Correlation Time and Diffusion Coefficient Imaging: Application to a Granular Flow System

Caprihan, Arvind; Seymour, Joseph D.

doi:10.1006/jmre.2000.2033

Cited by 44 publications

(41 citation statements)

References 38 publications

(66 reference statements)

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“…Three-dimensional granular systems have been studied experimentally by external probes such as capacitance [28], mutual inductance [29] and diffusingwave spectroscopy [30], as well as by non-invasive internal probes including NMR [31,32,33,34,35,36] and positron-emission particle tracking (PEPT) [37]. The PEPT method has been used to measure the granular temperature profile of a vibrofluidized bed at volume filling fractions up to 0.15 [37].…”

Section: Introductionmentioning

confidence: 99%

“…Other workers have used NMR to study the dense granular flows that occur in a rotating drum [31,36], for quasi-static tapping [32], in a period-doubled arching flow [33], and in a Couette shear apparatus [35]. In contrast to these earlier studies we probe a system sufficiently simple to be described by first-principles granular hydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

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NMR experiments on a three-dimensional vibrofluidized granular medium

et al. 2004

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A three-dimensional granular system fluidized by vertical container vibrations was studied using pulsed field gradient (PFG) NMR coupled with one-dimensional magnetic resonance imaging (MRI). The system consisted of mustard seeds vibrated vertically at 50 Hz, and the number of layers N ℓ ≤ 4 was sufficiently low to achieve a nearly time-independent granular fluid. Using NMR, the vertical profiles of density and granular temperature were directly measured, along with the distributions of vertical and horizontal grain velocities. The velocity distributions showed modest deviations from Maxwell-Boltzmann statistics, except for the vertical velocity distribution near the sample bottom which was highly skewed and non-Gaussian. Data taken for three values of N ℓ and two dimensionless accelerations Γ = 15, 18 were fit to a hydrodynamic theory, which successfully models the density and temperature profiles including a temperature inversion near the free upper surface.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

NMR experiments on a three-dimensional vibrofluidized granular medium

et al. 2004

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“…MRI has proven itself as a powerful tool for measuring the time-averaged velocity inside 3D granular flows [19][20][21] and has been used to measure the average flow properties within the bulk in granular Couette flow [10]. MRI has also been used to measure the diffusion coefficient and correlation times for flowing granular material [22,23].…”

Section: Introductionmentioning

confidence: 99%

Measurements of particle dynamics in slow, dense granular Couette flow

Mueth

2003

Phys. Rev. E

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Experimental measurements of particle dynamics on the lower surface of a 3D Couette cell containing monodisperse spheres are reported. The average radial density and velocity profiles are similar to those previously measured within the bulk and on the lower surface of the 3D cell filled with mustard seeds. Observations of the evolution of particle velocities over time reveal distinct motion events, intervals where previously stationary particles move for a short duration before jamming again. The cross-correlation between the velocities of two particles at a given distance r from the moving wall reveals a characteristic lengthscale over which the particles are correlated. The autocorrelation of a single particle's velocity reveals a characteristic timescale τ which decreases with distance from the inner moving wall. This may be attributed to the increasing rarity at which the discrete motion events occur and the reduced duration of those events at large r. The relationship between the RMS azimuthal velocity fluctuations, δv θ (r), and average shear rate,γ(r), was found to be δv θ ∝γ α with α = 0.52 ± 0.04. These observations are compared with other recent experiments and with the modified hydrodynamic model recently introduced by Bocquet et al. INTRODUCTIONThe detailed understanding of slow flow in dense granular systems has remained one of the central challenges in the field of granular materials [1]. While fast dilute granular flows are fluid-like and can be described well by granular kinetic theory [2][3][4], slow flows at high packing fraction preserve many of the complex properties of static granular packs and may be more accurately described as slow, plastic deformation of a metastable granular solid than flow of a fluid. Recent work by Howell and Behringer [5,6] showed that many of the intriguing properties of granular solids, such as the broad distribution of stresses and the presence of "force chains" which focus stresses along paths of many connected particles, play a crucial role. Direct visualization revealed that the flow is intermittant in time and that correlations, both in time and in space, exist [7]. These are seen as intervals over which one or more particles in a region become unjammed, move for a short time, and then become jammed again. Such properties of dense granular flow are reminiscent of behavior seen in glasses, dense colloidal suspensions, and foams [8]. Recent studies have been successful at relating stresses in stationary bead packs with those in glassy fluids [9], suggesting the two systems may also have similar flow properties for high packing fractions and low shearing rates. It is hoped that an understanding of dense granular flow will provide insight into the properties of static granular packs as well as the broader class of jammed systems.From previous work a number of unresolved fundamental questions about slow, dense granular shear flow emerge. Although videos and plots of particle trajectories suggest that particle velocities are correlated both in space and in time, the...

