[3] MD Shattuck, Flows in Porous Media: Visualization by Magnetic Resonance Imaging, PhD Dissertation, Department of Physics, Duke University, Durham, NC:(194 pages.) 1995. [pdf]
We have developed a Magnetic Resonance Imaging, MRI, technique which non-invasively measures local interstitial fluid velocity distributions in fullysaturated porous media. This was achieved by extending the standard threedimensional MRI sequence to include local velocity and temperature information and adapted the technique to use the fast spin echo technique. We then applied this novel technique to two important problems. First, we studied pressure-driven flow through a fully-saturated, cylindrical packed bed. In this flow, we observed for the first time flow channeling inside a porous medium, as previously predicted. The MRI technique can also measure the local relative density. Which provides a non-invasive way of determining the spacial distribution of porosity in a porous medium. We used this information to verify previous findings concerning long-range spacial order and spacial oscillations in the porosity of packed beds of spheres. We found that the distribution of velocities in the flowing system is exponential. To our knowledge, this surprising fact has never before been documented. In the second application, we studied Porous Media Convection, PMC, from onset to eight times the critical Rayleigh number, Rac. We analyzed both ordered and disordered packings of mono-disperse spheres, in circular, rectangular, and hexagonal planforms. The disordered media was characterized by large ordered regions of close packing with grain boundaries and isolated defects. The defects created regions of larger ii permeability, and thus spacial variations in the Rayleigh Number, Ra. We define the critical Ra, Rac, as Ra at the onset of convection in the ordered regions. We find that stable localized convective regions exist around grain-boundaries and defects at Ra < Rac and remain as pinning sites for the convection patterns in the ordered regions as Ra is increased above Rac. In ordered media, defects only occurred within a thin region near the vertical walls. Stable localized convection began at 0.5Rac in the wall regions, and did not seem to affect the pattern in the interior regions. We observed roll-like structures that decayed rapidly to stable patterns between 1 and 5Rac, which is consistent with theory. However, we found a wavenumber which is 0.7? compared to ? derived from linear stability theory. We found an asymmetry between the size of up-flowing and down-flowing regions, with their ratio decreasing as Ra is increased, and a time-dependent state beginning at 6Rac and continuing through 8Rac, the largest Ra that we studied. the slope of the Nusselt curve was determined to be 0.70 ± 0.05 which does not agree with the predicted value of 2.
