On the role of non-equipartition in the dynamics of rapidly flowing granular mixtures

Abstract

For rapidly flowing granular mixtures, existing kinetic-theory descriptions based on an assumed form of the velocity distribution function typically contain one of two simplifying assumptions: a Maxwellian velocity distribution or an equipartition of energy. In the current work, the influence of non-equipartition effects is explored in the context of two flow types: flow in which species segregation does not occur (namely, simple shear flow) and a segregating flow. For the former case, a comparison between existing kinetic theories and molecular-dynamics simulations of a binary system indicates that the incorporation of a non-Maxwellian velocity distribution is critical for reliable stress predictions, as is consistent with previous findings. However, the predictions are fairly insensitive to the equipartition versus non-equipartition treatment, despite the presence of a significant non-equipartition of energy. Nevertheless, an analysis of the diffusion equation for a segregating flow indicates that the presence of a non-equipartition of energy gives rise to additional components of the driving forces associated with size segregation. These additional components involve gradients of the species temperature, whereas theories based on an equipartition assumption only involve gradients in the mixture temperature. Molecular-dynamics simulations of the segregating flow, in conjunction with kinetic theory of binary systems, show that the non-equipartition effects are non-negligible for systems characterized by moderate values of mass differences and restitution coefficients. These simulations also reveal that the more massive particle may exhibit a lower species temperature than its lighter counterpart, contrary to previous observations in non-segregating systems. A physical explanation for this behaviour is provided.

Hydrodynamic profiles for an impurity in an open vibrated granular gas

“…Nevertheless, the relationship between this kind of driving and actual experiments is uncertain. The non-equipartition has also been confirmed by MD simulations of simple shear flows [5] and of vibrated granular gases (in absence of gravity) [6].…”

Modelling size segregation of granular materials: the roles of segregation, advection and diffusion

“…These studies have identified several driving mechanisms for segregation, pattern formation, and mixing of bidisperse particles. In the dilute, energetic flow regime, where particles interact mainly through binary collisions, the gradient of granular temperature alone can drive size segregation, which is successfully modeled by kinetic theory (Jenkins & Mancini 1989;Hsiau & Hunt 1996;Khakhar et al 1999;Arnarson & Willits 1998;Galvin et al 2005;Yoon & Jenkins 2006). In contrast, in the dense granular flow regime, particle geometry appears to be the primary driving mechanism.…”

Phase Transitions in Shear-Induced Segregation of Granular Materials

“…In sheared dilute energetic granular mixtures all particles accumulate in the regions of low shear rateγ corresponding to regions of low T and high f , and larger particles do so more efficiently (e.g., [8][9][10][11]) leaving the latter segregated at the regions of lowestγ and T , highest f . This has been successfully modeled using kinetic theory [8,[11][12][13][14] for sufficiently sparse flows. For moderate solids fractions, kinetic theory has been shown to overpredict segregation trends, though still qualitatively reproduce the outcome [10].…”

“…[8,11]). All particles move to regions of low-T , low-γ, high f in the center of chute, though large particles do so more efficiently [See Fig.…”