Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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: Reynolds and Peclet Numbers Navier-Stokes equations: 2 (ut u u ) p u nf Passive scalar dynamics: 2 ct u c D c Reynolds number: u u U 2 / L UL Re 2 2 u U / L Peclet number: u c UC / L UL Pe 2 2 D c DC / L D 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. Self-Concentration and the Chemotactic Boycott Effect 2 mm Video ~100x actual speed Dombrowski, et al. (2004); Tuval, et al. (2005) 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) The ZBN in Brightfield and Fluorescence 210 mm Velocity Field from Cinemagraphic PIV Peclet number ~10-100 (vs. 0.01-0.1 for individual bacterium) 35 mm Dombrowski, et al. (2004). See also Wu and Libchaber (2000) The ZBN in Brightfield and Fluorescence 210 mm PIV Velocity Field 210 mm Streamlines (Note intermittency) 210 mm Velocity-Velocity Correlation Function (spatial) I (r) v(x r, t ) v(x, t ) x v v 2 x I(r) r (mm) v 2 x 2 x Velocity-Velocity Correlation Function (temporal) J (t ) v(x, s t ) v(x, s) s v v 2 J(t) t (s) s v 2 s 2 s Vorticity (homage a Miró) 210 mm 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. Side Views of Sessile Drops drop Tuval, et al. PNAS 102, 227 (2005) Bacterial Swimming and Chemotaxis (Macnab and Ornstein, 1977) 1-4 mm 10-20 mm 20 nm Swimming speed ~10 mm/s Propulsive force ~1 pN Real-time Imaging of Fluorescent Flagella t Turner, Ryu, and Berg, J. Bacteriol. 182, 2793 (2000) “normal = LH helix “curly” = RH helix “straight” = straight Swimming Near the Contact Line Bacterial Bioconvection J.O. Kessler The Chemotactic Boycott Effect 1 cm Dombrowski, Cisneros, Chatkaew, Goldstein, and Kessler, PRL 93, 098103 (2004) Mechanism of Self-Concentration Dombrowski, et al. (2004) Historical Ideas •Flocking models (Toner and Tu, 1995, …; traffic flow…) v t ( v ) v v | v |2 v p D12 v t ( v) 0 A Landau theory in the velocity field – clever but not relevant to the physics of Stokes flow •Sedimentation (interacting Stokeslets) n ri v 0 av 0 U(ri r j ) j i U (r ) as few as three particles exhibit chaotic trajectories (Janosi, et al., 1997) 3a e (e r )r 3 4 r r •Conventional chemotaxis picture (e.g. Keller-Segel) - MISSES ADVECTION ct Dc2c f (c, ) t D 2 ( rc) ct (u )c t (u ) 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… Side Views of Sessile Drops Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, preprint (2004) Side Views: Depletion and Flow 2 mm Dombrowski, et al. (2004) Circulation Near the “Nose” Self-trapping in the corner Diffusion and Chemotaxis Oxygen diffusion/advection 2 ct u c Dc c nf (c) nt u n Dn n ( rn c) Chemotaxis 2 (u t (u )u) p u ngzˆ 2 Navier-Stokes/Boussinesq C(z) n(z) z depletion layer: D/v z Experiment vs. Theory Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, preprint (2004) Numerics (FEM) Experiment (PIV) Moffat Vortex Tuval, et al. (2004) Depletion Layers Geometry of the Contact Line Region c( r, ) cs am r m / 2 cos( m / 2 ) m 1 nt u n Dn n ( rn c) 2 Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, preprint (2004) Chemotactic Singularities & Mixing Tuval, et al. (2004) Supported Drops Tuval, et al. (2004)