Abstract
Granular chute flow simulations reveal an interesting transition from a random disordered structure to an ordered one with hexagonally ordered sheets of spherical particles, when the base roughness is modulated. Two types of base roughness are considered. The first is a fixed base, where glued spherical particles form the base, and the base roughness is varied by changing the ratio of diameters of the base and flowing particles. In the second sinusoidal base, a smooth wall with sinusoidal height variation is used; the amplitude and wavelength of the base modulation determine the base roughness. The transition is studied as a function of these roughness parameters. For the fixed base, there is a critical base particle diameter below which ordered states are observed. For the sinusoidal base, the critical amplitude increases linearly with the wavelength at lower wavelengths, reaches a maximum depending on the height of the flowing layer, and then decreases as the wavelength is further increased. There is flow for angles of inclination from 15 ° ≤ θ ≤ 25 ° for the ordered state and 20 ° ≤ θ ≤ 25 ° for the disordered state. Flow confinement by sidewalls also influences the rheology of the system and we see that the ordering is induced by the sidewalls as well. Experiments on chute flow at low angles indicate the presence of two types of rheology depending on the system height. A transition is observed from an erodible base configuration, where a dead zone at the bottom supports a free surface reposing at the top, to a Bagnold rheology with considerable slip at the bottom.
Highlights
Granular chute flow has been extensively used as a phenomenological model for understanding the mechanics of landslides, and industrial processes such as flow over a conveyor belt
The ordered states exhibit steady flow for a chute angle, θ, between 15 < θ < 25 and the disordered states flow between 20 < θ < 25. Both these states conform to the Bagnold rheology where the stress was proportional to the strain rate squared
We further present in this paper a series of simulations examining the effect of another type of base modulation, wherein a smooth wall at the bottom is provided a periodic structure of the form, w0 + a · sin(2πp/λ), where w0 is the reference position of the wall, a is the amplitude of the position perturbation, λ is the wavelength, p is either the flow direction x, or the span direction, y
Summary
Granular chute flow has been extensively used as a phenomenological model for understanding the mechanics of landslides, and industrial processes such as flow over a conveyor belt. A sharp discontinuous transition from a random disordered structure to one with hexagonally ordered layers of flowing sheets of particles was observed, when the fixed base particle diameter decreased from 0.62 to 0.61, relative to the flowing particles (of diameter 1). These observations were independent of the angle of inclination and system depth. The ordering is quantified through the 2D order parameter q6, which is defined as follows: qm
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