Mri Investigations of Particle Motion within a Three-Dimensional Vibro-Fluidized Granular Bed
Jon M. Huntley1, Mick D. Mantle2, T W martin1, Andrew J. Sederman2, Mark D. Shattuck3, R D Wildman1, and Lynn F. Gladden2. (1) Loughborough University, Wolfson School of Mechanical and Manufacturing Engineering, Loughborough, Loughborough, United Kingdom, (2) Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge, CB2 3RA, United Kingdom, (3) Phyics, Levich Institute, City College of New York, 140th and Convent Ave., New York, NY 10031
The unique ability of magnetic resonance imaging (MRI) to provide spatial and temporal information from optically opaque systems, in three dimensions, make it an ideal tool to study the internal motion of rapid granular flows. This talk will focus on the use of ultra-fast velocity compensated MRI measurements to study particle velocity and density distributions in a granular gas, produced by vibrating vertically a bed of mustard seeds at 40 Hz. Specifically, a velocity compensated, double spin-echo, triggered, one-dimensional MRI profiling pulse sequence was developed. This gives an MRI temporal resolution of approximately 2 ms and also minimises MRI velocity artefacts. 12 phase measurements per vibration cycle were used; appropriate transformation of the resulting three-dimensional dataset yields a phase resolved, probability density function for the vertical velocity component at different heights within the bed. Packing fraction, mean velocity, and granular temperature can subsequently be derived from the data as a function of time and height within the flow. Strong transient effects are apparent. A discussion of the data in terms of compression/dilation phases and shock waves, and an assessment of the potential of the technique to test constitutive equations of the granular gas will be presented.