Dresden 2014 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 43: Focus session: Slow Dynamics in Glasses and Granular Matter II (joint session DY/ CPP/ DF)
DY 43.7: Talk
Friday, April 4, 2014, 11:45–12:00, HÜL 186
Integration Through Transients Approach to the Rheology of a Sheared Granular Fluid — •Till Kranz1, Fabian Frahsa2, Matthias Fuchs2, Matthias Sperl3, and Annette Zippelius1 — 1Institut für Theoretische Physik, Universität Göttingen — 2Fachbereich Physik, Universität Konstanz — 3Institut für Materialphysik im Weltraum, DLR Köln
We generalize the Integration through Transients (ITT) formalism to the non-equilibrium stationary state of randomly driven inelastic hard spheres. ITT was first developed for Brownian suspensions [1] and recently extended to thermostated Newtonian systems [2]. As a result we get generalized Green-Kubo-relations and an equation of motion for the transient density correlator.
Since the seminal work of Bagnold [3] it has been recognized that dissipative hard spheres (i.e. granular particles) have an unusual rheology. In particular, the shear stress σ varies with the square of the shear rate γ, i.e., Bagnold scaling, σ = ηγ2, holds. We will discuss the response to shear and the dependence on the degree of inelasticity and packing fraction. This includes the transient density correlator and the prefactor, η, of the Bagnold scaling relation. We will comment on the relation to the elastic [1,2] and the unsheared case [4], clarifying how Bagnold scaling emerges.
[1] M. Fuchs, M. E. Cates, J. Rheol. 53, 957 (2009)
[2] K. Suzuki, H. Hayakawa, Phys. Rev. E 87, 012304 (2013)
[3] R. A. Bagnold, Proc. R. Soc. Lond. A 225, 49 (1954)
[4] W. T. Kranz, et al., Phys. Rev. E 87, 022207 (2013)