirmers at the cluster boundary that try to pump fluid out of the cluster. A large portion of the project work was devoted to study squirmers under gravity. Already a single squirmer has quite an involved dynamic if its swimming velocity is smaller than its bulk sedimentation velocity. Due to hydrodynamic interactions with the surface, the swimming velocity of a neutral squirmer points upwards and floats above the bottom surface with frequent excursion downwards when the swimming velocity tilts due to thermal noise. For strong pullers we see wall pinning and for strong pushers recurrent floating and sliding. Away from boundaries, single microswimmers show an exponential sedimentation profile. However, when simulating a large collection of the squirmers, we also observed a region with an exponential density profile, which is not at all obvious. The density profile is very dynamic and convection cells due collective squirmer motion are visible. Under very strong gravity and smaller squirmer number, a single monolayer of squirmers forms at the bottom surface. Depending on the squirmer type and mean area density, one observes a variety of different dynamic structures. Besides kissing and (chaotically) swarming squirmers, the most appealing one is a hydrodynamic Wigner fluid, where upwards pointing squirmers repel each other due to flow fields from their neighbors. Finally, making the squirmers bottom-heavy so that a torque acts, which aligns the swimming direction upwards, we observed further emergent collective dynamics. First, the exponential sedimentation profile becomes inverted for sufficiently large swimming velocities. Second, for large torques and smaller swimming velocities a porous cluster occurs that floats above the bottom surfaces, from which single squirmers spawn. Third and most interestingly, for medium torques and swimming velocities squirmer convection rolls develop at the bottom surface that are fed by plumes of collectively sinking squirmers. For all this gyrotaxis a combination of sensing gravity and reorienting by flow is relevant. The article was selected as EPJE highlight and chosen as "front cover picture". Towards the end of the project, we started to investigate squirmer rods made from squirmers linked together, which model, for example, E. coli bacteria. Depending on aspect ratio, area density, and swimmer type, swarms and jammed/dynamic clusters are observed. Most interestingly, pusher rods show active turbulence at intermediate densities, as a compromise between disordering hydrodynamic and aligning steric interactions.

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