NMR studies of granular media and two-phase flow in porous media
This dissertation describes two experimental studies of a vibrofluidized granular medium and a preliminary study of two-phase fluid flow in a porous medium using Nuclear Magnetic Resonance (NMR). The first study of granular medium is to test a scaling law of the rise in center of mass in a three-dimensional vibrofluidized granular system. Our granular system consisted of mustard seeds vibrated vertically at 40 Hz from 0g to 14g. We used Magnetic Resonance Imaging (MRI) to measure density profile in vibrated direction. We observed that the rise in center of mass scaled as ν 0α/Nlβ with α = 1.0 ± 0.2 and β = 0.5 ± 0.1, where ν 0 is the vibration velocity and Nl is the number of layers of grains in the container. A simple theory was proposed to explain the scaling exponents.
In the second study we measured both density and velocity information in the same setup of the first study. Pulsed Field Gradient (PFG)-NMR combined with MRI was used to do this measurement. The granular system was fully fluidized at 14.85g 50 Hz with Nl ≤ 4. The velocity distributions at horizontal and vertical direction at different height were measured. The distributions were nearly-Gaussian far from sample bottom and non-Gaussian near sample bottom. Granular temperature profiles were calculated from the velocity distributions. The density and temperature profile were fit to a hydrodynamic theory. The theory agreed with experiments very well. A temperature inversion near top was also observed and explained by additional transport coefficient from granular hydrodynamics.
The third study was the preliminary density measurement of invading phase profile in a two-phase flow in porous media. The purpose of this study was to test an invasion percolation with gradient (IPG) theory in two-phase flow of porous media. Two phases are dodecane and water doped with CuSO4. The porous medium was packed glass beads. The front tail width σ and front width of invading phase were extracted from fitting of the invading front profile. The front tail scaled as σ∞Ca −α, where Ca is capillary number and α is 0.4 ± 0.08. The result is very close to IPG predication 0.25.
0759: Fluid dynamics