Rheology of Inelastic Hard Spheres at Finite Density and Shear Rate

Abstract

Considering a granular fluid of inelastic smooth hard spheres, we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress σ to the shear rate _ γ and predictions of the yield stress complete our discussion of granular rheology derived from first principles.

Dynamical yield criterion for granular matter from first principles

“…The model we present in this paper is based on a simplification of the Granular Integration Through Transients (GITT) formalism. For more details about this model, the reader is referred to the more detailed previous publications on the subject [53][54][55][56][57][58][59], as well as the appendix. This formalism is based on the so-called Integration Through Transients (ITT) formalism [60,[63][64][65], which allows to compute statistical averages in a sheared fluid by relating them to averages computed in a quiescent state where no shear is applied.…”

“…In this paper, we propose a study of the yielding transition based not on a theory of the solid, but of the liquid state. More precisely, using a theory developed to describe the non-Newtonian features of granular liquid flows [53][54][55][56][57][58][59] in the limit of very low shear rates, we describe how an internal state of stress develops into the liquid as its behavior becomes more and more solid-like. Such a determination of a so-called dynamical yield criterion has previously been done for the study of colloidal suspensions close to the mode coupling glass transition [60].…”

Rheology of granular liquids in extensional flows: Beyond the $μ(\mathcal{I})$-law

“…In Mode Coupling Theory (MCT), the dynamical evolution of the system is studied by use of its dynamical structure factor Φ q (t) which is the normalised densitydensity correlation function: Φ q (t) = ρ q (t)ρ −q /S q , where S q = ρ q ρ −q is the static structure factor [27,28,[40][41][42][43][44][45]. The general MCT equation has the structure of a Mori-Zwanzig equation:…”

“…In that respect, one promising candidate is the Granular Integration Through Transients formalism (GITT in the following) [27][28][29][30]. Indeed, it has been shown that GITT predictions are quantitatively compatible with the existing experimental and numerical literature [29], and that GITT equations can be broken down to analytically tractable toy-models from which one can derive the expression Eq.…”

“…However the equations derived in previous works [27][28][29][30] only apply to simple shear flows. While this case is relevant to a number of natural flows, such as avalanches for example [13,24], it does not provide a full description of the possible rheological behaviors of granular liquids.…”