NMR experiments on a three-dimensional vibrofluidized granular medium

Abstract

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.

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

“…For higher densities the α range is more limited but the Enskog theory still captures the relevant qualitative features. The Enskog transport coefficients for a monocomponent gas [62] have also been tested against NMR experiments of a system of mustard seeds vibrated vertically [43,44]. The average value of the coefficient of restitution of the grains used in this experiment is α = 0.87, which lies outside of the quasielastic limit (α ≈ 0.99).…”

“…This is so since the reference state is a local HCS whose parameters change throughout the system to match the physical values in each cell. Another examples of good agreement between theory and simulation [42] and experiments [43,44] include the application of the Navier-Stokes hydrodynamics to describe density/temperature profiles in vertical vibrated gases, supersonic flow past at wedge in real experiments [45], and nonequipartition and size segregation in agitated granular mixtures [27,28,46]. In summary, the Navier-Stokes hydrodynamics with the constitutive equations obtained in this paper constitute an important and useful description for many different physical situations, although more limited than for elastic gases.…”

Heat flux in a granular gas

“…This new contribution to the heat flux was predicted by kinetic theory methods [6,7,8], and later on measured in molecular dynamic simulations [9]. Also, some implications of its existence have been observed in experiments [10,11,12,13]. The theoretical formal reasons why this density gradient contribution to the heat flux is present in granular fluids and absent in normal ones has been investigated.…”

Micromechanical analysis of inclusions in particulate media using digital photo stress analysis tomography

“…Other experimental approaches have also been used to characterize particulate assemblies. These include x-ray micro tomography, 12 nuclear magnetic resonance imaging, 13 and positron emission particle tracking, 14 but these are mostly aimed at probing the density and velocity distribution inside particulate samples. Visual information on how relatively big particulate inclusions sustain shear at different elevations inside a compaction chamber is still unclear.…”