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Bubble Motions in Bubble Rafts under Steady Shear

Bubble Motions in Bubble Rafts under Steady Shear. Michael Dennin Department of Physics U. C. Irvine. Supported by: Department of Energy grant DE-FG02-03ED46071, Sloan Foundation, Petroleum Research Fund, and UCI UROP. General Outline. Questions raised/addressed in this talk

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Bubble Motions in Bubble Rafts under Steady Shear

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  1. Bubble Motions in Bubble Rafts under Steady Shear Michael Dennin Department of Physics U. C. Irvine Supported by: Department of Energy grant DE-FG02-03ED46071, Sloan Foundation, Petroleum Research Fund, and UCI UROP

  2. General Outline • Questions raised/addressed in this talk • Overview of the system • Initial results

  3. Two Questions • What is the average flow behavior of slowly sheared bubble raft? (How does this relate to flow of foams?) • What is the connection between average flow behavior and individual bubble motions?

  4. General properties • Fluctuations in stress/energy. • “Particle” rearrangements (T1 events, non-affine motions) • Non-uniform shear • Diffusive motion of “particles”.

  5. Two “types” of non-uniform shear Non-uniform shear: region of non-zero and zero shear rate coexist • strain rate is continuous (usually exponential velocity). • strain rate is discontinuous.

  6. “Two-dimensional” foam Debregeas, Tabuteau, Di Meglio, PRL 87 (2001)

  7. Three dimensional suspension Coussot, Raynaud, et al., PRL 88, 218301 (2002)

  8. Definition of T1 Event T1 event: Neighbor switching

  9. Apparatus

  10. 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.

  11. Definition of Terms 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)

  12. Bubble Motions

  13. Reminder of Geometry Consequences • Couette Geometry: average stress, s, proportional to 1/r2 • Yield stress, sy: => critical radius beyond which “rigid” body or elastic behavior, strain rate is a continuous function of r.

  14. Effective Viscosity: stress/(strain rate)

  15. Stress versus strain rc=6.7 cm rc=6.3 cm sy= 0.8 mN/m (1) strain rate = 3 x 10-2 s-1 (2) strain rate = 4 x 10-3 s-1

  16. Average Velocity Profile V(r)/Wr = 1 => rigid body rotation. Fit is to vel. profile for a power law viscosity.

  17. Some Questions • What sets the “critical” radius? • Why is strain rate discontinuous? Consider “flow” during individual events and T1 events. • What is the role of stress chains, if they exist?

  18. T1 events and stress

  19. T1 events and bubble motions

  20. “Local” Displacements A,D B,C E

  21. T1 events and average velocity

  22. Summary • Apparent disagreement between average stress measurements and average velocity profile: strain-rate discontinuity needs to be understood. • Connection between T1 events and short time bubble motions. Not clear the connection between T1 events and average velocity. • Time averages rapidly converge despite very nonlinear short time motion.

  23. Acknowledgments • Video images of bubble raft: John Lauridsen • Viscosity measurements: Ethan Pratt • Initial Bubble tracking software: Gregory Chanan • Funding: Department of Energy grant DE-FG02-03ED46071, Sloan Foundation, Petroleum Research Fund, and UCI UROP

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