Granular flows

Granular matter is all around us. It ranges from natural materials such as sand and asteroids to artificial materials such as pharmaceutical tablets and dry cereal. There is great and practical interest in static granular matter from the standpoint, for 

With the rare exception of xenon gas NMR of fluidized beds, which we discuss later, granular flow studies by NMR detect signals from the particles and not the surrounding medium. Because it is technically easier to obtain NMR signals from liquids rather than solids, the majority of granular NMR studies so far use solid particles containing liquids. 

The beauty of MRI in medical imaging is its sensitivity to different chemical or physical properties that give useful contrasts between volumes having different properties, for example, cancerous tissue versus normal tissue, both having similar density. This greatly reduces the need for accurate density measurements because it shifts the burden of image contrast to a parameter that is more sensitive than density. 

The relative resolution of an MRI does not depend particularly on the size of the imaged object and usually is of the order of one part in 102. Thus, the absolute resolution obtainable by MRI depends on the size of the system being imaged. The density resolution depends on many factors, but is usually of the order of a few percent. 

A more quantitative method is the so-called phase method, the phase being one of two parameters that an MRI image yields, the other being signal amplitude. We show below (Section 4.8.2.6) that the phase is correlated with the velocity of the sample, so a spatially resolved image of the signal phase can yield a velocity image. 

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Ding, J. and Gidaspaw, D., Bubbling fluidization model using kinetie theory of granular flows, AIChE J, 36, 523, 1990. 

For many measurements specific to granular flows, such as velocity profiles, acceleration or of vibrating samples, a laboratory with NMR/MRI expertise is desirable. Therefore, much of the future progress in NMR/MRI studies of granular systems will come from collaborations of granular matter experts with such laboratories that have the expertise in NMR/MRI. 

M. Nakagawa, S.A. Altobelli, A. Caprihan, E. Fukushima 1997, (NMR measurement and approximate derivation of the velocity depth-profile of granular flow in a rotating, partially filled, horizontal cylinder), in Powders and Grains 97, Proceedings of the Third International Conference on Powders el Grains, eds. 

Tardos, G. I., and Khan, M. I., Study of Granulation in a Constant Shear Granular Flow Couette Device, Paper presented at the Annual AIChE Meeting, Miami Beach, Florida (1995)... 

The methods used for modeling pure granular flow are essentially borrowed from that of a molecular gas. Similarly, there are two main types of models the continuous (Eulerian) models (Dufty, 2000) and discrete particle (Lagrangian) models (Herrmann and Luding, 1998 Luding, 1998 Walton, 2004). The continuum models are developed for large-scale simulations, where the controlling equations resemble the Navier-Stokes equations for an ordinary gas flow. The discrete particle models (DPMs) are typically used in small-scale simulations or... 

Bokkers, G. A., Van Sint Annaland, M., and Kuipers, J. A. M., Comparison of continuum models using kinetic theory of granular flow with discrete particle models and experiments extent of particle mixing induced by bubbles. Proceedings of Fluidization XI, May 9-14, 2004, 187-194, Naples, Italy (2004). 

TFL. 10.1. Prigogine and R. Herman, Prologue, Proceedings of the Workshop Traffic and Granular Flow, World Scientific, Singapore. 

P.A. Langston, U. Tuzun, D.M. Heyes, Distinct element simulation of granular flow in 2D and 3D hoppers dependence of discharge rate and wall stress on particle interactions, Chem. Eng. Sci. 50 (1995) 967-987. 

R.J. Spurling, J.F. Davidson, D.M. Scott, The transient response of granular flows in an inclined rotating cylinder, Trans. I. Chem. E. 79 (2001) 51-61. 

Ding J, Gidaspow D. A bubbling fluidization model using the kinetic theory of granular flow. AIChE J 1990 36 523-538. 

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