Summer School: Granular Materials from Simulations to Astrophysical Applications

Transcription

1 Summer School: Granular Materials from Simulations to Astrophysical Applications Hosted by CSCAMM and the University of Maryland Burgers Program in Fluid Dynamics Organizers: Derek Richardson, Astronomy Wolfgang Losert, Physics Eitan Tadmore, CSCAMM Support: Burgers Program for Fluid Dynamics Center for Theory and Computation National Science Foundation European Space Agency [NASA support requested]

2 Labtours Friday June 17th 2pm Neutral Buoyancy Facility (test of weightless robotics) 2.30pm Dynamo Experiment (self generation of magnetic fields) 3pm Three dimensional imaging of granular flows 3.30pm Fluid Dynamics Lab (tentative)

3 Outline Intro: What are granular materials? Granular Materials Jam Granular Materials Age and Strengthen Granular Flow Granular Gas Segregation Astrophysical Applications Wolfgang Losert

4 Granular materials Gravel Rocks Coffee Sand

5 Astrophysical granular matter MARS ASTEROID McEwan, 1989 Mars rock avalanche. The landslide fell 5 miles and ran out 65 miles. Regolith migration on Eros

6 Static Granular Materials Nature, 387 (1997)

7 Flow of Granular Matter Avalanches Shear Flows x=3

8 Granular Materials Made up of many solid particles >> 1 micron. Lifting 1 mm bead by one bead diameter: k b T mgd Motion requires energy input >> thermal energy Interaction between grains (Friction and inelastic collisions) dissipates kinetic energy. System not in thermal equilibrium

9 Outline Intro: What are granular materials? Granular Materials Jam Granular Materials Age and Strengthen Granular Flow Granular Gas Segregation Astrophysical Applications DEMO Wolfgang Losert

10 Static granular matter: jammed state Without energy input, in confinement, granular matter is jammed Blue line: Contact force brightness ~ Magnitude From Corey O Hern Significant progress in past 10 years to define and characterize an idealized jamming transition for hard spheres without friction. (Liu, Makse, Nagel, O Hern, Radjai, Snoijer, Saarloos, etc)

11 Challenges in modeling jamming Since kt is too small to move grains noticeably, the system does not equilibrate Physical principles that rely on a thermal equilibrium reference state (e.g. minimization of free energy, maximization of entropy) do not apply.

12 Outline Intro: What are granular materials? Granular Materials Jam Granular Materials Age and Strengthen Granular Flow Granular Gas Segregation Astrophysical Applications Wolfgang Losert

13 Experiments on Aging and Strengthening Frame Horizontal displacement sensor Spring Vertical sensor Target Sliding plate granular layer Plate weight: g Granular material: Glass beads µm DIA Layer depth: 3 mm Spring constant: N/m High Sensitivity Measurements Displacement sensors: h = 0.1 µm Force measurement: F / F = 0.01 % W. Losert et al Phys. Rev. E. 61, 4060 (2000)

14 Friction between two solid objects Static friction coefficient: S FS / FN Dynamic friction coefficient: D FD / FN

15 Dynamics: Stick-Slip Motion Dynamics: Stick-slip motion 500 d (µm) B C s d 0 0 A 5 10 t (s) A L 0 V B L + d 0 M C L + d 0 m 0 X

16 Friction in granular material kept under shear stress for 10 hours s of first slip larger than s of other slips d Shear Stress for 10 hours time (s) Stick-Slip motion: m=26.6g, k=189 N/m 11/29/98 experiment Strengthening of granular layer under stress

17 Friction between two solid objects Static friction coefficient: Dynamic friction coefficient: S FS / FN D FD / FN *The above are (very good!) approximations. Static friction increases with stick time S S0 ln / is O(10-2 ) 0 Dynamic friction decreases with sliding speed ( V) ln V / V D D0 0 Hahner and Spencer, Phys. Today 51, 23 (1998) Krim, MRS Bull. 23, 20 (1998)

18 Waiting time strengthening Waiting Time Strengthening (Shear stress during waiting time) F max /F norm waiting time (s) Friction increases roughly logarithmically with waiting time (for t > 500 s)

