Shear Localization/Banding

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Shear Localization/Banding

• Michael Dennin
• UC Irvine

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Whats in this talk?

• Why study shear banding?
• Summary of experimental results.
• Brief comments on theory/modelling.

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Shear Banding/Localization

• Two or more distinct flow regimes
• Flow regimes distinguished by different rates of
  strain
• Average property steady state

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Three of many experiments
GRANULAR
SUSPENSION
Coussot, et al., PRL 88, 218301 (2002)
Bocquet,et al., PRE 65, 011307 (2001).
2D FOAM
All of these examples are in Couette geometries
Debregeas,et al., PRL 87 (2001)
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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.

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Foam issues

• Composition of fluid walls including
  stabilizers.
• Sample preparation.
• Pre-shear conditions.
• Dimensionality.
• wall drag.
• Flow induced structural changes.

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Question When is shear banding the coexistence
of two distinct states?
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Jamming Phase Diagram
Flow jammed state
The J-point
Liu and Nagel, Nature v 396, 1998
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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.

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Equilibrium case
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Example Thermal Convection
State of the system depends on the path in
parameter space!
Kolodner, et al., PRL 60, 1723 (1988)
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Summary of Experiments
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Wall drag
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Confined Bubbles
Debregeas,et al., PRL 87 (2001)
Couette Geometry two plates
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No top
J. Lauridsen, G. Chanan, M. Dennin, PRL, V 93,
018303 (2004).
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Parallel Shear
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Direct Comparison
Wang, Krishan, Dennin, PRE V. 73, 031401 (2006).
System with a top
System without a top
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Dispersity/Boundaries
bidisperse
monodisperse
Katgert, Phys. Rev. Lett. 101, 058301 (2008
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More Couette
Outer and inner shear bands.
Krishan and Dennin, PRE 78, 051504 (2008).
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Discontinuities is it all about attractions?
Review paper Dennin, J. Physics Cond. Matter
20, 283103 (2008).
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Bubble Raft
Yield stress fluid
Power law fluid
J. Lauridsen, G. Chanan, M. Dennin, PRL, V 93,
018303 2004).
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Effective Viscosity stress/(strain rate)
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3D Case
Rodts et al, Europhys. Lett. 69, 636 (2005)
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Interesting aside
discrete
continuum
Rodts et al, Europhys. Lett. 69, 636 (2005)
Gilbreth, et al., Phys. Rev. E 74, 051406 (2006).
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Discontinuous vs Continuous
G. Ovarlez, K. Krishan, R. Höhler, S.
Cohen-Addad, in preparation
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Leiden Results

• See later talks for pictures
• Couette flow in bubble raft continuous shear
  band.

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Experimental results
Parallel shear (thanks to Denkov)
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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

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Theories/models

• 2D Extra drag terms
• Other systems nonlinear flow curves/unstable
  regions gt structural changes.
• Stress focusing from T1 events

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What next?
Careful study of attractions in foams
Other issues
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Critical Strains/ Time evolution
Below critical strain linear
Above critical strain nonlinear
Rouyer, et al. Phys. Rev. E 67, 021405 (2003)
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Time dependence of critical radius
Gilbreth, et al., Phys. Rev. E 74, 051406 (2006).
Value of critical radius depends on averaging
time.
Wang, et al.Phys. Rev. Lett. 98, 220602 (2007)
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Path in Phase space
All four curves are for the same rotation rate in
a Couette geometry. All four curves take a
different path in phase space.
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Return to Coexistence Idea
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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 gt attractive interactions in foam?