Anisotropy in rotating drums

An anisotropic relationship between the stress and the strain rate has been observed in two-dimensional simulations of rotating drums.\footnote{\label{C}P.-P. Cortet et al., EPL, {\bf 88}, 2009} The objective of this work is to investigate the structure of the constitutive relation using three-dimensional discrete-element-method simulations of a rotating drum containing identical rigid spheres for a range of rotational speeds. Anisotropy is quantified from the alignment of the stress and strain rate tensors, with the strain rate computed using a least-squares fit.\footnote{C.H. Rycroft et al., JMPS, {\bf 57}, 2009} It is shown that in certain regions there is a strong anisotropic relationship, regardless of the speed of rotation. The effective friction coefficient\footnote{Jop et al., Nature, \bf{441}, 2006} is examined in order to determine the phase space in which the $\mu(I)$ rheology is valid. Lastly, a depth-averaged approach through the flowing layer is employed to determine the relationship between the velocity tangential to the equilibrium surface and the height of the flowing layer. A power-law relationship that approaches linear at high speeds is observed.