On the influence of rotational motion on MRI velocimetry of granular flows - Theoretical predictions and comparison to experimental data

Abstract

Continuum dynamics of granular materials are known to be influenced by rotational, as well as translational, motion. Few experimental techniques exist that are sensitive to rotational motion. Here we demonstrate that MRI is sensitive to the rotation of granules and that we can quantify its effect on the MRI signal. In order to demonstrate the importance of rotational motion, we perform discrete element method (DEM) simulations of spherical particles inside a Couette shear cell. The variance of the velocity distribution was determined from DEM data using two approaches. (1) Direct averaging of the individual particle velocities. (2) Numerical simulation of the pulsed field gradient (PFG) MRI signal acquisition based on the DEM data. Rotational motion is found to be a significant effect, typically contributing up to 50% of the signal attenuation, thus amplifying the calculated velocity variance. A theoretical model was derived to relate an MRI signal to the angular velocity distribution. This model for the signal was compared to previously published experimental data as well as simulated MRI results and found to be consistent.

Keywords: Discrete element method; Granular flow; Magnetic resonance imaging; Pulsed field gradient; Rotational motion; Velocimetry.