Flows and transverse forces of self-propelled micro-swimmers (FA0004)

Flows and transverse forces of self-propelled micro-swimmers

John O Kessler & Ricardo CortezUniv. of Arizona & Tulane Univ.

Reference

Cortez et al, Phys Fluids 17,031504(05), [Regularized Stokeslet method]

Bacillus subtilis TEM

(near cell division)

Width apprx 0.7m

Pic by C. Dombrowski

& D. Bentley

Bacteria swimming in very shallow water, near wetting edge. Spheres are 2um. Watch for parallel swimmers!

Wetting edge;Triple phase line

“Tail”

Transverse flows toward axis of a self-propelled “organism”. This quadrupole-like flow field attracts neighbors and nearby surfaces.

Extending rod/rotating helix

divU=0

“Body”

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.

R(f) V(f)

V(b)

W (internal push-velocity)

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)

Elongating rod, rotating helix or whatever, resistance R(2)

W–V(1)=V(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.Note radial influx near center & asymmetric vortices

Solid, no-slip boundary

Side view of

flow field

(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 rodagain, 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 arrangementchanged 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

Deep fluid

Monolayerat wetting edge

Getting deeper

“85”=05

Approximately 200microns

(RealTime)

`This one not shown