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Fluctuations in Flowing Foam: Does Einstein's Relation Define an Effective Temperature?

This study explores stress-induced fluctuations in flowing foam and their relation to thermal fluctuations, as well as the significance of the jamming transition. The research aims to understand the behavior of foams and other multiphase materials.

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Fluctuations in Flowing Foam: Does Einstein's Relation Define an Effective Temperature?

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  1. Fluctuations in Flowing Foam: Does Einstein's Relation Define an Effective Temperature? Michael Dennin U. C. Irvine Department of Physics and Astronomy

  2. When is a fluid a solid, and vice versa? FLOW JAMMED VERSUS

  3. Fluids Flow and Solids Stretch “Force Law” :Stress = (viscosity) x (rate of strain) Velocity profile Flow rate equation

  4. Fluctuation/dissipation Relations Equipartition Thermal distribution

  5. Jamming Phase Diagram • Plasticity in “molecular” systems • Glassy behavior in liquids • Flow of “multiphase” materials: granular, foams, colloids, pastes, etc.. The “J-point” Liu and Nagel, Nature v 396, 1998

  6. Big Questions • Are stress induced fluctuations the “same” as thermal fluctuations? (Effective T) • What does the jamming transition mean? What are its signatures?

  7. How do we approach these? • Look at athermal systems. • Look at systems that are in 2D MODEL FOAM SYSTEMS

  8. WHAT ABOUT FOAMS? http://www.joiff.com/technical/infoamation.htm FOAM: gas bubbles with liquid walls Size: microns to millimeters Useful parameter: Liquid fraction or gas fraction Durian, UPENN

  9. Main Features of Sheared foam • Initial elastic response (yield stress) • Flowing regimes: • Slow shear: “irregular” stress response • Fast shear: “smooth” flow BUBBLES PLAYS CENTRAL ROLE

  10. Definition of Terms: Part I T1 event: Neighbor switching

  11. Definition of Terms: Part II Outer barrier moves with V flowing stress Ds elastic Dr Strain:g =Dx/Dr Strain Rate: dg/dt = v/Dr Viscosity:h = stress/(strain rate) strain Shear stress:sxy = F/L (two-dimensions) Stress drop:Ds

  12. How to probe the transition?

  13. Apparatus

  14. Schematic of Apparatus Inner radius ri: 3.84 cm Outer radius ro: 7.43 cm Area fraction: 0.95 Boundary conditions: no slip at both walls, but inner cylinder is free to move.

  15. Basic measurements • Stress on inner cylinder • Individual bubble motions • Automatic tracking gives average properties and topological rearrangements

  16. Bubble Motions

  17. Continuum Facts: Part I Couette Geometry: average stress, s, proportional to 1/r2 Sample stress curve Yield Stress shear rate is a continuous function of r.

  18. Effective Viscosity: stress/(strain rate)

  19. Shear Discontinuity Yield stress fluid “solid” Power law fluid J. Lauridsen, G. Chanan, M. Dennin, PRL, 2004

  20. Another view Exponential

  21. Is this unique? THREE DIMENSIONAL Coussot, Raynaud, et al., PRL 88, 218301 (2002)

  22. Conclusion #1 We see coexistence of two “phases”. What about an effective temperature?

  23. Fluctuations

  24. Fluctuation Dissipation “kick” the system with stress s Measure the response in strain q Measure the fluctuations in q

  25. “Direction” Matters “opposite” applied shear “with” applied shear

  26. Summary • Velocity measurements imply a “phase” transition. => Is this a “new” type of material? • Response/correlation relations can give a temperature. => Why directional dependence? Is linear response achievable?

  27. Thanks to … Michael Twardos John Lauridsen Gregory Chanan Yuhong Wang Kapil Krishan Funded by: Department of Energy grant DE-FG02-03ED46071, Sloan Foundation, Petroleum Research Fund, and UCI UROP

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