Investigations of granular thermodynamics and hydrodynamics Experiments and Computer Simulations

1. Shaking and shearing in a vibrated granular layer Jeff Urbach, Dept. of Physics, Georgetown Univ. • Investigations of granular thermodynamics and hydrodynamics • Experiments and Computer Simulations • Identical particles, collisional regime, ‘ergodic’ • uniform energy injection • Outline: • Describe apparatus and simulation • Phase transitions in the absence of shear • Shear profiles: effect of friction • Wall slip instability at high shear? • Conclusions and Acknowledgements

2. Apparatus Light source Camera A sin(t) h ~1.7 ball diameters ~10,000 1.6 mm diameter stainless steel spheres 0.5% uniformity Accelerometer shaker MD simulation 3 parameters: Elastic restoring force, Dissipative normal force, tangential friction (X. Nie, et al., EPL ‘00; A. Prevost, et al, PRL ‘02) • Shake hard  no gravitational settling, collisional regime, ‘ergodic’

3. Crystal-liquid coexistence MD Simulation Experiment Red: Sphere in top half of cell Blue: Bottom half

4. Square or hexagonal symmetry? When close-packed, 2 square layers are 1.6  high hexagonal are 1.8 

5. Different Phases at different gap spacings (simulations) H=1.3, 1 hexagonal H=1.5, buckled C) H=1.7, 2 square H=1.9, 2 hexagonal Red: Sphere in top half of cell Blue: Bottom half Observed phases represent efficient packings

6. Same Phases O`bserved in Colloids Particles suspended in fluid in equilibrium Granular MD JPCM 17, S2689 (2005) Colloids Schmidt & Lowen, PRE ‘97 (MD, Analytic) Equilibrium transition driven by entropy maximization See also J.S Olafsen, JSU, PRL (2005) and P. M. Reis, R.A. Ingale, and M.D. Shattuck, PRL (2006).

7. Granular Temperature Mean square fluctuating horizontal velocities Experiment Simulation SOLID LIQUID Granular temperature does not obey ‘zeroth law’ Increased dissipation in solid -> higher density -> larger coexistence region

8. Shaking and shearing

9. Shaking and Shearing • Test granular hydrodynamics with independent control of shear rate and collision rate • Couette geometry - known velocity profile for simple fluids • Use ‘rough walls’ to minimize slipping

10. Angular velocity profiles • Varying shear(Δ: 100 rpm,▲: a=175 rpm,■: a=250 rpm). • Varying shaking amplitudeVarying Material • (Δ: =1.267 g,▲: =2.373 g,■: =4.055 g). (Δ: chrome steel,▲: stainless,■: copper ). Approximately exponential velocity profile, large slip, only weakly dependent on granular temperature

11. Field Profiles Temperature Density

12. Momentum Balance Couette flow: assume steady state, variation only in x direction  Linear shear profile if  is constant Include linear friction with top and bottom plates: constant   (Similar to simple fluid in thin Couette cell)

13. MD Simulation, parameters matching experiment Exp. Profile, Large slip Vary :

14. Remove Friction Linear Profile, Don’t observe expected deviations

15. Higher wall velocity

18. Evolution of mean velocity Time (oscillation periods)

19. Bulk shear rate vs. wall velocity

20. Dependence on shaking • Critical v ~ sqrt(T)

21. CONCLUSIONS • Complex phase diagram similar to colloids, with modifications due to non-eq. effects. • Exponential velocity profiles due to friction with plate and lid. • Approximately constant apparent viscosity. • Slip instability in simulations in the absence of wall friction. Acknowledgements: Paul Melby (now at Mitre Corp) Francisco Vega Reyes (now in Badajoz, Spain) Alexis Prevost (now at CNRS - Paris) Nick Malaya, J. Cameron Booth, Pramukta Kumar Prof. David Egolf