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We perform three-dimensional numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross-shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross-shear flow is a secondary flow with amplitude 10 % of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modelled using the elastoviscoplastic constitutive laws proposed by Saramito ( J. Non-Newtonian Fluid Mech. , vol. 158 (1–3), 2009, pp. 154–161). The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary method. Our results show that the fore–aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross-shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross-shear flow cannot be derived from the pure sedimentation drag law owing to the nonlinear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction. 

We experimentally investigate particle migration in a non-Brownian suspension sheared in a Taylor–Couette configuration and in the limit of vanishing Reynolds number. Highly resolved index-matching techniques are used to measure the local particulate volume fraction. In this wide-gap Taylor–Couette configuration, we find that for a large range of bulk volume fraction, $$\unicode[STIX]{x1D719}_{b}\in [20\,\%{-}50\,\%]$$ , the fully developed concentration profiles are well predicted by the suspension balance model of Nott & Brady ( J. Fluid Mech. , vol. 275, 1994, pp. 157–199). Moreover, we provide systematic measurements of the migration strain scale and of the migration amplitude which highlight the limits of the suspension balance model predictions. 

We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier–Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarizes. These different behaviours are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centreline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high-speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.