on the origin of the vorticity-banding instability 5 cm 2 cm constant shear rate throughout the...
TRANSCRIPT
![Page 1: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/1.jpg)
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
![Page 2: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/2.jpg)
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 )
![Page 3: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/3.jpg)
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
![Page 4: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/4.jpg)
almost crossed polarizers distinguishorientational order
vorticitydirection
P
A
100 m
![Page 5: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/5.jpg)
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
![Page 6: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/6.jpg)
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
![Page 7: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/7.jpg)
spinodal decomposition : nucleation and growth :
m100
( with Didi Derks, Arnout Imhof and Alfons van Blaaderen )
0.75nem 0.23nem
![Page 8: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/8.jpg)
tracking of a seed particle( counter-rotating couette cell )
with Bernard Pouligny (Bordeaux)
![Page 9: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/9.jpg)
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
![Page 10: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/10.jpg)
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
![Page 11: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/11.jpg)
( , , ) ( , , ) ( , , )( , , )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
![Page 12: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/12.jpg)
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
![Page 13: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/13.jpg)
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
![Page 14: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/14.jpg)
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
![Page 15: 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](https://reader035.vdocuments.net/reader035/viewer/2022062511/5515da16550346cf6f8b4a26/html5/thumbnails/15.jpg)
Kyongok Kang Pavlik Lettinga Wim Briels