1band

2band applied

On the origin of the vorticity-banding instability

5 cm

2 cm

constant shear rate throughout the system

multi-valued flow curve

isotropic and nematic branch different concentrations

shear-induced viscous phase

not clear what the origin of the banding instability is

low high

rolling flow within the bands normal stresses along the gradient direction

normal streses generated within the interface of a gradient-banded flow ( S. Fielding, Phys. Rev. E 2007 ; 76 ; 016311 )

Binodal

0.0 0.2 0.4 0.6 0.8 1.00

1

2

[s-1]

.

nem

]s[ 1Vorticity banding

Spinodals

Tumblingwagging

Critical point

concentration concentration

1

fd virus :

L = 880 nmD = 6.7 nmP = 2200 nm

( P. Lettinga )

nem0 1

almost crossed polarizers distinguishorientational order

vorticitydirection

P

A

100 m

1 2 3 4 5 6 7 8

0 10 20 30 40 50 60

60

80

100

120H[m]

Time [min]

1 2 3 4 5 6 7 8

stretching of inhomogeneities

growth of bands

Shear flow

vorticity direction

Gapwidth 2.0 mm

~ 1

mm

00( ) 1 expA

t tH t H

A

N

band width growth rate

00( ) 1 exp

t tH t H A

23 % :

35 % :

;A finite 0;A finite

heterogeneous vorticity banding

0H

A

interconnected

disconnected

spinodal decomposition : nucleation and growth :

m100

( with Didi Derks, Arnout Imhof and Alfons van Blaaderen )

0.75nem 0.23nem

tracking of a seed particle( counter-rotating couette cell )

with Bernard Pouligny (Bordeaux)

increasing shear rate

elastic instability for polymers :

non-uniform deformation equidistant velocity lines

1.0 1.5 2.0 2.560

70

80

90

100

H [m]

G [mm]

Weissenberg or rod-climbing effectK. Kang, P. Lettinga, Z. Dogic, J.K.G. Dhont Phys. Rev. E 74, 2006, 026307-1 – 026307-12

New viscous phases can be induced by the flow (under controlled shear-rate conditions )

stress

shear rate

new phase

homogeneous

inhomogeneous

personal communication with John Melrose

( , , ) ( , , ) ( , , )( , , )y y y

m y z y

u y z t u y z t u y z tu u B y z t

t y z

Stability analysis :

discreteness of inhomogeneities along the flow direction is of minor importance :

mass density gradient component of the body force

( , , ) ( ) expyu y z t u y ik z t

( , , ) ( ) expyB y z t B y ik z t

z-dependence exp ki z t 2 / k with the typical distance between inhomogeneities

ˆ( , , )yB F r u t

“Brownian contributions”

+”rod-rod interactions”

+“flow-structure coupling”

linear

bi-linear

linear

probability density for the position and orientation of a rod

r

u

xy

z

u

r

J.K.G. Dhont and W.J. Briels J. Chem Phys. 117, 2002, 3992-3999 J. Chem Phys. 118, 2003, 1466-1478

z

y

2

yB small 0 large

0 1ˆ ˆ ˆ( , , ) ( , ) ( ) ( , , )r u t A r u A y r u t

“renormalized base flow probability”

2

4( ) ( )1

yB y A y

linear contributions

22

4( ) ( )1

yB y A A y

bi-linear contributions

1

2 2

42 4( ) ( )1 1

yB y A A yC C

rod-rod interactions

2

41

2 2

4 41 2( ) ( )1 1

m u y A A yC C

0A 0A 0u

2

1

2

42 4 01 1

C AC

1 0C 2 0C

2

4 01

A C

l

u

2

4

( )

1 ( )A

C unstable stable

A C

4A C

2

4 01

A C

depends on the microstructuralproperties of the inhomogeneities

0.0 0.2 0.4 0.6 concentration

Wilkins GMH, Olmsted PD, Vorticity bandingduring the lamellar-to-onion transition in a lyotropic surfactantsolution in shear flow, Eur. Phys. J. E 2006 ; 21 ; 133-143.

Fischer P, Wheeler EK, Fuller GG, Shear-bandingstructure oriented in the vorticity direction observed forequimolar micellar solution, Rheol. Acta 2002 ; 41 ; 35-44.

Lin-Gibson S, Pathak JA, Grulke EA, Wang H,Hobbie EK, elastic flow instability in nanotube suspensions, Phys. Rev. Lett. 2004 ; 92, 048302-1 - 048302-4.

Vermant J, Raynaud L, Mewis J, Ernst B, Fuller GG,Large-scale bundle ordering in sterically stabilized latices, J. Coll. Int. Sci. 1999 ; 211 ; 221-229.

Bonn D, Meunier J, Greffier O, Al-Kahwaji A, Kellay H,Bistability in non-Newtonian flow : rheology and lyotropic liquidcrystals, Phys. Rev. E 1998 ; 58 ; 2115-2118.

Micellar worms

Nanotube bundles

Colloidal aggregates

-Worms- Entanglements- Shear-induced phase

Kyongok Kang Pavlik Lettinga Wim Briels