Petr Denissenko, University of Warwick, 25 June 2008

1. Propagation of discontinuities in a pipe flow of suspension of motile microorganisms(A thread of motile algae for real-time bio-monitoring) 3 image/sec Petr Denissenko, University of Warwick, 25 June 2008

2. Microorganism motility. Diffusion, low Re Stationary microorganism Thick depleted zone Thin depleted zone Moving microorganism To provide thrust motion of flagella must be irreversible For the experiments we used Chlamydomonas nivalis (phototrophic regime), a biflagellate Crypthecodinium cohnii (heterotrophic regime), a dynoflagellate

3. Motility of bacteria and unicellular Algae. Flagellates salmonella

4. Bioconvection. Examples The reason for the bioconvection is that microorganisms are heavier than water. Gyrotactic algae in a flask. Standing plumes Oxytactic bacteria in a Petri dish. Pattern selection (from PhD thesis by Martin Bees)

5. O2 * * * * * * * * * * * * * * * * * * * Gravitaxis + gyrotaxis: cells swim upwards and turned by the flow shear * * * * g * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Bioconvection. Mechanism The reason for the bioconvection is inhomogeneity in concentration of microorganisms which are heavier than surrounding water. Chemotaxis. Cells swim towards O2 Downwelling pipe flow Upwelling pipe flow Kessler, J. Hydrodynamical focusing of motile algal cells. Nature313 (1985)

6. Patterns formed by C. nivalis Wall plumes in a shaker Wall plumes in upwelling pipe flow Thread in the downwelling pipe flow Dendrites above the water surface

7. Microorganism motility. Random walk Cells advance forward with constant velocity performing BiasedRandom Walk in swimming directions …another mechanism of a taxis is Run-and-Tumble, but it is unaffected by the flow shear. Thermal noise motion in flagella etc Bottom-Heavy cells (gravitaxis), gyrotaxis, phototaxis

8. Bioconvection. Modelling Continuum models: Diffusion of admixture (cells) + convection where diffusion tensor is derived from solutions of Fokker-Planck equation for the cell velocity distribution Based on the Biased Random walk model. Linear, weakly non-linear, DNS. Pedley & Kessler (1990), Bees & Hill (1997), Metcalfe & Pedley (2001), Ghorai & Hill (2002). A problem: cell velocity distribution varies in space e.g. faster cells go further up (Vladimirov et al., 2004). Separate simulation of the flow and cell motility: DNS for the viscous flow with variable density, which is defined by the cell concentration at each step. Motility of each cell is simulated separately at each step. Hopkins, Fauci (2002). A problem: hard to learn how the flow depends on parameters.

9. Pipe flow. Experimental setup, observations g Cell suspension Thread of algae PIV field of view Air nodules train-like disturbance Light sheet Flow Laser T=20oC P. Denissenko, S. Lukaschuk, Physics Letters A362, 298-304 (2007)

10. Evolution of nodules. Change of the propagation rate Cell concentration Axial velocity z

11. Pipe flow of the suspension. Velocity profile Navier Stokes equation in cylindrical coordinates, z- independent axisymmetric flow: Flow velocity 400 mm/s Cell forward velocity 70 mm/s Cell drift velocity 10 mm/s Cell “gyration” radius 0.5 mm General solution Singular at r=0 (at the axis) Poiseuille flow

12. The model. Pipe flow with the heavy core Non-dimensional numbers Microorganism concentration Vertical velocity General solution for w Solution for w, satisfying boundary and continuity conditions r = 0 r = 1 r = b Non-dimensional pressure gradient

13. Discontinuities (as in shock waves and bores) Continuity Eqn. + kinematic condition at r=b Notation: A = b2 = thread cross-sectional area / p Cell conservation in the core A system of PDE in conservative form Notation: N = An = cell linear concentration real l1, l2: hyperbolic Rankine-Hugoniot conditions across the discontinuity Lax conditions

14. State 1 Discontinuity D State 0 Discontinuities (as in shock waves and bores) Nodule Hyperbolic system A ( z , t ) N ( z , t ) Train-like Discontinuity (bore) State 1 State 0

15. Velocity profile in a pipe with algae suspension Distinct nodules P. Denissenko, S. Lukaschuk, Physics Letters A362, 298-304 (2007)

16. A thread of motile algae for real-time bio-monitoring 3 image/sec

17. Real-time Biomonitoring tool. Is it competitive? A standard tool: measuring the culture growth rate Video-tracking: assessing individual motility Nodules on the thread: assessing motility in bulk by measuring nodule spacing and propagation speed Electronic noses: detecting chemicals by luminescence or change of the resistance of the substrate An established technique, but slow (few days) + the pollutant may decay complicated hardware (microscope, lighting), not instantaneous since needs averaging over many cells, needs the controlled culture stirring Measurements may be done by a naked eye, instant response to change in motility Reliability and repeatability questionable, needs testing Maintenance problems: requires cleaning of sensor surfaces, Sensor calibration etc.