shear localization/banding michael dennin uc irvine
TRANSCRIPT
Shear Localization/Banding
Michael Dennin
UC Irvine
What’s in this talk?
• Why study shear banding?
• Summary of experimental results.
• Brief comments on theory/modelling.
Shear Banding/Localization
• Two or more “distinct” flow regimes
• Flow regimes distinguished by different rates of strain
• Average property – “steady state”
Three of many experiments
Coussot, et al., PRL 88, 218301 (2002) Bocquet,et al., PRE 65, 011307 (2001).
Debregeas,et al., PRL 87 (2001)
GRANULAR
2D FOAM
SUSPENSION
All of these examples are in Couette geometries
General Issues
• Inhomogeneous applied stress.
• Interesting flow curves (stress as a function of rate of strain).
• Discontinuities in the rate of strain.
• Changes in the microscopic structure of the material.
• Impact of boundaries (2D issue mainly)
• Path in “parameter” space.
Foam issues
• Composition of “fluid walls” including stabilizers.
• Sample preparation.
• Pre-shear conditions.
• Dimensionality.
• “wall drag”.
• Flow induced structural changes.
Question: When is shear banding the coexistence of
two distinct states?
Jamming Phase Diagram
Liu and Nagel, Nature v 396, 1998
The “J-point”
Flow + jammed state
WARNING
• Equilibrium systems minimize a free energy – coexistence occurs at unique and well defined points.
• Nonequilibrium systems do not necessarily obey a minimization principle – coexistence of states can be more complicated.
Equilibrium case
Example: Thermal Convection
State of the system depends on the path in parameter space!
Kolodner, et al., PRL 60, 1723 (1988)
Summary of Experiments
Wall drag
Confined Bubbles
Debregeas,et al., PRL 87 (2001)
Couette Geometry: two plates
No top
4.5 5.0 5.5 6.0 6.54.5x10-4
5.0x10-4
5.5x10-4
6.0x10-4
4 6 8 100
2x10-4
4x10-4
6x10-4
v(r)
/r (
s-1)
radial position (cm)
radial position (cm)
v(r
)/r
(s-1
)
J. Lauridsen, G. Chanan, M. Dennin, PRL, V 93, 018303 (2004).
Parallel Shear
Direct Comparison
-10 -5 0 5 10
-1.0
-0.5
0.0
0.5
1.0
Bubble
velo
city
/Belt
velo
city
y/<d>
shear rate=0.0014 s-1
shear rate=0.0028 s-1
shear rate=0.014 s-1
-10 -5 0 5 10
-0.4
-0.2
0.0
0.2
0.4
Bubble
velo
city
/Belt
velo
city
y/<d>
shear rate=0.0014 s-1
shear rate=0.0028 s-1
shear rate=0.014 s-1
System without a top System with a top
Wang, Krishan, Dennin, PRE V. 73, 031401 (2006).
Dispersity/Boundaries
Katgert, Phys. Rev. Lett. 101, 058301 (2008
bidisperse monodisperse
More Couette
Outer and inner shear bands.
Krishan and Dennin, PRE 78, 051504 (2008).
Discontinuities – is it all about attractions?
Review paper: Dennin, J. Physics: Cond. Matter 20, 283103 (2008).
Bubble Raft
4.5 5.0 5.5 6.0 6.5 7.00.0
0.2
0.4
0.6
0.8
1.0
v(
r)/(r
)
radial position (cm)
Yield stress fluid
Power law fluid
J. Lauridsen, G. Chanan, M. Dennin, PRL, V 93, 018303 2004).
Effective Viscosity: stress/(strain rate)
-3 -2 -1 01
2
3
4
log
(vis
cosi
ty)
log (strain rate)
1/3 1/3 1/3(0.8 mN/m)( / ) (1.8 mNs /m)( / ) y a d dt d dt
3D Case
Rodts et al, Europhys. Lett. 69, 636 (2005)
Interesting aside …
0.00 0.05 0.10 0.15 0.200.00
0.02
0.04
0.06
0.08
0.10
Cri
tica
l Ra
te o
f Str
ain
(s-1
)
(s-1)
“discrete”
“continuum”
Gilbreth, et al., Phys. Rev. E 74, 051406 (2006).
Rodts et al, Europhys. Lett. 69, 636 (2005)
Discontinuous vs Continuous
G. Ovarlez, K. Krishan, R. Höhler, S. Cohen-Addad, in preparation
Leiden Results
• See later talks for pictures
• Couette flow in bubble raft – continuous shear band.
BASE+MAc, 20 wt % Glycerol
z, mm
0.0 0.5 1.0 1.5 2.0 2.5 3.0
V, m
m/s
0.0
0.1
0.2
0.3
0.4
0.5
10.13 s
cr
Parallel shear (thanks to Denkov)
Experimental results
Lessons from other systems
• Unstable flow curves
• Impact of system interactions – attractive/repulsive
• Impact of structural changes (and connection to unstable flow curves)
• Changes in density resulting in changes in other properties
Theories/models
• 2D: Extra drag terms
• Other systems: nonlinear flow curves/unstable regions => structural changes.
• Stress focusing from T1 events
What next?
Careful study of attractions in foams …
Other issues …
Critical Strains/ Time evolution
Rouyer, et al. Phys. Rev. E 67, 021405 (2003)
Below critical strain: linear
Above critical strain: nonlinear
Time dependence of critical radius
Gilbreth, et al., Phys. Rev. E 74, 051406 (2006).
4.5 5.0 5.5 6.0 6.54.5x10-4
5.0x10-4
5.5x10-4
6.0x10-4
4 6 8 100
2x10-4
4x10-4
6x10-4
v(r)
/r (
s-1)
radial position (cm)
radial position (cm)
v(r
)/r
(s-1
)
Value of critical radius depends on averaging time.Wang, et al.Phys. Rev. Lett. 98, 220602 (2007)
Path in Phase space
40 50 60 70 80 900
5
10
15
20
25
s/r
r(mm)
regular quench quench w/delay adiabatic decrease
All four curves are for the same rotation rate in a Couette geometry.All four curves take a different “path in phase space”.
Return to Coexistence Idea
Summary
• What nonequilibrium transitions occur in driven foams?
• Are shear bands the coexistence of different nonequilibrium states?
• What are the “microscopic” mechanisms for shear banding => attractive interactions in foam?