This collaboration project was created to use the experimental facilities available in the lab of Karen Daniels (North Carolina State University) to test a nonlocal rheological model by Prabhu Nott (Indian Institute of Science), beyond the work already presented in FRR-12-07. The experiments and image analysis were carried out during July 2022 by graduate students Gautam Vatsa (IISc), Ravi Gautam (IISc), and Farnaz Fazelpour (NCSU) during a month-long visit of the students from IISc, supported by the collaboration funds. The open question is to address the formulation of reliable and robust continuum models for the slow, dense flow of cohesionless granular media. Of particular interest is to examine the interrelation between shear dilatancy (change in packing fraction caused by shear) and the kinematics, which is incorporated in a model recently developed by Nott and collaborators. In this final report, we present the results of successful validation of the model and interpret the significance of these findings.
Our experiments are performed in a 2D cylindrical Couette device (rheometer) developed by Fazelpour & Daniels [1], in which particle-scale measurements of both kinematics and stress as possible through image-processing of digital movies of the single layer of particles. By video imaging the flow in the dense, slow flow regime, we extract the radial variation of the azimuthal velocity and the packing fraction in the steady state. We find that the velocity decays roughly exponentially and the packing fraction increases with radial distance from the rotating inner cylinder. We make a quantitative comparison to the non-local rheological model of Dsouza & Nott [2], and find the model predictions to be in excellent agreement with the experimental data for several different boundary roughness imposed at the outer wall of the rheometer. Moreover, by considering initial states of different packing fraction profiles (but having the same average), we show a coupling between the velocity and density fields, as predicted by the model. Our results establish the importance of shear dilatancy even in systems held at constant volume.