Dilatancy-driven secondary flows in dense granular materials. (5th March 2021) - Dsouza, Peter Varun; Nott, Prabhu R.
Abstract: Abstract : Flowing granular materials exhibit several features that distinguish them from molecular fluids. A prominent feature is dilatancy, or volume deformation caused by shear deformation. Its significance in sustained flow has not been much appreciated, as its effect was thought to be confined to thin shear layers. However, it was demonstrated recently by Krishnaraj & Nott ( Nat. Commun., vol. 7, 2016, 10630) that dilatancy drives a large-scale secondary flow in a cylindrical Couette device. They hypothesized that the combination of shear and gravity, when their directions are non-collinear, is necessary for the occurrence of the secondary flow. In this paper we investigate the phenomenon by considering a more complex primary flow generated in a split-bottom Couette device, wherein a part of the base of the container filled with a granular material is translated or rotated. It is known from previous studies that the height to which the material is filled determines the shape and extent of the shearing region in the primary flow. We show that the fill height also determines the form of the secondary flow, and argue that the two are intricately coupled and evolve together. Though the secondary flow is more complex than in a cylindrical Couette device, the mechanism is indeed what Krishnaraj & Nott hypothesized: the combined effect of dilatancy driven expansion, and gravity-driven flow down regions of low density. Unlike fluid instabilities that are typically driven by inertia, the secondary flow occurs at arbitrarily low shear rate and appears to be an integral part of the kinematic response.