Granular materials and pattern formation

Transcription

1 Granular materials and pattern formation Ask not what you can do for pattern formation, ask what pattern formation can do for you! sand dunes flowing layers vibrated layers avalanche

2 Granular materials are complex materials for which the intrinsic equations of motion are not, in general, known What can the empirical observations of patterns in forced granular systems tell us about the underlying physics of granular flows? How generic are such insights? In other words, how do we figure out what matters?

3 Outline General observations about patterns and structures in granular materials Examples where ideas developed for pattern formation in (primarily) fluid systems have application to granular problems Two problems of granular flow on an inclined plane Conclusions - Insights developed from pattern formation can get you started - then there s lots of hard work to do.

4 Similar Patterns Similar Physics? Convection Vibrated Granular

5 Dislocation dynamics - Stability boundaries: Skew-Varicose Rayleigh-Benard Convection Hu, Ecke & Ahlers, PRE 1995 vertically-vibrated granular layer de Bruyn et al, PRL 1998

6 Traveling Waves Granular segregation & Traveling Waves Side wall traveling wave in rotating convection Liu & Ecke, PRE 1999 Choo et al, PRL 1997

7 Continuous wave crests Forterre & Pouliquen, JFM 2003 Similar to waves in thin films on an incline Liu & Gollub, 1994 Glass beads

8 Solitary Waves on an Inclined Plane Shock-like solution Liu & Gollub, Phys. Fluids (1994)

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10 Granular Flow on an Inclined Plane A model system for granular physics First: Avalanche Dynamics - All granular material is not alike Second: Longitudinal vortices - Convection rolls or something else?

11 Phase diagram of flow on an inclined plane h/d c r Steady Flow Avalanches Unstable Flow Accelerating? Patterns? Simulations Silbert, Grest, etc. Theory Halsey, Ertas, Rajchenback, etc. 5 0 No Flow hs( ) r Steady Flow Experiments Pouliquen et al Louge, Clement, Douady, Daerr, etc.

12 Granular Physics - Avalanche disruption in Greenland After tragic event destroyed part of town, the plan was to build a dam to hold back the snow. Unfortunately... Andrew Hogg, Bristol KITP workshop 2005

13 Experimental Setup Top lighting High Speed Camera Flow Rate Q L ~ 100 cm h W ~ 20 cm particle size d ~ 0.5 mm layer height h/d ~ 3-20 θ Back lighting Laser line

14 Sand 38o Sand 33o Image differencing

15 Are granular avalanches universal in the sense that the exact details of the granular material is not so important. Glass bead avalanches Look qualitatively similar - How about quantitative aspects?

16 Quantitative aspect of avalanche: Structure Sand Glass Beads

17 Laser Sheet Determination of the Height Profile Laser sheet aligned along the flow direction

18 Shocks & Breaking Waves in Granular Avanlanche Flows u / (g h s cos foam Sand =36.8 o h /h s u / (g h s cos Glass Beads =24.3 o h / h s x / h s BHE, PRL 2005

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21 Numerical simulation of Avalanche The avalanche spreads out and develops a (viscous) shock front - valid for small Fr (glass beads)

22 What s the difference in the avalanche dynamics? Glass beads - progressive, grain velocity < front velocity Sand - breaking, grain velocity > front velocity

23 Some conclusions about avalanches Additional quantitative experimental results demonstrate that all avalanches are not alike but that a theory based on depth averaged equations captures at least some of those differences (Borzsonyi & Ecke, PRL 2005) Avalanches are complicated because of the phase coexistence between solid phases (ahead and behind the avalanche) and the fluidized avalanche. Thus, the depth averaged approach must fail near the boundaries. Indeed, it s somewhat of a miracle that it works at all!

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25 Particle image velocimetry Velocity Height

26 The Picture of Forterre & Pouliquen Our recent results top velocity height bottom velocity intensity

27 State only seems to exist for accelerating flow

28 Amplitude of the stripes continues to evolve over the whole length of the experiment (3 m)

29 Other patterns (smaller d = 0.25 mm)

30 Conclusions Notions from generic pattern formation ideas - developed large in fluid systems where the equations are typically well known can get you started. Often, however, things are a good bit more complicated than they might first appear and care is needed (almost always the case!) in interpreting the results.