bacterial microﬂuidics: the physics and engineering of ... · dead carpet ♦ tumbly bacteria ent...

Kenny Breuer

School of Engineering, Brown University,

Providence, RI

In collaboration with:

Tom Powers, Bin Liu, Qian Bian, MinJun Kim, Dave Gagnon

Bacterial Microfluidics:

The physics and engineering of

flagellated bacterial motility

Wednesday, February 23, 2011

Stuff going on in my lab

y

Slip Length

Solid Boundary

Electrospray dynamics

droplets and contact lines

Animal Flight

Bacterial motility

Cilia and flagella in viscous fluids


Motility of flagellated bacteria

L. Turner, W. S. Ryu, and H. C. Berg (2000)

H. Berg, Physics Today, Jan 2000;

Tumble

RunIn “real life”: Newtonian and non-Newtonian media


• Physics questions:

• How fast does a “bacterium” swim in a Newtonian fluid?

• How fast does a “bacterium” swim in a non-Newtonian fluid?

• How does an elastic flagellum interact with a viscous fluid?

• What is the flow field associated with rotating flagella?

• How do adjacent elastic filaments bundle?

• How do adjacent elastic filaments synchronize using hydrodynamic forces?

• How important are non-local viscous interactions?

• “Engineering” questions:

• Can bacteria affect the macroscopic world?

• Can we harness their motion?

• Can we control them?

• etc.

• What next?

Interesting questions


apologies to Picasso, thanks to Christophe Clanet

Bull #11














• etc.

• What next?



Experimental setup (low-Re swimming helix)

fluids with high viscosity: • silicone oil (Newtonian)• Polybutene+ Polyisobutylene (viscoelastic)


Fluidic force on a rotating helix (Newtonian)

Fluidic force per unit length saturates with L>5

infinitely long helixWednesday, February 23, 2011

0 2 4 6 8 100

100

200

300

400

500

600

Fluidic force on a rotating helix (Newtonian)

Fluidic force per unit length saturates with L>5

infinitely long helixWednesday, February 23, 2011

00.1

0.20.3

0.4

0

10

20

30

40

0

2

400

0

0

0

0 0.1 0.2 0.3 0.4

0

2

8

6

4

2

0

2

4

4

6

8

free swimming state ( )

sensitivity of swimming speed ~ 0.3

Force-free swimming of a rotating helix (Newtonian)

sensitivity of force ~


0 2 4 6 8

0

1

2

0 2 4 6 8 100

0.5

1

1.5

2

0 5 100.09

0.1

Free swimming speed at different rotation rate


x y

z

zy

x

Computation of free swimming speed

1. Resistive force theory (no long-range interactions)

when swimming freely,

2. Slender body theory (incl. long range, no thickness effects)


Comparison between experiment and theory

: diameter of the cross-section of helical fiber

: arc-length within a pitch

3 42400.4

0.3

0.2

0.1

0

0.1

0.2

0.3

0.4

Slender Body TheoryResistive Force Theory

Straight filament

Tightly coiled


Relaxation time:

10 100 101 102101

102

100

101

102

103

104

Rotating helix in Viscoelastic fluids

Polyisobutylene (PIB) suspended in Polybutene (PB)

Rheology: Boger fluid

10 10 100 101 1010

10

100

101

10

103

G’G’’


0 2 4 6 8 10

0.9

0.95

1

1.05

1.1

Rotating helix in Viscoelastic fluids

free swimming speed of rotating helix in viscoelastic fluids

Next: fluid with stronger elasticity

Newtonian

Boger fluid














• etc.

• What next?



• Motivation

– Understand simplified behavior of flexible filaments in viscous flows

– Look at a simpler model for microrobotic propulsion

– Understand previous numerical experiments• (Manghi, Schlagberger & Netz, PRL 2006)

Filament rotates in two modes: constant torque: M constant velocity: ω

Viscous fluid (Re << 1) Elastic filament

Root set at fixed angle, θ

Elastic filament interacting with a viscous flow


after bifurcationbefore bifurcation(Video Sped up x10)

Shape Bifurcation of an Elastic Rotating Rod


Motion around the bifurcation

Reconstructed motion from expt. data


• Stokes flow (reversible flow)

– Analyze in the rotating frame (steady)

– No forces due to non-inertial frame

• disregard twist– Only bending stiffness

• resistive force theory:

• Hydrodynamic forces are local

• balance of forces and moments

• Key non-dimensional parameters:

Theory


Constant torque

Constant velocity

Ascending

Descending

Torque, MmL/A

Spee

d, χ

= (ηω

L4 )

/A

Low torque: MmL/A~ χ

Intermediate regime: MmL/A~ χ1/2 High torque: MmL/A~ χ 1/4

(Qian et al. PRL 2008)

Comparison between theory and experiment














• etc.

