Viewing granular flow from inside


Over a century ago, Faraday discovered that vibrating a granular medium can produce large-scale convection. As in a liquid heated from below, material continuously moves around the container from bottom to top and back again. The mechanisms giving rise to this ubiquitous phenomenon which has implications for a wide variety of industrial processes are even now poorly understood. One unusual and perplexing feature is that the grains flow rapidly at the container walls rather than having a non-slip boundary condition appropriate for normal fluids. Experimental investigations have been hampered by an inability to see motion deep inside a container so as to determine the full, three-dimensional convection pattern. Magnetic resonance imaging (MRI) can provide a non-invasive measurement of the convection pattern. With this technique it is possible to image
arbitrary cross-sections through the three-dimensional interior of a granular aggregate and provide direct velocity information. Click for a fairly detailed reference on using MRI to visualize granular flow.

schematic of magnet set-up MRI of white poppy seeds in cylinder

Above left is a sketch of how the sample fits in the magnetic resonance imaging magnet. The sample is a 3 cm diameter glass jar of white poppy seeds---oil-containing seeds which provide sufficient free protons in the liquid state to produce an acceptable NMR signal. The picture on the right shows a magnetic resonance image of a 1 mm thick vertical slice through the center of the jar. A layer of seeds is glued to the side walls to provide a rough surface.

An outstanding problem at present concerns the detailed spatial shape and depth-dependence of the interior flow profile for a granular convection roll. Convection was induced in this granular medium by vibrating it vertically inside the bore of the MRI magnet. Click to view a photo of the vibrator that fits inside the magnet bore. For more info on granular convection and a detailed description of the pictures on this page, see our papers on this topic.

spatially modulated MRI; image before shaking spatially modulated MRI; image after one shake

The left image shows the same poppy seeds as the one above, except that now the longitudinal spin polarization throughout the sample has been modulated in the vertical direction. The peaks of this modulation appear as bright bands in the image and are used to label narrow regions in the granular material. The image on the right shows the evolution of the bands after a single shake of peak acceleration G = 8g.

Individual grains have moved, carrying with them the spin modulation and creating a distortion of the originally horizontal bands. The bands near the top have clearly bent but remained well-defined, indicating collective motion of the granular material. The material in the center has moved up while the material along the edges has moved down. The bands close to the bottom of the container stayed relatively straight and unperturbed after one shake, indicating a decrease of net motion with increasing depth into the material. From these images, it is possible to measure the flow velocities of the beads as a function of position in the container as well as a function of the acceleration used to vibrate the container.
Click to find out more about convection, size separation and analysis of MR images such as the ones above.
Check out some neat images of coffee beans rising in a vibrated bed of coffee grounds
We do our MR imaging in collaboration with the Center for Magnetic Resonance Imaging at the University of Chicago. You can find out more about their programs and capabilities by clicking here.

Reference on MRI techniques applied to vibrated granular materials:

You can also view a complete listing of our papers and preprints, or go back to the main page.

last updated: June 17, 1997