Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers

Abstract

We study the incipient motion of single spheres in steady shear flow on regular substrates at low particle Reynolds numbers. The substrate consists of a monolayer of regularly arranged fixed beads, in which the spacing between beads is varied resulting in different angles of repose and exposures of the particle to the main flow. The flow-induced forces and the level of flow penetration into the substrate are determined numerically. Since experiments in this range had shown that the critical Shields number is independent of inertia but strongly dependent on the substrate geometry, the particle Reynolds number was fixed to 0.01 in the numerical study. Numerics indicates that rolling motion is always preferred to sliding and that the flow penetration is linearly dependent on the spacing between the substrate particles. Besides, we propose an analytical model for the incipient motion. The model is an extension of Goldman’s classical result for a single sphere near a plain surface taking into account the angle of repose, flow orientation with respect to substrate topography and shielding of the sphere to the linear shear flow. The effective level of flow penetration is the only external parameter. The model, applied to triangular and quadratic arrangements with different spacings, is able to predict the dependence of the critical Shields number on the geometry and on the orientation of the substrate. The model is in very good agreement with numerical results. For well-exposed particles, we observed that the minimum critical Shields number for a certain angle of repose does not depend sensitively on the considered arrangement. At large angles of repose, as expected in fully armoured beds, the model is consistent with experimental results for erodible beds at saturated conditions.

Water Polishing improved controlled-release characteristics and fertilizer efficiency of castor oil-based polyurethane coated diammonium phosphate

“…The AOR of granular material is the inclination angle relative to the horizontal plane when the particle is at static condition. At this angle, the material on the slope is at the edge of sliding 39 . Generally, the decrease of AOR is indicative of improved fluidization characteristics of particles.…”

The Physics of Sediment Transport Initiation, Cessation, and Entrainment Across Aeolian and Fluvial Environments

“…It is also not equivalent to the comparably simple physics of fluid entrainment by a nonfluctuating flow. For example, when a laminar flow of a Newtonian fluid shears a target particle resting on the sediment bed, there are critical values of the fluid shear stress , which depend on the local bed arrangement, above which this particle begins to roll and slide, respectively (Agudo et al, ; Deskos and Diplas, ). Once motion begins, resisting forces weaken and, since the flow does not fluctuate, the particle will inevitably leave its bed pocket (i.e., become entrained).…”

The Cessation Threshold of Nonsuspended Sediment Transport Across Aeolian and Fluvial Environments

“…Mean flow entrainment models derive a transport initiation threshold Shields number from a force balance, and/or torque balance, between mean fluid forces and resisting contact forces acting on a representative particle resting on the bed surface (Agudo et al, 2017;Ali & Dey, 2016;Bagnold, 1936Bagnold, , 1941Bravo et al, 2014Bravo et al, , 2017Claudin & Andreotti, 2006;Dey, 1999Dey, , 2003Dey & Papanicolaou, 2008;Duan et al, 2013;Durán et al, 2011;Edwards & Namikas, 2015;He & Ohara, 2017;Iversen et al, 1976Iversen et al, , 1987Iversen & White, 1982;Lee et al, 2012;Lehning et al, 2000;Ling, 1995;Lu et al, 2005;Luckner & Zanke, 2007;Recking, 2009;Rousar et al, 2016;Schmidt, 1980;Shao & Lu, 2000;Vollmer & Kleinhans, 2007;Ward, 1969;Wiberg & Smith, 1987;White, 1940;Wu & Chou, 2003). Many of these models have been proposed to reproduce the Shields diagram, which displays two kinds of fluvial thresholds: a threshold obtained from extrapolating measurements of the transport rate to (nearly) vanishing transport and visual measurements of the initiation threshold of individual transport (see section 4.3 for details).…”

“…The former criteria are typically used for turbulent fluvial flows (Buffington & Montgomery, 1997;Miller et al, 1977;Paphitis, 2001, and references therein), whereas the latter criteria are preferred for laminar fluvial (Govers, 1987;Yalin & Karahan, 1979) and turbulent aeolian flows (Bagnold, 1936(Bagnold, , 1937(Bagnold, , 1941Burr et al, 2015;Carneiro et al, 2015;Chepil, 1945;Dong et al, 2003;Greeley et al, 1976;Iversen et al, 1976;Iversen & Rasmussen, 1994;Iversen & White, 1982;Lyles & Krauss, 1971;Webb et al, 2016) because bulk transport can be easily visually identified in these environments: by the formation of grain carpets in laminar fluvial flows and by very large particle hops in turbulent aeolian flows. A further situation sometimes studied in the laboratory is the beginning motion of a single particle on top of a prearranged substrate (Agudo et al, 2014(Agudo et al, , 2017(Agudo et al, , 2018Agudo & Wierschem, 2012;Celik et al, 2010;Charru et al, 2007;Deskos & Diplas, 2018;Diplas et al, 2008;Fenton & Abbott, 1977;Kudrolli et al, 2016;Valyrakis et al, 2010Valyrakis et al, , 2011Valyrakis et al, , 2013. Moreover, it is worth highlighting that Salevan et al (2017) proposed a fundamentally different criterion for the onset of significant motion based on analyzing the particle velocity distribution of all particles, including those nearly static ones that belong to the bed surface.…”