Theory of Dilute Binary Granular Gas Mixtures

Abstract

Abstract. A computer-aided method for accurately carrying out the Chapman-Enskog expansion of the Boltzmann equation, including its inelastic variant, is presented and employed to derive a hydrodynamic description of a dilute binary mixture of smooth inelastic spheres. Constitutive relations, formally valid for all physical values of the coefficients of restitution, are calculated by carrying out the pertinent Chapman-Enskog expansion to sufficient high orders in the Sonine polynomials to ensure numerical convergence. The resulting hydrodynamic description is applied to the analysis of a vertically vibrated binary mixture of particles (under gravity) differing only in their respective coefficients of restitution. It is shown that even with this "minor" difference the mixture partly segregates, its steady state exhibiting a sandwich-like configuration.

Hydrodynamics of binary mixtures of granular gases with stochastic coefficient of restitution

“…Thermal segregation in granular mixtures has been identified as one of the main factors of the Brazil Nut effect (Hsiau & Hunt 1996;Schröter et al 2006) in the case of granular gases, and its dependence on the particle properties has been studied in the past (Arnarson & Willits 1998;Jenkins & Yoon 2002;Brey et al 2005;Garzó 2008). In particular, it was predicted (Serero et al 2006) and observed in molecular dynamic simulations (Brito et al 2008;Brito & Soto 2009;Serero et al 2009;Serero, Noskowicz & Goldhirsch 2011) that the species in a binary mixture may segregate even when they differ only in their respective coefficients of restitution, demonstrating a direct influence of inelasticity on the properties of binary granular gas mixtures. Here, we proceed with a similar analysis by considering particles of the same mass, size and average coefficient of restitution, and Laplacian distributions for the three types of coefficient of restitution, with different standard deviations.…”

Experimental determination of temperature profiles in a sheared granular bed containing two and three sizes of particles

“…Hrenya [20] simulated particles of different size and identified the tendency to segregate. Various kinetic theory based models have been proposed [21][22][23][24][25] with varying degrees of applicability and accuracy. Binary systems are becoming better understood.…”