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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
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