Incipient motion of a single particle on regular substrates in laminar shear flow

Abstract

We study experimentally the critical conditions for incipient motion of a single spherical particle deposited on a regular substrate under laminar flow conditions. The substrates are triangular and quadratic arrangements of identical glass spheres. For the latter configuration, the distance between the substrate spheres is varied, resulting in different partial shielding of the deposited particle to the shear flow. For the studied particle Reynolds numbers range between 3 × 10−4 and 3, the critical Shields number is independent from the particle density and from the particle Reynolds number but it depends significantly on the geometry of the substrate. Depending on the spacing between the substrate beads and thus on the exposure of the particle to the flow, we have observed an increase of about 50 percent in the critical Shields number. Studying the onset of particle motion as a function of the orientation of the substrate to the flow direction we find that the critical Shields number changes by up to a factor of 2, which is mainly due to the fact that the particle travels through the troughs of the substrate and hence the shear force in travel direction diminishes if not in line with the flow direction. Besides the critical Shields number we study the initial stage of particle motion by detecting the minimum time that is necessary for maintaining a certain Shields number to change the position of a single particle on the regular substrates. In the range studied, the initial stage of motion on the scale of the substrate's periodicity is mainly governed by the equilibrium particle motion.

How do neighbors affect incipient particle motion in laminar shear flow?

“…31 In recent experiments, we corroborated the strong impact of the substrate geometry on the incipient motion of a single bead. 32 Depending solely on the substrate's geometrical arrangement, we obtained critical Shields numbers ranging between 0.015 and 0.06 in laminar shear flows. These values for incipient motion of a single particle resulted considerably lower than those of irregularly arranged granular beds.…”

“…As shown in Ref. 32, the chosen parameter range is independent from any boundary effects within the range of particle Reynolds numbers considered. The larger substrates, together with a Plexiglas or glass plate of 150 mm diameter, are used for studies of several mobile spheres.…”

“…The smaller ones are identical to those used for studies on a single particle. 32 In this case, the beads are located in the middle of the substrate. The substrates themselves are placed off-centered into the container such that the mobile beads are at a distance, r, of 21 mm from the rheometer's turning axis.…”

“…Like in Ref. 32, the substrates are fixed on supports and placed on the bottom of a circular container with an inner diameter of 176 mm and with 25 mm high sidewalls made from Plexiglas. The container is placed in an MCR 301 rotational rheometer from Anton Paar.…”

Advection and dispersion of bedload tracers

“…The entrainment of particles strongly depends on the arrangement of the bed: grains highly exposed to the flow move first (Charru et al, 2004;Turowski et al, 2011;Agudo and Wierschem, 2012). In most gravel-bed rivers, this configuration is rare.…”