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 VERSUS JAMMED

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

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

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 Strain:   x/  r Strain Rate: d  /dt = v/  r Viscosity:  = stress/(strain rate) rr strain elastic flowing stress  Shear stress:  xy = F/ L (two- dimensions) Stress drop: 

12. How to probe the transition?

13. Apparatus

14. Schematic of Apparatus Inner radius r i : 3.84 cm Outer radius r o : 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. Yield Stress Sample stress curve Continuum Facts: Part I Couette Geometry: average stress, , proportional to 1/r 2 shear rate is a continuous function of r.

18. Effective Viscosity: stress/(strain rate)

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

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  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