Sidewall-friction-driven ordering transition in granular channel flows: Implications for granular rheology

Abstract

We report a transition from a disordered state to an ordered state in the flow of nearly monodisperse granular matter flowing in an inclined channel with a bumpy base, in discrete element method simulations. For low particle-sidewall friction coefficients, the particles are disordered and the Bagnold velocity profile is obtained. However, for high sidewall friction, an ordered state is obtained, characterized by a layering of the particles and hexagonal packing of the particles in each layer. The extent of ordering, quantified by the local bond-orientational order parameter, varies in the crosssection of the channel, with the highest ordering near the side walls. The flow transition significantly affects the local rheology -the effective friction coefficient is lower, and the packing fraction is higher, in the ordered state compared to the disordered state. A simple model, incorporating the extent of local ordering, is shown to describe the rheology of the system.Understanding the flow of granular materials is important in the context of natural phenomena and industrial processes [1][2][3][4][5]. Considerable progress has been made in the development of theories for the rheology of granular flows, with the objective of developing continuum models for the analysis and design of large systems [6][7][8][9][10]. Granular materials exhibit many complex phenomena [11,12]. The ordering of monodisperse granular materials, when subjected to vibration or shear flow, is one example [13][14][15][16][17][18]. The transition from a disordered state to an ordered state is marked by a significant increase in the solid fraction manifested as a compaction of the material [13,17]. In sheared systems, which are the focus of the present study, ordered states show a layering of particles with adjacent particle layers sliding past each other without much interchange of particles between the layers [15,16,19]. Shear stresses are consequently lower compared to the disordered state. Order-disorder transitions thus affect system behavior significantly, however, they have not been explicitly incorporated in the analysis of granular rheology.The most detailed studies of order-disorder transitions in granular shear flow are computational, using the discrete element method (DEM) to simulate the flow of monodisperse particles (diameter d) on a rough inclined plane with periodic boundary conditions (no sidewalls) [19][20][21]. Kumaran and Maheshwari [20] carried out a study of the transition using a base comprising particles of diameter, d b , arranged on a square lattice. When the base roughness parameter (d b /d) was less than 0.6, the system underwent a transition to an ordered state, comprising hexagonally close packed particle layers sliding on each other. The shear stress (τ xy ) in the ordered state followed the Bagnold scaling (τ xy ∝γ 2 , whereγ is the shear rate) but with smaller values of the Bagnold coefficients compared to the disordered state. The transition was very sharp, occurring over a 1% change in the roughness parameter. A...

Boundary-induced inhomogeneity of particle layers in the solidification of suspensions

“…This geometrical constraint breaks the 3D random packing and induces correlations in particles positions, so that modifications of the particle volume fraction φ l are expected. In particular, in granular materials, a wall-induced ordering has been largely evidenced and documented in monodisperse [50][51][52] or bidisperse mixtures [53]. It may even induce crystallization near the walls as found for monodisperse mixtures in channel flows [52], Couette flows [54], or by shaking [55].…”

“…In particular, in granular materials, a wall-induced ordering has been largely evidenced and documented in monodisperse [50][51][52] or bidisperse mixtures [53]. It may even induce crystallization near the walls as found for monodisperse mixtures in channel flows [52], Couette flows [54], or by shaking [55].…”

Shell Crystallization in Granular Hopper Flow

“…The initial crystallized 'nucleus' appeared not only at the boundary but also in the central region [10,29]. Other examples, such as for inclined flow under gravity, the ordering arises upon ordered base or driven by the side wall friction [11,30]. Our observation of the remaining crystallized granular shell also reminds for comparison with the slow motion of retention of viscous fluid on a vertical plate as investigated by Jeffreys in 1930 [31] and by Gutfinger and Tallmadge [32] in non-Newtonian fluids.…”

DEM simulations of quasi-two-dimensional flow of spherical particles on a heap without sidewalls

“…The role of sidewalls in such flows has been investigated by varying the channel width from 20 particle diameters to about 600 particle diameters, and it has been observed that, with increase in the channel width, flows become slower and thicker [9]. It has also been reported that frictional side-walls aid in order-disorder transition of granular flows of monodisperse spheres down an incline with a bumpy base, whereby both the friction coefficient and the packing fraction is altered [10]. Recently, it has also been reported that, for surface flow over an unconfined asymmetric conical heap, the surface angle is significantly lower than the angle of repose as well as independent of flow rates [11].…”