Characterization of base roughness for granular chute flows

Abstract

Base roughness plays an important role in the dynamics of granular flows but is still poorly understood due to the difficulty of its quantification. For a bumpy base made of spheres, at least two factors should be considered in order to characterize its geometric roughness, namely, the size ratio of flow to base particles and the packing arrangement of base particles. In this paper, we propose an alternative definition of base roughness, R_{a}, as a function of both the size ratio and the distribution of base particles. This definition is generalized for random and regular packings of multilayered spheres. The range of possible values of R_{a} is presented, and optimal arrangements for maximizing base roughness are studied. Our definition is applied to granular chute flows in both two- and three-dimensional configurations, and is shown to successfully predict whether slip occurs at the base. A transition is observed from slip to nonslip conditions as R_{a} increases. Critical values of R_{a} are identified for the construction of a nonslip base at various angles of inclination.

Effect of geometric base roughness on size segregation

“…Φ = 2.0, the sliding can not be avoided by varying base constructions. In fact, as [20] pointed out, neither the size nor the packing is a sole indicator of the slip/non-slip regimes. With the base roughness R a defined in Eq.…”

“…Both the size and packing of base particles are influential to the flow kinetics [20]. As seen in Fig.…”

“…In this case, A i /A m is truncated such that R a 1, and a non-zero weight is assigned to the underneath layer. This process is referred to as multi-layer composition and is elaborated in [20]. Clearly, R a is a function of spacing ε k and size ratio Φ, with limits of zero and unity; for each layer, a wider spacing or a larger size of base particles tends to enhance the geometric roughness.…”

“…By contrast, a flat surface with only mechanical friction usually leads to a shear layer near the base, above which plug flows may occur with poorly-developed shear [5,9,10]. In discrete element modelling (DEM), one can construct a rough base by fixing a layer of particles with a regular/random packing [5,9,[11][12][13][14][15][16][17][18][19][20][21]. For such a bumpy base, both the size and spatial distribution of the fixed particles are influential factors of the geometric roughness.…”

“…To better understand the basal effect on flow dynamics, it is favorable to characterise geometric rougness in terms of these two factors. A recent work by Jing et al [20] proposes an alternative indicator of base roughness, R a . It is shown that in mono-disperse flows R a well describes the geometric roughness of any arbitrary base composing equally-sized e-mail: fiona.kwok@hku.hk spheres; as R a increases, a phase transition occurs from slip (R a < 0.51) to non-slip (R a > 0.62) regimes, with an intermediate regime of R a ∈ [0.51, 0.62].…”