shaking and shearing in a vibrated granular layer jeff urbach, dept. of physics, georgetown univ....
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![Page 1: Shaking and shearing in a vibrated granular layer Jeff Urbach, Dept. of Physics, Georgetown Univ. Investigations of granular thermodynamics and hydrodynamics](https://reader035.vdocument.in/reader035/viewer/2022062714/56649d605503460f94a4130f/html5/thumbnails/1.jpg)
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
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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)
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Crystal-liquid coexistence
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Experiment MD SimulationRed: Sphere in top half of cellBlue: Bottom half
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Square or hexagonal symmetry?
When close-packed, 2 square layers are 1.6 high hexagonal are 1.8
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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
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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).
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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
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Shaking and shearing
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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
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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
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Field Profiles
Temperature Density
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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)
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MD Simulation, parameters matching experiment
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Vary :
€
yo ~ 1/ α
Exp. Profile,Large slip
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Remove Friction
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Linear Profile,Don’t observeexpected deviations
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Higher wall velocity
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Evolution of mean velocity
Time (oscillation periods)
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Bulk shear rate vs. wall velocity
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Dependence on shaking
• Critical v ~ sqrt(T)
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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