Granular Matter: How Structure Determines Response Far From Equilibrium

• Applicant: Dr. Wolf Till Kranz
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 335058789

• Final Report Year: 2023

Final Report Abstract

Fluidized granular media are pervasive in nature and industry. Avalanches, land slides and the transport of agricultural grains or construction sand are examples of processes that would benefit from a detailed understanding of the granular flow behavior. Despite its importance, a comprehensive granular rheology had been missing so far. In this project, I developed the Granular Integration Through Transients (GITT) formalism and validated it by dedicated experiments in a state of the art commercial rheometer. In a nutshell, granular rheology is captured by a few time scales: (i) Newtonian behavior is observed when the shear rate is slow compared to the structural relaxation rate. Shear thinning and in the Taylor-Couette geometry, shear banding, is found for higher shear rates until shear heating dominates over fluidization and the rheology follows Bagnold scaling. Promising initial results for a compatible description of the jamming transition and for the use in continuum simulations pave the way for future work. In summary, it is indeed the structure in form of the structural relaxation rate that largely determines graular rheology. Including finer details, GITT can also explain the empirical µ(I)-law valid in the Bagnold regime and make quantitative predictions for difficult to measure quantities like the granular temperature.

Publications

• Kinetic theory for strong uniform shear flow of granular media at high density. EPJ Web of Conferences, 140, 03064.
  Kranz, W. Till & Sperl, Matthias
  
• Rheology of Inelastic Hard Spheres at Finite Density and Shear Rate. Physical Review Letters, 121(14).
  Kranz, W. Till; Frahsa, Fabian; Zippelius, Annette; Fuchs, Matthias & Sperl, Matthias
  
• Trail-mediated self-interaction. The Journal of Chemical Physics, 150(21).
  Kranz, W. Till & Golestanian, Ramin
  
• Asymptotically Exact Solution of the Fredrickson-Andersen Model
  K. Önder, M. Sperl & W. T. Kranz
  
• Granular rheology: a tale of three time scales
  O. Coquand, W. T. Kranz & M. Sperl
  
• Integration through transients approach to the µ(I) rheology. Phys. Rev. E 102, 032602.
  Coquand, O.; Sperl, M. & Kranz, W. T.
  
• Integration through transients for inelastic hard sphere fluids. Physical Review Fluids, 5(2).
  Kranz, W. Till; Frahsa, Fabian; Zippelius, Annette; Fuchs, Matthias & Sperl, Matthias
  
• A gravity-independent powder-based additive manufacturing process tailored for space applications. Additive Manufacturing, 47, 102349.
  D.’Angelo, Olfa; Kuthe, Felix; Liu, Szu-Jia; Wiedey, Raphael; Bennett, Joe M.; Meisnar, Martina; Barnes, Andrew; Kranz, W. Till; Voigtmann, Thomas & Meyer, Andreas
  
• Comment on “Explicit Analytical Solution for Random Close Packing in d=2 and d=3”
  W. T. Kranz
  
• Granular piston-probing in microgravity: powder compression, from densification to jamming
  D.’Angelo, Olfa; Horb, Anabelle; Cowley, Aidan; Sperl, Matthias & Kranz, W. Till
  
• Granular piston-probing in microgravity: powder compression, from densification to jamming. npj Microgravity, 8(1).
  D.’Angelo, Olfa; Horb, Anabelle; Cowley, Aidan; Sperl, Matthias & Kranz, W. Till
  
• Understanding dense granular flow from first principles. Science Talks, 3, 100049.
  Kranz, W. Till; Coquand, Olivier & D.’Angelo, Olfa