1 / 36

Experiments Dan Goldman (now Berkeley) Mark Shattuck ( now City U. New York )

Southern Workshop on Granular Materials Puc ón, Chile 10-13 December 2003. Patterns in a vertically oscillated granular layer: (1) lattice dynamics and melting, (2) noise-driven hydrodynamic modes, (3) harvesting large particles. Experiments Dan Goldman (now Berkeley)

bell
Download Presentation

Experiments Dan Goldman (now Berkeley) Mark Shattuck ( now City U. New York )

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Southern Workshop on Granular Materials Pucón, Chile 10-13 December 2003 Patterns in a verticallyoscillated granular layer: (1) lattice dynamics and melting, (2) noise-driven hydrodynamic modes, (3) harvesting large particles • Experiments • Dan Goldman(now Berkeley) • Mark Shattuck (now City U. New York) Harry Swinney University of Texas at Austin • Simulations • Sung Jung Moon (now Princeton) • Jack Swift

  2. Particles in a vertically oscillating container light f = frequency(10-200 Hz)  = (acceleration amplitude)/g = 42f2/g(2-8)

  3. Square pattern f = 23 Hz acceleration = 2.6g Particles: bronze, d=0.16 mm layer depth = 3d 1000d

  4. peak OSCILLONS • localized • oscillatory: f /2 • nonpropagating • stable crater Umbanhowar, Melo, & Swinney, Nature (1996)

  5. Oscillons:nointeractionat adistance

  6. Oscillons: building blocks for moleculeseach molecule is shown in its two opposite phases dimer tetramer polymer chain

  7. Oscillons:building blocks of a granular lattice? each oscillon consists of 100-1000 particles

  8. Dynamics of a granular lattice time evolution snapshot: close up snapshot 18 cm Goldman, Shattuck, Moon, Swift, Swinney, Phys. Rev. Lett. 90 (2003) G = 2.90, f = 25 Hz, lattice oscillation 1.4 Hz

  9. Coarse-graining of granular lattice: A lattice of balls connected by Hooke’s law springs? Then the dispersion relation would be: frequency at edge of Brillouin zone wherek is wavenumber and a is lattice spacing

  10. Compare measured dispersion relation with lattice model From space-time FFT I(kx,ky,fL) fLattice (Hz) lattice model kBrillouin Zone (for (1,1)T modes) G = 2.75

  11. DEFECTS apply FM 52 cycles later 235 cycles later FFT FFT FFT Create defects: make lattice oscillations large Resonant modulation: FM at lattice frequency: modulation rate = 2 Hz container position: 32 Hz G = 2.9

  12. Frequency modulate the container, andadd graphite to reduce friction MELTING add graphite by 175 cycles:melted 56 cycles later G = 2.9, f = 32 Hz, fmr(FM) = 2 Hz

  13. m = 0.5 m= 0 100 cycles later: melted 22 cycles later MD simulation: reduce friction to zerocrystal melts (without adding frequency modulation) G = 3.0, f = 30 Hz

  14. Lindemann criterion for crystal melting Lindemann ratio: where um and un are displacements from the lattice positions of nearest neighbor pairs, and a is the lattice constant. Simulations of 2-dimensional lattices in equilibrium show lattice melting when Bedanov, Gadiyak, & Lozovik , Phys Lett A (1985) Zheng & Earnshaw, Europhys Lett (1998)

  15. Test Lindemann criterion on granular latticeMD simulations g m = 0.1 melting threshhold lattice melts Lindemann criterion m = 0.5: no melting Goldman, Shattuck, Moon, Swift, Swinney, Phys. Rev. Lett. 90 (2003)

  16. Conclude: granular lattice is described well by discrete lattice picture.How about a continuum description? • Granular patterns: as in continuum systems -- vertically oscillated liquids, liquid crystals, … --- squares, stripes, hexagons, spiral defect chaos • Instabilities as in Rayleigh-Bénard convection --- skew-varicose, cross-roll

  17. Spiral defect chaos Rayleigh-Bénard convection Granular oscillating layer Plapp and Bodenschatz Physica Scripta (1996) deBruyn, Lewis, and Swinney Phys. Rev. E (2001)

  18. Skew-varicose instabililty observed in granular expt:same properties as skew-varicose instability of Rayleigh-Bénard convection rolls 2 1 deBruyn et al., Phys. Rev. Lett. (1998) 3 4 wavelength increases

