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

Apparatus A sin(  t) Camera h ~1.7 ball diameters shaker Light source Accelerometer ~10, 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 Experiment MD Simulation Red: Sphere in top half of cell Blue: 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 , buckled C) H=1.7 , 2 square D)H=1.9 , 2 hexagonal Red: Sphere in top half of cell Blue: Bottom half Observed phases represent efficient packings

Same Phases O`bserved in Colloids Particles suspended in fluid in equilibrium Colloids Schmidt & Lowen, PRE ‘97 (MD, Analytic) Equilibrium transition driven by entropy maximization Granular MD JPCM 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 ExperimentSimulation 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

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

Field Profiles TemperatureDensity

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

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

Remove Friction Linear Profile, Don’t observe expected deviations

Higher wall velocity

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 Kumar Prof. David Egolf