Motion of a particle near a rough wall in a viscous shear flow

Abstract

The motion of a spherical particle along a rough bed in a simple shear viscous flow is studied experimentally for a wide range of parameters, varying the particle size and density, the fluid viscosity and the shear rate γ. The instantaneous particle velocity is calculated in the stream, transverse and vertical directions, using a high-speed video imaging system. It is found that the normalized streamwise mean particle velocity U/US, where US is the Stokes settling velocity, depends only on the dimensionless shear rate μ γ/(Δ ρ g d), this relationship being independent of the particle Reynolds number Rep. This result holds for small Rep, which was the case in our experiments (Rep < 10). The characteristic amplitude and frequency of the velocity fluctuations are also given and discussed. A model is then proposed for the mean streamwise velocity, based on ideas of Bagnold (Proc. R. Soc. Lond. A, vol. 332, 1973, p. 473) and calculations of Goldman et al. (Chem. Engng Sci., vol. 22, 1967b, p. 653) for the velocity of a particle close to a smooth plane. From this model an equivalent bed roughness and an effective friction coefficient are deduced.

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

“…We remark that the critical Shields numbers detected in our study and also in that by Charru et al 20 are considerably lower than those around 0.12 provided by Ouriemi et al, 17 Charru et al 20 and Derksen 19 for the onset of particle motion in irregularly arranged granular beds. In view of our results, this can be understood due to the strong dependence of the critical Shields number on the burial degree as well as on the angle between flow and substrate orientation.…”

“…Deviations from this linear dependency at higher Shields numbers could be traced back to detachment of the particle from the substrate. 20 In line with Bagnold 30 who considered the mean horizontal force as a superposition of a fluid force and a friction force due to interactions with the substrate, Charru et al described the mean travelling velocity by…”

“…20 The packing coefficient of our substrates, defined as the fraction of an area filled with circles, corresponds to the optimal density in the plane for the triangular arrangement, 0.91 and around 0.76 for the quadratic substrate with a gap of 14 μm between particles.…”

“…In particular, Charru et al obtained for their irregular bed of identical particles and for Shields numbers up to 0.17 the following values: 18u eff = 6.67, μ F = 0.38, and C D = 2.4. 20 The last term in (5) is a threshold value that takes into account the resistance to motion due to the uneven substrate and thus depends on the critical Shields number. Extending the model by Charru et al to account for different substrates, we assume the resistance to be proportional to the critical Shields number of the substrates.…”

“…Studying a single particle on an irregularly arranged bed of identical particles, Charru et al observed an influence of the local substrate geometry on the onset of particle motion and the traveling trajectory. 20 Accordingly, they provided a critical Shields number range around 0.02-0.04 for onset of single particle motion. Likewise, the authors showed that the fluctuating motion of the particle was due to the irregular bed geometry.…”