  19. Cross-roll instabilityobserved in granular experiment:same properties as cross-roll instability in convection wave- length decreases de Bruyn, Bizon, Shattuck, Goldman, Swift, and Swinney, Phys. Rev. Lett. (1998)

  20. Continuum models of granular patterns • Tsimring and Aranson, Phys. Rev. Lett. (1997) • Shinbrot, Nature (1997) • Cerda, Melo, & Rica, Phys. Rev. Lett. (1997) • Sakaguchi and Brand, Phys. Rev. E (1997) • Eggers and Riecke, Phys. Rev. E (1998) • Rothman, Phys. Rev. E (1998) • Venkataramani and Ott, Phys. Rev. Lett. (1998)

  21. Convecting fluids:thermal fluctuations drive noisy hydrodynamic modes below the onset of convection Theory: Swift-Hohenberg eq., derived from Navier-Stokes Swift & Hohenberg, Phys Rev A (1977) Hohenberg & Swift, Phys Rev A (1992) Experiments: convecting fluids and liquid crystals: Rehberg et al., Phys Rev Lett (1991) Wu, Ahlers, & Cannell, Phys Rev Lett (1995) Agez et al., Phys Rev A (2002) Oh & Ahlers, Phys. Rev. Lett. (2003) Granular systems are noisy. Can hydrodynamic modes be seen below the onset of patterns?

  22. G = 2.6, f = 30 Hz Noise below onset of granular patterns snapshot time evolution time (T) 6.2 cm x  170 mm stainless steel balls (e  0.98)

  23. P(f) S(kx,ky) Increase G towardpattern onset at Gc = 2.63 :Smax(k) increases |k| 0 15 30 45 60 Hz

  24. Emergence of square pattern with long-range order G = 2.8 S(kx,ky) P(f) frequency of square pattern container frequency S(k) k

  25. Swift-Hohenberg model for convection:from Navier-Stokes eq. with added noise If no noise (F = 0) (“mean field”), pattern onset is at But if F 0, onset of long-range (LR) order is delayed, Xi, Vinals, Gunton, Physica A (1991); Hohenberg & Swift, Phys Rev A (1992)

  26. Compare granular experiment to Swift-Hohenberg model Goldman, Swift, & Swinney Phys. Rev. Lett. (Jan. 2004) Experiment SQUARES e = (G – Gc)/Gc DISORDERED Granular noise is: -- 104 times the kBT noise in Rayleigh-Bénard convection [Wu, Ahlers, & Cannell, Phys. Rev. Lett. (1995)] --10 times the kBT noise in Rayleigh-Bénard convection near Tc [Oh & Ahlers, Phys. Rev. Lett. (2003)] e Swift-Hohenberg

  27. Segregation:separate particlesof different sizes

  28. Kink: boundary between regions of opposite phase --layer on one side of kink moves down while other side moves up flat with kinks OSCILLONS f* = f x [(layer depth)/g]1/2

  29. kink Kink: a phase discontinuity3-dimensional MD simulation G =6.5 x/d container 0 100 200 x/d Moon, Shattuck, Bizon, Goldman, Swift, Swinney Phys. Rev. E65, 011301 (2001)

  30. Convection toward a kink This is NOT a snapshot: the small black arrows show the displacement of a particle in 2 periods (2/f ) rising falling

  31. Larger particles rise to top (Brazil nut effect)and are swept by convection to the kink glass particles dia. = 4d bronze particles dia. = d • this segregation is intrinsic to the dynamics(not driven by air or wall interaction)

  32. kink oscillating kink t = 0 EXPERIMENT:controlled motion ofthe kink harveststhe larger particles particle trajectory black glass dia. = 4d bronze d = 0.17 mm Moon, Goldman, Swift, Swinney, Phys. Rev. Lett. 91 (2003) 247 cycles 566 cycles

  33. Dynamics of a granular lattice • Granular lattice: like an equilibrium lattice of harmonically coupled balls and springs • Lindemann melting criterion supports the coupled lattice picture • Question: • Would continuum pattern forming systems, e.g., • Faraday waves in oscillating liquid layers, • Rayleigh-Bénard convection patterns, • falling liquid columns, • Taylor-Couette flow, • viscous film fingers, … • exhibit similar lattice dispersion and melting phenomena?

  34. Noise Near the onset of granular patterns, noise drives hydrodynamic-like modes, which are well described by the Swift-Hohenberg equation.

  35. Harvesting large particles Segregation of bi-disperse mixtures has been achieved for particles with • Diameter ratios: 1.1 – 12 • Mass ratios: 0.4 - 2500

  36. END

More Related