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SUMMARY:Collective Hydrodynamics of Swimming Micro-Organisms - Tim Pedley 
 (Department of Applied Mathematics and Theoretical Physics)
DTSTART:20080521T102000Z
DTEND:20080521T110500Z
UID:TALK11839@talks.cam.ac.uk
CONTACT:Danielle Stretch
DESCRIPTION:Since the work of Kessler in the 1980s\, and before\, there ha
 s been\nconsiderable interset among fluid dynamicists and physicists in th
 e\ncollective behaviour of swimming micro-organisms in suspension. Since\n
 all such cells are denser than the water in which they swim\,\nbioconvecti
 on patterns result from upswimming of cells in a chamber of\nfinite depth 
 and from gyrotaxis of bottom-heavy cells in a uniform\nfluid. Bioconvectio
 n has been analysed for dilute suspensions\; the\ntheory will be briefly r
 e-examined with emphasis on the additional\nstress induced by the cells' s
 wimming motions (each cell can be\nregarded as a force-dipole\, or stressl
 et)\, because of the new\ninstabilities revealed by Simha & Ramaswamy (200
 2) for uniform\nsuspensions in the absence of gravity.\n\nEven more fascin
 ating coherent structures arise in concentrated\nsuspensions\, of bacteria
  for example\, in which cell-cell interactions\ncannot be ignored. The hyp
 othesis is that such structures emerge from\npurely hydrodynamic interacti
 ons between cells. A variety of models\nhave been developed\, which are ou
 tlined briefly\, but particular\nattention will be paid to our own model i
 n which cells are represented\nas inertia-free "spherical squirmers"\, who
 se behaviour is dominated by\nnear-field hydrodynamics. Pairwise interacti
 ons are computed\nprecisely\, and Stokesian dynamics in a periodic box is 
 used to\nsimulate an infinite suspension. Trajectories are computed\ndeter
 ministically\, but the long-time spreading of a 3D suspension\,\nfrom rand
 om initial conditions\, is diffusive\; scaling arguments can be\nused to e
 stimate the effective diffusivity. However\, in 2D there is a\nstrong tend
 ency towards aggregation into clumps or bands. [Recent work\nreported here
  has been performed in collaboration with T Ishikawa and\nJ T Locsei.]\n
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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