• What next?



Hydrodynamic interactions

• Cilia and flagella occur in many biological (and engineering) systems.

• Collective motion important for transport and motility

• Interesting questions for flagella and cilia:

• synchronization through hydrodynamic interactions

• synchronization vs. chaotic motion

• role of compliance

• time-scales for interactions

• effects of multiple filaments

• effects of long range hydrodynamic forces

webmd.com


Two-paddle model system

siliconeoil

free surface

TOP VIEW

SYMMETRIC ASYMMETRIC

SIDE VIEW flexible

coupling

!1!1!2 !2

M1 M1M2 M2

"DD

2R 2R R R

##

h


Two-paddle interactions

a) Rigid shafts – no synchronization

b) Rigid shafts – torque mismatch– Phase wandering

c) Flexible shafts – synchronization!

(Qian et al, PRE 2009)


Numerical simulation - Regularized

Kim & Powers (2004) - rigid helices – no synchronizationReichert & Stark (2005) - flexible coupling leads to synchronization

(Cortez, 2001)


Simulation and experiment!

!/"

t/

!!/

"

t/

!!/

"

t/

0 100 200 300 400 500

0.0

0.4

0.2

0.6

0.8

1.0

T0

0.00!0.05

0.05

0.520.500.48

325

325

350

350

300

300

T0

T0symmetric

asymmetric


Analytical approach

velocity on ball i, induced by ball j

Sum of forces and moments; for two balls:

multiple-scale (slow) evolution equation for phase difference:

1/T time constant for synchronization

ignore “far field” term

!1 !2

D(x1, y1) (x2, y2)

x

yRR

a

a

M1M2

r1

r2

Niedermeyer et al. (Chaos, 2008)

Qian et al. (PRE, 2009)














• etc.

• What next?



(Images courtesy of Károlyi György)

Tumble

Run

Motile bacteria as chaotic mixers• Chaotic advection (Aref 1984)

• Viscous laminar flow

• Random switching of “blinking vortices”

• Bacteria have flagella that alternate rotation direction randomly

• Cell bodies execute random walk

• Chaotic mixing in zero Re flow?


Length = 28 mm

InletOutlet

Fluorescence

No Fluorescence

Width = 200 µm

Depth = 40 µm

Mixing using freely swimming bacteria


U

Diffusion Equation:

Intensity:

-dI/d

y

y [μm]

Intensity Gradient:

Theory

Experiment

Amplitude

σ

Similarity Variable:

Theory for standard diffusion.


• Diffusion of small molecule rises from 20 – 80 um2/s

– Large molecules and 1 um beads show 50x enhancement

• Diffusion faster than standard “Fickian” diffusion

– Introduction of new time scale

● Dead carpet

♦ Tumbly bacteria

■ Wild-type bacteria

Diff

usio

n C

oeffi

cien

t [u

m2 /

s]

Diff

usio

n Exp

onen

t

Bacterial concentration [x109/ml] Bacterial concentration [x109/ml]

(Kim & Breuer,Phys Fluids 2004)

Enhanced diffusion due to bacteria


Brownian motion

(Darnton, Turner, Breuer & Berg Biophys J. 2003)

Bacterial carpet motion

Motion (μm) of 0.5μmfluorescent particles during

1/30 sec

substrate

fluid

Bacterial carpets and enhanced mixing


• Pumping arises spontaneously

• Direction determined by “last flush”

• “Crystallization” processChannel floor

(Kim & Breuer, Small 2008)

15µm

~500µm

Top View

Side View

Width

Height

Bacterial pumps


• Translates 5 um/s

• Rotation 4.6 deg/s

• Surface area 4350 um2

• Long axis 92 um

• Bacteria 1100

PDMS barge

Glass substrate

Bacterial barges

• Rotation 33 deg/s

• Surface area 1400 um2

• Long axis 65 um

• Bacteria 300


• Force-free swimming speed measured:

• newtonian fluids

• viscoelastic fluids underway

• Fluids-filament interactions:

• coiling of an elastic filament due to viscous stresses

• Synchronization of adjacent filaments

• hydrodynamic interactions

• elastic compliance necessary

• multiple paddles illustrate signficantly more complex (& chaotic) behavior

Summary:


• Acknowledgements: Tom Powers, Bin Liu, Min Jun Kim, Qian Bian, Dave Gagnon

• Support: NSF


bacterial microﬂuidics: the physics and engineering of ... · dead carpet ♦ tumbly bacteria ent...

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