Unifying Suspension and Granular flows near Jamming

Abstract

Abstract. Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we review a theoretical framework that gives a scaling description of stationary flows of frictionless particles. Our analysis applies both to suspensions and inertial flows of hard particles. We report numerical results in support of the theory, and show the phase diagram that results when friction is added, delineating the regime of validity of the frictionless theory.

Integration through transients approach to the $μ(\mathcal{I})$ rheology

“…Therefore, some caution has to be taken when looking at predictions of packing fractions close to 60%. Moreover, around I = 10 −3 , it is expected that the flow enters a friction dominated regime [25,37,38,82], which effects should begin to come into play in the lowest Is of our data, but are completely absent of our frictionless model. However, the extent to which such failures are responsible for the behavior observed on Fig.…”

“…4 is its superlinear character above the granular glass transition ϕ g [61,62]. This is indeed quite surprising since at low I the corrections to the linear behavior imposed by the approach of jamming are typically sublinear [37,38,82]. As explained above, it is expected that our hard spheres equation of state underestimates the true value of the pressure, which is all the more problematic that its contribution is typically half of the total pressure at the highest packing fractions we investigated.…”

“…Indeed, even within the liquid phase, the physics of granular flows does not seem to be unified. More particularly, at high enough densities, a whole range of new phenomena arise, including the jamming physics due to increased importance of friction [34][35][36][37][38], discontinuous shear thickening [39,40], turbulent-like power laws in the energy spectrum [41][42][43][44], and the development of creep flows and plastic deformations that make the rheology non-local [10,[45][46][47][48][49][50][51][52][53][54][55]. Our target regime is therefore densities high enough so that the granular sample can be qualified as liquid, but moderate enough so that the µ(I) rheology can still be applied, so roughly a packing fraction in the range 0.40 ϕ 0.60 (see Fig.…”

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

“…We thus restrict ourselves to high densities but sufficiently far away from the friction dominated regime. It should be noted however that defined in that way, the liquid state of granular matter does not extend up to the transition to the solid state which depends on the value of the interparticle friction coefficient [35][36][37][38][39]. The transition between the liquid and interparticle friction dominated regime has been estimated to take place for inertial numbers I 0.003 [38].…”

Granular rheology: a tale of three time scales

“…Despite the absence of attractive force in the simplest granular flows, three distinct flow regimes can be identified depending on the granular fluid's density [17]: at low density, collisions are relatively scarce, this is the gaseous regime; at higher densities -typically 0.4 ϕ 0.6the grains experience very frequent collisions, which significantly affect their qualitative behavior, this regime is called the liquid regime; finally, close to the jamming transition, interparticle friction becomes relevant with deep consequences [18][19][20][21]. Most examples of granular flows on Earth are in the liquid regime [17], this study focuses on this latter one.…”