Shaking and shearing in a vibrated granular layer Jeff Urbach, Dept. of Physics, Georgetown Univ. Investigations of granular thermodynamics and hydrodynamics.
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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 ~10,000 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 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 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
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)
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