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Shear Localization/Banding

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

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Shear Localization/Banding

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  1. Shear Localization/Banding Michael Dennin UC Irvine

  2. What’s in this talk? • Why study shear banding? • Summary of experimental results. • Brief comments on theory/modelling.

  3. Shear Banding/Localization • Two or more “distinct” flow regimes • Flow regimes distinguished by different rates of strain • Average property – “steady state”

  4. 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)

  5. 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.

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

  7. Question: When is shear banding the coexistence of two distinct states?

  8. Jamming Phase Diagram Flow + jammed state The “J-point” Liu and Nagel, Nature v 396, 1998

  9. 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.

  10. Equilibrium case

  11. Example: Thermal Convection State of the system depends on the path in parameter space! Kolodner, et al., PRL 60, 1723 (1988)

  12. Summary of Experiments

  13. Wall drag

  14. Confined Bubbles Debregeas,et al., PRL 87 (2001) Couette Geometry: two plates

  15. No top J. Lauridsen, G. Chanan, M. Dennin, PRL, V 93, 018303 (2004).

  16. Parallel Shear

  17. Direct Comparison Wang, Krishan, Dennin, PRE V. 73, 031401 (2006). System with a top System without a top

  18. Dispersity/Boundaries bidisperse monodisperse Katgert, Phys. Rev. Lett. 101, 058301 (2008

  19. More Couette Outer and inner shear bands. Krishan and Dennin, PRE 78, 051504 (2008).

  20. Discontinuities – is it all about attractions? Review paper: Dennin, J. Physics: Cond. Matter 20, 283103 (2008).

  21. Bubble Raft Yield stress fluid Power law fluid J. Lauridsen, G. Chanan, M. Dennin, PRL, V 93, 018303 2004).

  22. Effective Viscosity: stress/(strain rate)

  23. 3D Case Rodts et al, Europhys. Lett. 69, 636 (2005)

  24. Interesting aside … “discrete” “continuum” Rodts et al, Europhys. Lett. 69, 636 (2005) Gilbreth, et al., Phys. Rev. E 74, 051406 (2006).

  25. Discontinuous vs Continuous G. Ovarlez, K. Krishan, R. Höhler, S. Cohen-Addad, in preparation

  26. Leiden Results • See later talks for pictures • Couette flow in bubble raft – continuous shear band.

  27. Experimental results Parallel shear (thanks to Denkov)

  28. 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

  29. Theories/models • 2D: Extra drag terms • Other systems: nonlinear flow curves/unstable regions => structural changes. • Stress focusing from T1 events

  30. What next? Careful study of attractions in foams … Other issues …

  31. Critical Strains/ Time evolution Below critical strain: linear Above critical strain: nonlinear Rouyer, et al. Phys. Rev. E 67, 021405 (2003)

  32. 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)

  33. 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”.

  34. Return to Coexistence Idea

  35. 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?

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