19 Geophysical friction laws for granular materials: Dietrich/Ruina V V0 D( V ) D0 ln ln V D 0 C Strain dependent strengthening A. Ruina, J. Geophys. Res. 88, (1983): d V V (1) ln dt DC DC Time dependent Strengthening J.H. Dieterich, J. Geophys. Res. 84, 2161 (1979) d (2) 1 dt V D C

20 Waiting without shear stress for 16 hours 450 spring displacement (µm) time (s) No strengthening without applied stress No strengthening, if direction of shear stress during waiting and during motion are opposite (not shown)

21 Aging under thermal cycling OVEN Glass beads and plastic container From: Peter Schiffer, Penn State

22 Compaction through thermal cycling System: glass container filled with plastic beads (or vice versa) Heating expands plastic more than glass (Schiffer group, Nature, 2006) Slow compaction of granular matter (without giving individual grains significant kinetic energy)

23 han1.5cgeinpackingfractionsimple thermal cycling results Clear and systematic change in packing fraction! (%) 0.5mm 0.9mm 2mm Change in temperature ( C) From: Peter Schiffer, Penn State

24 Thermal packing dependence on repeated cycles Packing Fraction (%) T = 107 o C T = 41 o C Cycle number Peter Schiffer, Penn State

25 Effect of repeated cycles can be understood through simple two-component model Packing Fraction (%) T = 107 o C T = 41 o C Cycle number n max 1 2 Peter Schiffer, Penn State PF PF A e A e n 1 2 Barker and Mehta

26 Outline Intro: What are granular materials? Granular Materials Jam Granular Materials Age and Strengthen Granular Flow Granular Gas Segregation Astrophysical Applications Wolfgang Losert

27 Granular Flow Inertia Number I d: particle diameter : particle density

28 Effects of mesoscale structure Schematic Contact network steady shear Schematic Contact network shear reversal Toiya et al. PRL 2004 Observations - Notable rolling/sliding during steady shear - Significantly different motion during shear reversal Masahiro Toiya

29 Small initial torque during shear reversal shear reversal Derek Updegraaf with E. Wandersman, J. Dijksman, M. van Hecke DEMO

30 Outline Intro: What are granular materials? Granular Materials Jam Granular Materials Age and Strengthen Granular Flow Granular Gas Segregation Astrophysical Applications Wolfgang Losert

31 Excited Granular Matter An example of a granular gas Energy input into a granular gas Experimental Setup CCD Camera (up to 10,000 frames/s) 32 cm Vertical Shaker ( Hz) granular material: spherical beads, 4 mm Dia

32 Velocity Distribution Acceleration= 5g ; frequency = 100Hz ; coverage = 0.42 Gaussian Velocity distribution best fit by in agreement with recent theoretical predictions. P ( v ) e v 1.5 Granular gases have non-gaussian velocity distribution

33 Energy of particle mixtures No Equipartition of energy

34 Bistability

35 Outline Intro: What are granular materials? Granular Materials Jam Granular Materials Age and Strengthen Granular Flow Granular Gas Segregation Astrophysical Applications Wolfgang Losert

36 Granular Segregation (Image by H. Makse) Flowing granular materials segregate according to particle properties (size, density, shape, and more). (Image by H. Makse)

37 Axial Bands See Newey et al. Europhysics Letters 2004

38 Particle Speed on Surface

39 Outline Intro: What are granular materials? Granular Materials Jam Granular Materials Age and Strengthen Granular Flow Granular Gas Segregation Astrophysical Applications Wolfgang Losert

40 Anisotropic yield surface

41 Aging/Strengthening in Astrophysics? Thermal Cycling on the Moon Daytime: +120 o C Night: -150 o C [lunarpedia.org] The pole is a regions not exposed to thermal cycling. Will it be equally compacted? DEMO

42 Long Runout Rock Avalanches The Blackhawk event in California Field Data: Rock avalanche probabilities are correlated with the direction of prior shear (Friedmann, Kwon & Losert, J. Geophys. Res 2003)

43 Forces in Astrophysical Applications Holding Granular Matter together: Rearranging Granular Matter: Gravity Van der Waals Charges Tidal forces Seismic forces Centrifugal forces

44 Outline Intro: What are granular materials? Granular Materials Jam Granular Materials Age and Strengthen Granular Flow Granular Gas Segregation Astrophysical Applications Wolfgang Losert