Velocity Correlations in Dense Granular Flows

Abstract

Velocity fluctuations of grains flowing down a rough inclined plane are experimentally studied. The grains at the free surface exhibit fluctuating motions, which are correlated over few grains diameters. The characteristic correlation length is shown to depend on the inclination of the plane and not on the thickness of the flowing layer. This result strongly supports the idea that dense granular flows are controlled by a characteristic length larger than the particle diameter.PACS numbers: 45.70.Mg, 83.50.Ax Dry cohesionless granular material can flow like a liquid, for example in an hourglass or on an inclined plane. However, the flow properties are not yet well understood and constitutive equations appropriate to describe the dense flow regime when particles are in close contact are still matter of debate [1,2]. One of the difficulty is that, in the dense regime, particles do not interact through binary collisions like in dilute and agitated granular gases [3,4]. They rather experience contact with several neighboring particles at the same time. The description of the multi-particles interactions is important in the development of constitutive equations. Recent theoretical models try to take into account the existence of this contact network through different approaches. Some models describe the flow as a mixture of solid and liquid phases [5] or try to account for the frictional contacts by adding a frictional term in collisional theories [6,7]. Other models consider the presence of arches in the flow [8,9] or account for some non local propagation of momentum through the contact network [10,11]. In this paper we will more specifically refer to a recent model proposed by Ertas and Halsey [12] to describe granular flows on an inclined plane. By introducing the idea of correlated motion of grains in clusters-like structures, they have been able by simple scaling arguments to recover some important results observed for flows down inclined plane. The experimental study presented in this paper is inspired by their approach, trying to evidence the existence of correlated motions in granular flows down inclined planes.The inclined plane configuration is obtained when a granular layer of thickness h flows down a rough surface inclined at an angle θ (Fig. 1). Experiments [1,13] and numerical simulations [14,15] have revealed two important results. First, for a given inclination θ, a minimum thickness h stop (θ) exists below which no flow is possible. This thickness is evidenced by the deposit remaining on the plane once the flow stops. Second, the variation of the depth averaged velocity u with the inclination θ and thickness h appears to be linked to the deposit function h stop (θ) through a flow rule:where g is gravity and β is a constant equal to 0.13 for spheres. The fact that the influence of θ on the flow velocity comes into play through the deposit function h stop (θ) is not straightforward and could be simply the result of a coincidence [7]. However, an interesting interpretation of relation 1 has been pro...

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“…In spite of the differences in their formulations, these nonlocal models are all based on the key assumption that there exists a meso-scale length which is larger than the grain size d and that it represents the extent of non-locality, i.e., the influence on the flow at one point due to flows at its neighbouring points. An association of this length with the critical stopping height of grains on inclined plane [13][14][15] has been made [16], which suggested possible link between jamming and non-locality. Here we show how this length representing non-locality can be attributed to the development of correlated structures of jammed particles within the flow.…”