Hydrodynamic instabilities in a two-dimensional sheet of microswimmers embedded in a three-dimensional fluid

被引:3
|
作者
Skultety, Viktor [1 ]
Bardfalvy, Dora [2 ]
Stenhammar, Joakim [2 ]
Nardini, Cesare [3 ,4 ]
Morozov, Alexander [1 ]
机构
[1] Univ Edinburgh, Sch Phys & Astron, SUPA, James Clerk Maxwell Bldg,Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Scotland
[2] Lund Univ, Div Phys Chem, Box 124, S-22100 Lund, Sweden
[3] CEA Saclay, Serv Phys Etat Condense, CNRS UMR 3680, F-91191 Gif Sur Yvette, France
[4] Sorbonne Univ, CNRS, Lab Phys Theor Mat Condensee, F-75005 Paris, France
基金
瑞典研究理事会; 英国工程与自然科学研究理事会;
关键词
collective behaviour; micro-organism dynamics; Stokesian dynamics; COLLECTIVE MOTION; MICRO-SWIMMERS; BACTERIAL; DIFFUSION; SUSPENSIONS; RHEOLOGY;
D O I
10.1017/jfm.2023.985
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
A collection of microswimmers immersed in an incompressible fluid is characterised by strong interactions due to the long-range nature of the hydrodynamic fields generated by individual organisms. As a result, suspensions of rear-actuated 'pusher' swimmers such as bacteria exhibit a collective motion state often referred to as 'bacterial turbulence', characterised by large-scale chaotic flows. The onset of collective motion in pusher suspensions is classically understood within the framework of mean-field kinetic theories for dipolar swimmers. In bulk two and three dimensions, the theory predicts that the instability leading to bacterial turbulence is due to mutual swimmer reorientation and sets in at the largest length scale available to the suspension. Here, we construct a similar kinetic theory for the case of a dipolar microswimmer suspension restricted to a two-dimensional plane embedded in a three-dimensional incompressible fluid. This setting qualitatively mimics the effect of swimming close to a two-dimensional interface. We show that the in-plane flow fields are effectively compressible in spite of the incompressibility of the three-dimensional bulk fluid, and that microswimmers on average act as sources (pushers) or sinks (pullers). We analyse the stability of the homogeneous and isotropic state, and find two types of instability that are qualitatively different from the bulk, three-dimensional case: first, we show that the analogue of the orientational pusher instability leading to bacterial turbulence in bulk systems instead occurs at the smallest length scale available to the system. Second, an instability associated with density variations arises in puller suspensions as a generic consequence of the effective in-plane compressibility. Given these qualitative differences with respect to the standard bulk setting, we conclude that confinement can have a crucial role in determining the collective behaviour of microswimmer suspensions.
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页数:23
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