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
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.
- NMR measurements of grain and gas motion in a gas-fluidized granular bed. D. Candela, C. Huan, K. Facto, R. Wang, R.W. Mair and R.L. Walsworth. Granular Matter, 9, 331-335 (2007). cond-mat/0510611.
- Noninvasive measurements of gas exchange in a three-dimensional fluidized bed using hyperpolarized
129XeNMR. T. Pavlin, R. Wang, R. McGorty, M.S. Rosen, D.G. Cory, D. Candela, R.W. Mair and R.L. Walsworth. Applied Magnetic Resonance, 32, 93-112 (2007). cond-mat/0605436.
- Understanding the breakdown of Fourier’s law in granular fluids. D. Candela and R.L. Walsworth. American Journal of Physics, 75, 754-757 (2007). cond-mat/0510295.
- Study of Gas-Fluidization Dynamics with Laser-Polarized
129Xe. R. Wang, M.S. Rosen, D. Candela, R.W. Mair and R. L. Walsworth. Magnetic Resonance Imaging, 23, 203-207 (2005). cond-mat/0407708.
- Xenon NMR Measurements of Permeability and Tortuosity in Reservoir Rocks. R. Wang, T. Pavlin, M.S. Rosen, R.W. Mair, D.G. Cory and R. L. Walsworth. Magnetic Resonance Imaging, 23, 329-331 (2005). cond-mat/0407710.
- Simultaneous Measurement of Rock Permeability and Effective Porosity using Laser-Polarized Noble Gas NMR. R. Wang, R.W. Mair, M.S. Rosen, D.G. Cory, and R.L. Walsworth. Physical Review E, 70, 026312 (2004). cond-mat/0312543.
- NMR Experiments on a Three-DimensionalVibrofluidized Granular Medium. C. Huan, X. Yang, D. Candela, R.W. Mair, and R.L. Walsworth. Physical Review E, 69, 041302 (2004). cond-mat/0305267.
- Applications of Controlled-Flow Laser-Polarized Xenon Gas to Porous and Granular Media Study. R.W. Mair, R. Wang, M.S. Rosen, D. Candela, D.G. Cory, and R.L. Walsworth. Magnetic Resonance Imaging 21, 287 (2003). cond-mat/0211180.
- Diffusion NMR Methods Applied to Xenon Gas for Materials Study. R.W. Mair, M.S. Rosen, R. Wang, D.G. Cory, and R.L. Walsworth. Magnetic Resonance in Chemistry, 40, S29 (2002). cond-mat/0211179.
- The Narrow Pulse Approximation and Long Length Scale Determination in Xenon Gas Diffusion NMR Studies of
Model Porous Media. R.W. Mair, P.N. Sen, M.D. Hürlimann, S. Patz, D.G. Cory, and R.L. Walsworth. Journal of Magnetic Resonance 156, 202 (2002). cond-mat/0211182.
- Measurements of Grain Motion in a Dense, Three Dimensional Granular Fluid. X. Yang, C. Huan, D. Candela, R.W. Mair, and R.L. Walsworth. Physical Review Letters 88, 044301 (2002). cond-mat/0108256.
- Novel MRI Applications of Laser-Polarized Noble Gases. R.W. Mair and R.L. Walsworth. Applied Magnetic Resonance 22, 159 (2002).
- Measuring surface-area-to-volume ratios in soft porous materials using laser-polarized xenon interphase exchange NMR. J.P. Butler, R.W. Mair, S. Patz, D. Hoffmann, M.I. Hrovat, R.A. Rogers, G.P. Topulos, and R.L. Walsworth. Journal of Physics: Condensed Matter 14, L297 (2002). cond-mat/0108344.
- Tortuosity Measurement and the Effects of Finite Pulse Widths on Xenon Gas Diffusion NMR Studies of Porous Media. R.W. Mair, M.D. Hürlimann, P.N. Sen, L.M. Schwartz, S. Patz, and R.L. Walsworth. Magnetic Resonance Imaging 19, 345 (2001). cond-mat/0211184.
- Probing porous media with gas diffusion NMR. R.W. Mair, G.P. Wong, D. Hoffmann, M.D. Hurlimann, S. Patz, L.M. Schwartz, and R.L. Walsworth. Physical Review Letters 83, 3324 (1999).
- Pulsed-field-gradient measurements of time-dependent gas diffusion. R.W. Mair, D.G. Cory, S. Peled, C.H. Tseng, S. Patz, and R.L. Walsworth. Journal of Magnetic Resonance 135, 478 (1998).