Pair-particle trajectories in a shear flow of a Bingham fluid

Abstract

We study numerically the pair trajectories of rigid circular particles in a two dimensional inertialess simple shear flow of a (Binghamian) yield stress fluid. We use a Lagrange multiplier based fictitious domain method, following Glowinski et al. [26, 28, 29], for solving the problem. Contacts between the particles at a finite interparticle distance interpreted as a roughness are taken into account with the da Cunha and Hinch [12] model. Another model, introduced by Glowinski et al. [27], is shown to provide similar results in the limit of infinite contact stiffness. Due to the nonlinear behavior of the suspending fluid, it is found that the trajectories of the particles depend on the shear rate, the relevant dimensionless parameter being here the Bingham number, which compares plastic forces to viscous forces. In absence of interparticle contacts, fore-aft symmetry is observed in all cases; however, the particles are found to come closer to each other as the Bingham number is increased: the plastic behavior of the suspending fluid decreases the range of hydrodynamic interactions. As contacts are introduced, fore-aft asymmetry is observed. Plastic effects are found to enhance surface roughness effects: contacts between particles occur for smaller surface roughness at large Bn. Moreover, the magnitude of the asymmetry is increased as the Bingham number is increased. These observations may explain why the microstructure of suspensions of particles in a yield stress fluid is shear-rate-dependent [45] leading to a complex nonlinear macroscopic behavior.

The interaction of two spherical particles in simple-shear flows of yield stress fluids

“…Second, for trajectories with small initial offsets, the second particle moves downward along the velocity gradient direction on the approach side while it moves upward on the recession side. The same pattern is observed in the simulations by Fahs et al in [93] for yield stress fluids as well as Newtonian fluids. These local minima in trajectories disappeared in their results for the Newtonian fluid when the domain size is increased from 24a 12a to 96a 48a.…”

“…3.2). This feature, which has been also x/a y/a observed in simulations of Fahs et al [93], implies larger asymmetry in the PDF, and consequently, larger normal stress differences in the yield stress suspensions as we increase the Bingham number. Fig.…”

“…We think that this pattern can be attributed to the elasticity of the test fluid since no such behavior is observed in simulations when the fluid is considered ideal visco-plastic (e.g. Bingham model) [93]. Second, for trajectories with small initial offsets, the second particle moves downward along the velocity gradient direction on the approach side while it moves upward on the recession side.…”

“…While the majority of the experimental works and simulations focused on the settling of particles in yield stress fluids, there are no simulation or experimental work on the interaction of two particles in a linear shear flow of a yield stress fluid in the literature. However, a paper relating a numerical 2D study of the interaction of pairs of particles in an ideal Bingham fluid is under review at the same time as our paper; our experimental results will be qualitatively compared to the simulation results when relevant [93].…”

Effects of Tailings Gradation on Rheological Properties of Filling Slurry

“…e ultimate goal of measuring the rheological parameters of a slurry is to calculate its friction loss coe cient to indicate its performance in a pipeline. e pipe friction loss under di erent ow rates based on the Bingham ow model is calculated using the following formula [41][42][43][44]:…”