1. Fluid entrainment by individual microswimmers Dmitri (Mitya)
Pushkin, Henry Shum and Julia Yeomans University of OxfordOctober,
2012 Pushkin et al., University of Oxford 1
2. Swimmers enhance diffusion Leptos et al., PRL 103
(2009)October, 2012 Pushkin et al., University of Oxford 2
3. Do small swimmers mix the ocean? K. Katija & J. O.
Dabiri, Nature (2009), A. W. Visser, Science (2007), A. M.
Leshansky & L. M. Pismen, PRE (2010).October, 2012 Pushkin et
al., University of Oxford 3
4. Mixing by swimmers: our view Important biologically
Evolutionary strategies Mixing the ocean Unsolved problem Anomalous
diffusion on the short time scales, yet Brownian on the large time
scales Dimensionality effects: In films biomixing is 100 times
greater Our focus Different mixing mechanisms have not been
compared No reliable expression for the effective diffusivity
Universality issuesOctober, 2012 Pushkin et al., University of
Oxford 4
5. Jorn Dunkel et al (2010) : In the far field tracers move in
closed loops, which survive thermal fluctuation on the average
.October, 2012 Pushkin et al., University of Oxford 5
6. Multipole expansionOctober, 2012 Pushkin et al., University
of Oxford 6
7. Multipole flow fields Dipole flow fieldOctober, 2012 Pushkin
et al., University of Oxford 7
8. Multipole flow fields dipole loop Dipole flow fieldOctober,
2012 Pushkin et al., University of Oxford 8
9. Multipole flow fields dipole loop Dipole flow fieldOctober,
2012 Pushkin et al., University of Oxford quadrupole loop 9
10. Tracer advection by Chlamydomonas reinhardtii J. Guasto
website, PRL (2010)October, 2012 Pushkin et al., University of
Oxford 10
11. ?? enhanced diffusion and loops ?? 1. When does the loop
picture break down? 2. Darwin drift 3. Squirmers 4. Numerics for
more realistic examples 5. ConclusionsOctober, 2012 Pushkin et al.,
University of Oxford 11
12. Why loops? entrainmentOctober, 2012 infinite swimmer path
Pushkin et al., University of Oxford 12
13. Mixing mechanismsOctober, 2012 Pushkin et al., University
of Oxford 13
14. Darwin driftOctober, 2012 Pushkin et al., University of
Oxford 14
15. Darwin drift Darwin Benjamin Eames Belcher Hunt Gobby Total
fluid volume moved by swimmer Dalziel Leshansky PismenOctober, 2012
Pushkin et al., University of Oxford 15
16. Darwin driftOctober, 2012 Pushkin et al., University of
Oxford 16
17. Rhodobacter sphaeroidesBoundary element simulationsSolve
Stokes equations, no slip on swimmer surface, swimmer force and
torque freeSwimmer radius 1; swimmer velocity 1; ~ 10 rotations of
tail to advance one body lengthNet displacement along z deviations
from the z-direction very smallSwimmer moves from z= -1000 to z=
+1000, and extrapolate to infinite swimmer path October, 2012
Pushkin et al., University of Oxford 17
18. October, 2012 Pushkin et al., University of Oxford 18
19. Rhodobacter sphaeroidesOctober, 2012 Pushkin et al.,
University of Oxford 19
20. Comparison of analytic and numerical results for the Darwin
driftOctober, 2012 Pushkin et al., University of Oxford 20
21. Comparison of analytic and numerical results for the Darwin
driftOctober, 2012 Pushkin et al., University of Oxford 21
22. SquirmerOctober, 2012 Pushkin et al., University of Oxford
22
23. Squirmer :October, 2012 Pushkin et al., University of
Oxford 23
24. Squirmer Darwin drift:October, 2012 Pushkin et al.,
University of Oxford 24
25. Summary Drift depends strongly on the shape of the
swimmerOctober, 2012 Pushkin et al., University of Oxford 25
26. Open questions Other loop-destroying mechanisms -- finite
swimmer trajectories Link between entrainment and diffusion
Fluctuations Why do swimmers stir?October, 2012 Pushkin et al.,
University of Oxford 26
