A Fluctuating Energy Model for Dense Granular Flows
We address the slow, dense flow of granular materials as a continuum with the incompressible Navier-Stokes equations plus the fluctuating energy balance for granular temperature. The pseudo-fluid is given an apparent viscosity, for which we choose an Arrhenius-like dependence on granular temperature; the fluctuating energy balance includes a ‘mobility enhancing’ term due to shear stress and a jamming, dissipative term which we assume to depend on the isotropic part of the stress tensor and on shear rate. After having proposed a ‘chemical’ interpretation of the phenomenology described by the model in terms of reaction rates, we report results for some 2-D standard geometries of flow, which agree semi-quantitatively with experimental and DEM observations. In particular, our model well reproduces the formation of stagnant zones of a characteristic shape (e.g. wedge-shaped static zones in a silo with flat bottom) without prescribing them a-priori with erosion techniques.
Unable to display preview. Download preview PDF.
- 7.Pouliquen, O., Cassar, C., Forterre, Y., Jop, P., and Nicolas, M. (2006) In Proc. Powders & Grains 2005: A. A. Balkema, Rotterdam. Google Scholar
- 11.Goddard, J. D. (to appear) In Mathematical models of granular matter, Lecture Notes in Mathematics. Berlin: Springer. Google Scholar
- 13.Artoni, R., Santomaso, A., and Canu, P. (to appear) Europhys. Lett. e-print: cond-mat/0705.3726.
- 18.Losert, W., Bocquet, L., Lubensky, T. C., and Gollub, J. P. Phys. Rev. Lett. 85(7), 1428–1431. Google Scholar
- 19.Bocquet, L., Losert, W., Schalk, D., Lubensky, T. C., and Gollub, J. P. Phys. Rev. E 65, 011307. Google Scholar
- 21.Brown, R. L. and Hawksley, P. G. W. (1947) Fuel 27, 159–173. Google Scholar