(477b) Extension of Kinetic Theory for Granular Binary Mixtures to Moderately Dense Flows

Rapid granular flows of polydisperse mixtures have been shown to exhibit particle segregation (de-mixing) by means of experiments, molecular dynamics simulations, and continuum models. However, the derivation of kinetic theory models becomes exceedingly difficult when one considers polydispersity, as well as finite-volume effects. Consequently, most of the previous polydisperse models have been limited to simplifying assumptions, such as a Maxwellian velocity distribution and/or an equipartition of energy. A few models have been proposed which assume neither of these conditions, specifically the theories formulated by Garzó and Dufty (GD02) [1] and Garzó, Hrenya, and Dufty (GHD07) [2,3] for binary granular mixtures. The derivation of the GD02 theory considers the mass of particles, but not the size, which restricts the use of such a model to dilute flows only. In the theory proposed by GHD07, finite-volume effects are taken into account, which allows this model to be used in moderately dense systems. Because these two theories differ in the starting kinetic equation (Boltzmann for GD02 and Enskog for GHD07), the resulting constitutive relations, or more specifically the corresponding transport coefficients, also differ. The objective of this work is to quantify these differences between all 11 transport coefficients. Namely, to demonstrate the importance of a dense-phase extension (GHD07) relative to the previous dilute-phase theory (GD02), the transport coefficients predicted by each theory were compared over a range of volume fractions (dilute to moderately dense). As hypothesized, a significant discrepancy exists between the dense and dilute-phase predictions, especially in moderately dense systems. During this discussion, some of the essential differences between the above theories, as well as the results of their comparison, will be discussed.

References:

1.) Garzó, V. & Dufty, J. W. 2002 Hydrodynamics for a granular binary mixture at low density. Phys. Fluids 14, 1476.

2.) Garzó, V., Dufty, J. W. & Hrenya, C.M. 2007 Enskog theory for polydisperse granular mixture. I. Navier-Stokes order transport. Phys. Rev. E 76, 031303.

3.) Garzó, V., Hrenya, C.M. & Dufty, J.W. 2007 Enskog theory for polydisperse granular mixture. II. Sonine polynomial approximation. Phys. Rev. E 76, 031304.