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“…Multiple gradient methods provide the ability to determine multiple displacement directional correlations [16,57], velocity time and directional correlations [58], frequency dependent dispersion [59] and velocity autocorrelation functions [60,61]. In addition rapid 'single shot' techniques for the measurement of effective diffusion and flow provide the means to acquire complete data in the millisecond time scale to study transient behavior [62,63].…”

Section: Advanced Techniquesmentioning

confidence: 99%

Finla Technical Report DE-FG02-03ER63576

Seymour¹

2007

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The magnetic resonance microscopy (MRM) work at Montana State University has extended the imaging of a single biofilm in a 1 mm capillary reactor to correlate T 2 magnetic relaxation maps displaying biofilm structure with the corresponding velocity patterns in three dimensions in a Staphylococcus epidermidis biofilm fouled square capillary. A square duct geometry is chosen to provide correlation with existing experiments and simulations, as research bioreactors tend to be of square or rectangular cross section for optical or microelectrode access. The spatially resolved velocity data provide details on the impact of biofilm induced advection on mass transport from the bulk fluid to the biofilm and through the capillary bioreactor. These issues are of significant importance in biosensor and bioseparations applications based on microfluidics or 'lab on a chip' technology, as well as a model for a flow in fractured geological media. Extension of published work in Journal of Magnetic Resonance applied concepts from the theory of fluid mixing to quantify the secondary flows induced by the spatially heterogeneous biofilm. The secondary flows are measured to be 20% of the axial velocity and indicate a significant alteration of transport from the bulk fluid to the biomass from diffusive to convective dominated. A paper has been published in Biotechnology and Bioengineering detailing the experimental results and analysis. The impact of microbial activity, particularly surface attached biofilms, on the transport of fluids in porous systems is relevant to fields as seemingly diverse as geophysics and medicine. Few direct experimental data on the impact of bioactivity on transport dynamics in three-dimensional media are available due to sample opacity. Non-invasive magnetic resonance microscopy (MRM) directly measures length and time scale dependent dynamics in porous media. Our research demonstrates by direct measurement of the propagator, i.e. the displacement conditional probability or van Hove scattering function, the transition from normal to anomalous hydrodynamic dispersion as a function of bioactivity. The microbial activity transforms the porous media from a homogeneous to heterogeneous structure, increasing system complexity as defined in terms of dynamics. Continuous time random walk (CTRW) based fractional advection-diffusion equation (ADE) models which generate anomalous or fractional dynamics are compared to the measured dynamics in both the propagator displacement space and the Fourier reciprocal displacement wavelength space. The data provide insight into the application and development of fractional calculus based models and indicates their direct applicability to biofilm impacted porous media transport. A manuscript reporting these results was published in Physical Review Letters. Unsaturated flow in porous media has been analyzed using magnetic resonance (MR) propagator measurements of scale dependent displacement. The data show a change in dynamics from Gaussian to non-Gaussian. Velocity and pore distrib...

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Correlation Time and Diffusion Coefficient Imaging: Application to a Granular Flow System

Cited by 44 publications

References 38 publications

NMR experiments on a three-dimensional vibrofluidized granular medium

NMR experiments on a three-dimensional vibrofluidized granular medium

Measurements of particle dynamics in slow, dense granular Couette flow

Finla Technical Report DE-FG02-03ER63576

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