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