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.
Fig. 1a 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. Fig. 1b 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. Here is a photo of the vibrator that fits inside the magnet bore.
|Figure 1a||Figure 1b|
Fig. 2a shows the same situation as Fig. 1, 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. Fig. 2b 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.
|Figure 2a||Figure 2b|
S. R. Nagel, 11/95
- "Granular Convection Observed by Magnetic Resonance Imaging", E. E. Ehrichs, H. M. Jaeger, G. S. Karczmar, J. B. Knight, V. Yu Kuperman, and S. R. Nagel, Science, 267, 1632-1634 (1995).