Probing porous and granular media with noble gas NMR

In recent years, much interest has focused on the physics of granular media: assemblies of macroscopic particles such as sand, gravel, ore, powders, or pharmaceutical pills that interact primarily through contact forces. Granular materials are ubiquitous in a wide range of industrial processes and complex systems. The properties of flowing granular matter are dominated by rapid inelastic collisions between the grains, which quickly dissipate the kinetic energy unless it is replenished by gravity, external vibration, or interstitial gas flow. Granular flows have revealed a host of behaviors that are unexpected from ordinary fluids, such as non-Newtonian boundary layers, propagating density waves, and avalanches. Furthermore, if a mixture of the material is stirred, shaken or rotated, different particle sizes or masses typically segregate into different regions of the confining container, in contrast to the homogenizing effect stirring has in ordinary fluids.

Theories of granular media dynamics have attempted to extend established notions from fluid mechanics, kinetic theory, or nonequilibrium thermodynamics. However, testing these theories is difficult for 3D systems, because the opacity of most granular materials presents a key difficulty to obtaining structural and dynamical information from within the system. Thus an outstanding problem in this field is to develop non-invasive, high-resolution spatial probes of 3D granular media and their interstitial spaces.

To address this problem, we applied novel technologies such as pulsed-field-gradient (PFG) NMR, MRI, and hyperpolarized noble gas. Our projects included the use of PFG NMR and MRI (i) to map grain density and displacements in a three-dimensional vibrofluidized granular medium, and (ii) to probe the flow and dynamics of hyperpolarized noble gas in a gas-fluidized granular bed. We were able to determine, for the first time, the "granular temperature" (proportional to the random kinetic energy per motional degree of freedom of the grains) as a function of height in a 3D vibrated sample; and found reasonable agreement with the predictions of "granular hydrodynamic" theory. This work was collaboration with Prof. Don Candela of UMass-Amherst.

We also used video observation to investigate the role of interstitial gas in the segregation by mass of a two-component, vertically-vibrated granular medium (bronze and glass spheres). Click here to see examples of the different segregation phenomena that occur in the presence of interstitial gas -- for different vibration frequencies and amplitudes -- and also to see how these segregation phenomena disappear when the interstitial gas is removed (i.e., under vacuum).

We also developed noble gas nuclear magnetic resonance (NMR) as a non-destructive probe of the structure of porous media. We used pulsed-field-gradient (PFG) NMR and magnetic resonance imaging (MRI) to measure the flow and diffusion of noble gas (3He and 129Xe) imbided into the pore space of granular materials, animal lungs, and oil- or water-reservoir rocks. Diagnosing the structure of these materials is relevant to a wide range of scientific and technological problems. For example, knowledge of the fluid transport properties of reservoir rocks is important for the monitoring of contaminant percolation and for oil extraction. Similarly, knowledge of the evolution of the porous structure of materials subjected to large thermal or mechanical stress may help characterize the dynamics of cracking and material failure. Also, non-invasive mapping of lung structure could advance our understanding of normal physiology as well as disease diagnosis. 

The advantages of noble gas NMR as a porous media diagnostic arise from three physical effects: (i) gas diffusion coefficients are orders of magnitude larger than those of liquids, which allows long distances to be probed; (ii) noble gas atoms interact weakly with pore surfaces, which enables long NMR lifetimes; and (iii) noble gases are chemically inert and biologically compatible. We employed both hyperpolarized and thermally-polarized noble gas in our measurements.

We showed that noble gas NMR can characterize important porous media parameters such as permeability, effective porosity, tortuosity, and the distribution of pore sizes. Permeability is a measure of the ability of a porous material to transmit fluid. Effective porosity is the volume fraction of a pore space that is fully interconnected and contributes to fluid flow through the material, excluding dead-end or isolated pores that cannot be part of a flow path. Tortuosity is a measure of the long-distance pore connectivity of the medium.

 

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