Dynamic settling of particles in shear flows of shear-thinning fluids

Abstract

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractDynamic settling is the phenomenon whereby a relatively dense particle settles through a sheared flow of a non-Newtonian fluid at a speed that depends on the shear rate of the background flow. This means that due to the nonlinear rheology, the settling velocity may vary spatially and temporally as the background shear rate of the suspending fluid varies, an effect which does not occur in Newtonian fluids. In this contribution, the consequences of this dependency are explored for a dilute suspension of particles released uniformly from a source in a sustained and externally-driven flow of shear-thinning fluid. It is shown theoretically that the concentration field does not remain uniform, but evolves downstream, allowing calculation of the runout length, settling times and distribution of the deposited particles. Flows with a velocity maximum are demonstrated to affect the concentration field very strongly as they develop a 'kinematic barrier' over which settling times are considerably lengthened. Flows with bidisperse suspensions are shown to produce deposits that vary nonmonotonically in thickness and composition with distance downstream, an effect which is solely due to dynamic settling. Finally flows of viscoplastic fluids which exhibit yielded and unyielded regions may accentuate the role and effects of the kinematic barrier to settling.

Direct numerical simulation of particle sedimentation in a Bingham fluid

“…Settling of suspensions in viscoplastic fluids can be categorized as static settling or dynamic settling, depending on the background flow conditions (quiescent in the former). It is well known in the oil industry that background shear enhances settling [15] in shear-thinning fluids. For viscoplastic fluids, Merkak et al [16] and Ovarlez et al [17] demonstrated shearinduced settling in fluids regardless of the yield number, showing that particles settle as soon as the fluid yield stress is overcome by macroscopic shear.…”

Shear settling in laminar open channel flow: analytical solution, measurements and numerical simulation

“…An example of a numerical calculation of tailings deposition and sand segregation along a longitudinal beach cross-section is shown in Figure 4. Analytical linear theories for segregation in these open channels are provided by Sisson et al (2012) (1DV), Childs (2013) (2DV) and Childs et al (2016). Gelled bed formation is not contained in these analytical approaches.…”

“…The static settling has been removed in our analysis. With reference to Chapter 5 of the PhD thesis by Childs (2013), the solution for the concentration distribution in the 2DV x-z plane is obtained by the mathematical method of characteristics, giving: Figure 6 shows the gross correspondence between the theories. There are, however, differences in the lower 20% of the flow.…”

“…. With particle settling in the Stokes regime, the dimensionless horizontal coordinate ofChilds et al (2016) is cast into:…”