Transcript Flows and transverse forces of self

Flows and transverse forces of selfpropelled micro-swimmers (FA0004)
Flows and transverse forces of selfpropelled micro-swimmers
John O Kessler & Ricardo Cortez
Univ. of Arizona & Tulane Univ.
Reference
Cortez et al, Phys Fluids 17,031504(05), [Regularized
Stokeslet method]
Bacillus subtilis TEM
Pic by C. Dombrowski
(near cell division)
& D. Bentley
Width apprx 0.7mm
Bacteria swimming in very shallow water, near wetting
edge. Spheres are 2um. Watch for parallel swimmers!
Wetting edge;
Triple phase line
Transverse flows toward axis of a self-propelled “organism”. This
quadrupole-like flow field attracts neighbors and nearby surfaces.
divU=0
“Body”
Extending rod/rotating helix
“Tail”
The flows around microswimmers:
Time independence of Stokes flow permits the calculation
of flow by increments. Linearity allows superposition, eg
flow fields due to several particles. A swimmer, no matter
how driven exerts = and opposite forces forward and
backward on the fluid. But there can be net directional
velocity if the swimmer is asymmetric. Since we need to
consider only an increment of motion, we do not need to
model details of flagellar helix; all we want is ~magnitude
of transverse flows and forces. We ignore the mutual
influence of swimmer boundaries on each other.
W (internal push-velocity)
V(f)
R(f)
V(b)
R(b)
Self-propelled swimmer
•
•
•
•
R(1)V(1)=R(2)V(2)
V(2)=W-V(1)
V(1)=WR(2)/[R(1)+R(2)]
W=(helix pitch) X (freq of rotation)
W
V(1)
W–V(1)=V(2)
Elongating rod, rotating helix or whatever, resistance R(2)
Flow field of two spheres moving in opposite
directions (connected by an elongating Gedanken rod)
R(1)|V(1)|=R(2)|V(2)|radial inward flow transverse attraction…wall, neighbors
Two spheres modelling locomotion of a
single organism swimming parallel to a wall
Two-separating-sphere “microorganism”. Flow
field, at level of axis, viewed from top
“Far field” of two-sphere model swimmer.
Side
Note radial influx near center & asymmetric vortices
view of
flow field
Solid, no-slip boundary
(wall)
(above two “swimmers”)
Approaching geometry of self-propelled bacteria:
top view with no slip plane below
How is this going to look when several nearby swimmers interfere w each other?
Sphere and rod
again, just one
SIDE VIEW
No slip plane
Top view of 5 coplanar “swimmers” above a no-slip ground plane. The
spheres are “bodies” and the sticks are propelling “flagellar bundles”
Flow field around five swimmers, spatial arrangement
changed from previous slide
Side view, middle plane, of five ball and
stick swimmers
Going that
way
“turbulence” driven by the swimming of apprx
close-packed bacteria, at airbubble surface
Monolayer
at wetting
edge
(Real
Time)
Getting
deeper
Deep fluid
“85”=05
Approximately 200microns
This one not shown
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