Subdiffusive behavior in a two-dimensional planar shear granular flow

We study the rheology of a compact ensemble of beads in a two-dimensional planar shear configuration by means of molecular dynamics. The rheology obtained shows a plateau for low shear rates. In this parameter region we observe the presence of a collective behavior, sticking agglomerates of particles, characterized by a velocity lower than the mean flow velocity. The lifetime of this blocking regions can stand several thousands time units. Moreover, our analysis of the mean square displacement shows a growth of the form 〈(Δr(τ))2〉∼τβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle (\Delta r({\tau }))^2\rangle \sim {\tau }^{\beta }$$\end{document} with β<1.0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta < 1.0$$\end{document}. This indicates the presence of a subdiffusive flow in the quasi-static regime characterized by the presence of vortices. In this work we detail how the observed transient agglomerates of particles deform the flow and we used a local relaxation time analysis for characterizing the inhomogeneities.