Ken Kamrin et al 2007 Modelling Simul. Mater. Sci. Eng. 15 S449 doi:10.1088/0965-0393/15/4/S10
Ken Kamrin, Chris H Rycroft and Martin Z Bazant
Show affiliationsIn spite of many attempts to model dense granular flow, there is still no general theory capable of describing different types of flows, such as gravity-driven drainage in silos and wall-driven shear flows in Couette cells. Here, we summarize our recent proposal of the stochastic flow rule (SFR), which is able to describe these cases in good agreement with experiments, and we focus on testing the theory in more detail against brute-force simulations with the discrete-element method (DEM). The SFR is a general rate-independent constitutive law for plastic flow, based on diffusing 'spots' of fluidization. In the case of quasi-two-dimensional granular materials, we assume limit-state stresses from Mohr–Coulomb plasticity and postulate that spots undergo biased random walks along slip-lines, driven by local stress imbalances. We compare analytical predictions of the SFR against DEM simulations for silos and Couette cells, carrying out several parametric studies in the latter case, and find good agreement.
45.70.Mg Granular flow: mixing, segregation and stratification
62.20.F- Deformation and plasticity
47.10.A- Mathematical formulations
81.40.Lm Deformation, plasticity, and creep
47.20.Qr Centrifugal instabilities (e.g., Taylor-Couette flow)
Issue 4 (July 2007)
Received 15 November 2006, in final form 31 January 2007
Published 30 May 2007
Ken Kamrin et al 2007 Modelling Simul. Mater. Sci. Eng. 15 S449
Rostislav V Lapshin 2004 Nanotechnology 15 1135
D Liu et al 2004 J. Micromech. Microeng. 14 567
A Picard 2006 Metrologia 43 46
I Sauers and G Harman 1992 J. Phys. D: Appl. Phys. 25 761
Danny van Noort et al 2002 Smart Mater. Struct. 11 756
Thomas S Duffy 2005 Rep. Prog. Phys. 68 1811
K Esfarjani and Y Kawazoe 1995 J. Phys.: Condens. Matter 7 7217
H Gopalkrishna Gadiyar et al 2003 J. Phys. A: Math. Gen. 36 L109
D J Littler and E E Lockett 1953 Proc. Phys. Soc. A 66 700