Dense granular flows are involved in a variety of situations, from natural avalanches to industrial processes. We are interested in the fundamental question of the scales at which these flows develop, from the grain to the system size. However, granular matter does not flow like ordinary fluids: their rheology is frictional and depend on the ratio between the macroscopic time scale imposed by the shearing and the microscopic one associated with the local motion of a grain under confining pressure. In some cases, in particular close to yielding conditions, they exhibit creep flows, which expand over scales significantly larger than the grain size (see Figure).
We have recently developed a continuum model to describe such creep flows. Although the governing equations are nonlinear, they admit analytical asymptotic solutions leading to non-trivial scaling laws. The internship will combine analytical calculations and numerical solutions of the model, with the aim of understanding the structure and characteristic length scales of shear zones. The theoretical predictions will then be tested quantitatively against existing experimental and simulation data for the split-bottom and other geometries [1-3]. A particular objective will be to identify regimes in which further analytical approximations or scaling solutions can be obtained.
[1] T.S. Komatsu, S. Inagaki, N. Nakagawa and S. Nasuno, Creep motion in a granular pile exhibiting steady surface flow, Phys. Rev. Lett. 86, 1757 (2001).
[2] D. Fenistein, J.W. van de Meent and M. Van Hecke, Universal and wide shear zones in granular bulk flow, Phys. Rev. Lett. 92, 094301 (2004).
[3] M. Bouzid, M. Trulsson, A. Izzet, A. Favier de Coulomb, P. Claudin, E. Clément and B. Andreotti, Non-local rheology of dense granular flows, Eur. Phys. J. Web of Conf. 140, 11013 (2017).
Expected skills: This is a theoretical physics project requiring a strong background in mathematics and good numerical/programming skills. The student should be comfortable with differential equations, and analytical calculations, as well as with the numerical solution of nonlinear ODEs and PDEs. Experience with Python, Mathematica, or a similar scientific computing tools would be useful. The internship can be continued as a PhD project, extending the theory to other flow geometries and rheological properties, with the objective of uncovering new scaling regimes and analytical solutions.
Location: PMMH, Jussieu Campus
Contact: Thorsten Emig and Philippe Claudin
e-mail: thorsten.emig@cnrs.fr, philippe.claudin@espci.fr