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 \(\langle (\Delta r({\tau }))^2\rangle \sim {\tau }^{\beta }\) with \(\beta < 1.0\). 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.