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PIV Studies of the Zooming Bionematic Phase

PIV Studies of the Zooming Bionematic Phase. Luis Cisneros Department of Physics University of Arizona. NSF: MCB (NER). Chris Dombrowski John O. Kessler Raymond E. Goldstein. Earlier work: Dombrowski, et al., PRL 93, 098103 (2004). Advection, Dissipation & Diffusion:

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PIV Studies of the Zooming Bionematic Phase

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  1. PIV Studies of the Zooming Bionematic Phase Luis Cisneros Department of Physics University of Arizona NSF: MCB (NER) Chris Dombrowski John O. Kessler Raymond E. Goldstein Earlier work: Dombrowski, et al., PRL 93, 098103 (2004)

  2. Advection, Dissipation & Diffusion: Reynolds and Peclet Numbers Navier-Stokes equations: Passive scalar dynamics: Reynolds number: Peclet number: If U=10 mm/s, L=10 mm, Re ~ 10-4, Pe ~ 10-1 At the scale of an individual bacterium, dissipation dominates inertia, and diffusion dominates. With multicellularity, Pe > or >> 1.

  3. Self-Concentration and the Chemotactic Boycott Effect 2 mm Video ~100x actual speed Dombrowski, et al. (2004); Tuval, et al. (2005)

  4. Experimental Details Bacterial protocols using B. subtilis strain 1085 (and various mutants) Simple: Overnight growth in Terrific Broth in a still petri dish More controlled: Start with -20o C stock, prepared from spores stored on sand. [Add to TB at RT, 24h of growth, 1 ml + 50 ml TB, incubated for 18 h. Then 1 ml + 50 ml TB, incubated for 5 hrs. 0.75 ml + 0.25 ml glycerol]. 1 ml of -20o stock + 50 ml TB, incubate for 18 h (shaker bath, 37o, 100 rpm), then 1 ml + 50 ml TB (5 hr), then into chamber Fluorescent microspheres (Molecular Probes, Nile Red, 0.1-2.0 mm)

  5. The ZBN in Brightfield and Fluorescence 210 mm

  6. Peclet number ~10-100 (vs. 0.01-0.1 for individual bacterium) Velocity Field from Cinemagraphic PIV 35mm Dombrowski, et al. (2004). See also Wu and Libchaber (2000)

  7. The ZBN in Brightfield and Fluorescence 210 mm

  8. PIV Velocity Field 210 mm

  9. Streamlines (Note intermittency) 210 mm

  10. Velocity-Velocity Correlation Function (spatial) I(r) r (mm)

  11. Velocity-Velocity Correlation Function (temporal) J(t) t (s)

  12. Vorticity (homage a Miró) 210 mm

  13. Summary: Peclet Number Revisited In the Zooming Bionematic (ZBN) phase, there are large coherent regions of high-speed swimming, whose internal fluid velocities and scale generate an effective diffusion constant DZBN =L2/T~10-4 cm2/s which is an order of magnitude larger than the molecular oxygen diffusion constant. Alternatively, the (chaotic) Peclet number is >> 1. In the ZBN, the bacterial concentration is so high that dissolved oxygen is used up in the time T~1 s, matching the time scale of the coherent structures.

  14. Side Views of Sessile Drops drop Tuval, et al. PNAS 102, 227 (2005)

  15. Bacterial Swimming and Chemotaxis (Macnab and Ornstein, 1977) Real-time Imaging of Fluorescent Flagella 1-4mm 10-20mm 20 nm Turner, Ryu, and Berg, J. Bacteriol. 182, 2793 (2000) “normal = LH helix “curly” = RH helix “straight” = straight Swimming speed ~10mm/s Propulsive force ~1 pN

  16. Swimming Near the Contact Line

  17. Bacterial Bioconvection J.O. Kessler

  18. The Chemotactic Boycott Effect 1 cm Dombrowski, Cisneros, Chatkaew, Goldstein, and Kessler, PRL 93, 098103 (2004)

  19. Mechanism of Self-Concentration Dombrowski, et al. (2004)

  20. Flocking models (Toner and Tu, 1995, …; traffic flow…) Historical Ideas A Landau theory in the velocity field – clever but not relevant to the physics of Stokes flow • Sedimentation (interacting Stokeslets) as few as three particles exhibit chaotic trajectories (Janosi, et al., 1997) • Conventional chemotaxis picture (e.g. Keller-Segel) - MISSES ADVECTION Velocity field must be determined self-consistently with density field • A synthesis is emerging from coarse-grained models of sedimentation • (Bruinsma, et al.) and self-propelled objects (Ramaswamy, et al. 2002, 2004)… IMPLICATIONS FOR QUORUM SENSING…

  21. Side Views of Sessile Drops Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, preprint (2004)

  22. Side Views: Depletion and Flow 2 mm Dombrowski, et al. (2004)

  23. Circulation Near the “Nose” Self-trapping in the corner

  24. Diffusion and Chemotaxis Oxygen diffusion/advection Chemotaxis Navier-Stokes/Boussinesq depletion layer: D/v n(z) C(z) z z

  25. Experiment vs. Theory Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, preprint (2004)

  26. Moffat Vortex Experiment (PIV) Numerics (FEM) Tuval, et al. (2004)

  27. Depletion Layers

  28. Geometry of the Contact Line Region Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, preprint (2004)

  29. Chemotactic Singularities & Mixing Tuval, et al. (2004)

  30. Supported Drops Tuval, et al. (2004)

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