Shaking and shearing in a vibrated granular layer Jeff Urbach, Dept. of Physics, Georgetown Univ.
Investigations of granular thermodynamics and hydrodynamicsExperiments 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
Apparatus
A sin(t)
Camera
h ~1.7 ball diameters
shaker
Light source
Accelerometer
~10,000 1.6 mm diameter stainless steel spheres 0.5% uniformity
• Shake hard no gravitational settling, collisional regime, ‘ergodic’
MD simulation 3 parameters: Elastic restoring force, Dissipative normal force, tangential friction(X. Nie, et al., EPL ‘00; A. Prevost, et al, PRL ‘02)
Crystal-liquid coexistence
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
Experiment MD SimulationRed: Sphere in top half of cellBlue: Bottom half
Square or hexagonal symmetry?
When close-packed, 2 square layers are 1.6 high hexagonal are 1.8
Different Phases at different gap spacings (simulations)
A) H=1.3, 1 hexagonal B) H=1.5, buckledC) H=1.7, 2 squareD) H=1.9, 2 hexagonal
Red: Sphere in top half of cellBlue: Bottom half
Observed phases represent efficient packings
Same Phases O`bserved in ColloidsParticles suspended in fluid in equilibrium
ColloidsSchmidt & Lowen, PRE ‘97 (MD, Analytic)
Equilibrium transition driven by entropy maximization
Granular MDJPCM 17, S2689 (2005)
See also J.S Olafsen, JSU, PRL (2005) and P. M. Reis, R.A. Ingale, and M.D. Shattuck, PRL (2006).
Granular Temperature
SOLID
LIQUID
Experiment Simulation
Granular temperature does not obey ‘zeroth law’Increased dissipation in solid -> higher density
-> larger coexistence region
Mean square fluctuating horizontal velocities
Shaking and shearing
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
QuickTime™ and aH.264 decompressor
are needed to see this picture.
Angular velocity profiles• Varying shear (Δ: 100 rpm,▲: a=175 rpm,■: a=250 rpm).
• Varying shaking amplitude Varying 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
Field Profiles
Temperature Density
Momentum BalanceCouette flow: assume steady state, variation only in x direction
€
∂∂x
[ν∂Vy∂x
] = 0
Include linear friction with top and bottom plates:
€
∂∂x
[ν∂Vy∂x
] =αVy
Linear shear profile if is constant
€
Vy ~ e−y / yo yo = ν /αconstant
(Similar to simple fluid in thin Couette cell)
MD Simulation, parameters matching experiment
QuickTime™ and aVideo decompressor
are needed to see this picture.
Vary :
€
yo ~ 1/ α
Exp. Profile,Large slip
Remove Friction
QuickTime™ and aVideo decompressor
are needed to see this picture.
Linear Profile,Don’t observeexpected deviations
Higher wall velocity
QuickTime™ and aVideo decompressor
are needed to see this picture.
Evolution of mean velocity
Time (oscillation periods)
Bulk shear rate vs. wall velocity
Dependence on shaking
• Critical v ~ sqrt(T)
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 KumarProf. David Egolf