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We consider the micro- and the macro-scale to investigate the motion of single grains in a dilute suspension under shear flow and Poiseuille flow to analyze effects like shear-wall migration and rolling of grains as observed in physical experiments. To be able to simulate the behavior of fresh concrete or mud flow, as realistically as possible, we are taking into account a non-Newtonian Bingham–Papanastasiou rheology for the carrier fluid. Due to a surface coupled approach, Smoothed Particle Hydrodynamics (SPH) gives the opportunity to consider both, the motion of a solid particle, by tracking its center of mass and also surface points, and the interaction and influence on the near field of the velocity field in the fluid phase. We show an independence of the motion of solid grains from the surrounding carrier fluid. While the macroscopic flow reaches a stationary flow field quite fast, the motion of the solid grains still oscillates between parts of the fluid that flow with different velocities and does not show a stable steady state. Providing a comparison between the motion in a Newtonian and a non-Newtonian fluid, we point out the differences and thus the importance of the choice of the material model for the carrier fluid in numerical simulations. • SPH simulations of suspensions with Newtonian or non-Newtonian carrier fluid. • Detailed analysis of the motion of solid grains in a suspension on different scales. • Focus on the analysis of the near velocity field at the surface of solid grains. [Display omitted] [ABSTRACT FROM AUTHOR]

Analytical solutions are derived for the cessation of annular Poiseuille and Couette flows of a Newtonian fluid in the presence of dynamic wall slip. We employ linear dynamic slip law involving a slip relaxation parameter, which results in the appearance of the eigenvalue parameters in the boundary conditions and thus leads to distinct Sturm–Liouville problems that differ from their static slip counterparts. The proper orthogonality condition is derived and closed-form analytical solutions are obtained for both flows of interest. Representative results are then presented and discussed. In agreement with previous reports for other flows with dynamic wall slip, the present solutions show that wall slip slows down flow dynamics and this effect becomes more pronounced as the slip-relaxation parameter is increased. • Analytical solutions of Newtonian annular flows with dynamic wall slip are derived. • The proper Sturm-Liouville problems are considered. • The cessation of annular Poiseuille and annular Couette flows is investigated. • Wall slip and the slip relaxation parameter are shown to damp flow dynamics. [ABSTRACT FROM AUTHOR]

For a horizontal channel flow of a weakly viscoelastic liquid that follows the constitutive model of Walters' liquid B ′ ′ , a linear stability analysis is performed when the channel walls are slippery. In this case, the viscoelastic channel flow is driven by the streamwise pressure gradient. We explore the primary instability for a symmetric slip flow with the same slip length of the channel walls, an asymmetric slip flow with different slip lengths of the channel walls, and an analogy to the Poiseuille–Couette flow of a viscoelastic liquid with a slip effect on the lower wall but no slip effect on the upper wall. We observe that the viscoelastic parameter shows a destabilizing impact, but the slip length shows a stabilizing impact on the most unstable shear mode in all three flow configurations. Moreover, the Poiseuille and Poiseuille–Couette flows for the viscoelastic liquid are linearly more unstable to infinitesimal disturbances than those of the Newtonian liquid. As a result, wall velocity needs to be higher than in the Newtonian liquid to stabilize the viscoelastic Poiseuille–Couette flow. Using the asymptotic analysis, we have determined the critical value of the slip length, or equivalently, the critical value of the lower wall velocity, above which the asymmetric slip flow and the Poiseuille–Couette flow of the viscoelastic liquid are permanently stable to infinitesimal disturbances. [Display omitted] • Viscoelastic parameter shows a destabilizing influence on shear mode instability. • Slip length shows a stabilizing influence on shear mode instability. • Viscoelastic asymmetric slip flow is more unstable than viscoelastic Poiseuille–Couette flow. • Viscoelastic asymmetric slip flow is linearly stable if slip length exceeds critical value. • Viscoelastic Poiseuille–Couette flow is linearly stable if wall velocity exceeds critical value. • Critical value of slip length for Walters' liquid B ′ ′ is larger than that of Newtonian liquid. • If slip effect is included on upper wall, transition from laminar to turbulence becomes slower. [ABSTRACT FROM AUTHOR]

We comment on the series solutions presented in the paper "Newtonian Poiseuille flow in ducts of annular-sector cross-sections with Navier slip" for the no-slip case. [ABSTRACT FROM AUTHOR]

Abstract We consider the Newtonian Poiseuille flow in a duct the cross section of which is either a circular or an annular sector assuming that Navier slip occurs either along both the cylindrical walls or only along the outer cylindrical wall. A general analytical solution is derived and the results for the latter case are discussed and the effects of the angle of the sector, the radii ratio and the slip number are analysed. Highlights • The Newtonian Poiseuille flow in ducts of annular-sector or circular-sector cross-sections is considered. • Navier slip is assumed to occur along the circular walls. • A general analytical solution is derived for the above flow. • The effects of the sector angle, the radii ratio and the slip number are analysed. [ABSTRACT FROM AUTHOR]

In this paper, we address a new wall slip formulation based on a series expansion of both differential and exponential forms of wall shear stress. As this is initially considered as an infinite series, we use a truncated version of it to get a slip law having three slip coefficients, where we have considered the exponential form only. We use our new truncated triple-slip-coefficients wall slip law to analyze a particular class of viscoelastic non-Newtonian fluid. This special case follows the Phan–Thien–Tanner fluid model. Moreover, for this fluid, we identify Weissenberg number as one salient parameter affecting slip. In particular, our new model is tested on a familiar planar Couette and planar Poiseuille flow problem, where two parallel and infinitely long plates have been used. Furthermore, slip-dependent analytical expressions for field quantities such as velocity and shear stress at the walls and beyond, are derived and numerically analyzed for both problems. In addition, the pressure and flow-rate are derived for various slip coefficients for Poiseuille flow case. Our results obtained prove reasonable as represented by physically realistic plots herein. This feasibility is especially dictated by the velocity profile across channel width for both application problems. Thus, we can infer from all these, that this new model has the potential of providing results which can match experimental data, that is, if the three slip-coefficients are properly chosen. [ABSTRACT FROM AUTHOR]

We consider both the axisymmetric and planar steady-state Poiseuille flows of weakly compressible Newtonian fluids, under the assumption that both the density and the shear viscosity vary linearly with pressure. The primary flow variables, i.e. the two non-zero velocity components and the pressure, as well as the mass density and viscosity of the fluid are represented as double asymptotic expansions in which the isothermal compressibility and the viscosity–pressure-dependence coefficient are taken as small parameters. A standard perturbation analysis is performed and asymptotic, analytical solutions for all the variables are obtained up to second order. These results extend the solutions of the weakly compressible flow with constant viscosity and those of the incompressible flow with pressure-dependent viscosity. The combined effects of compressibility and the pressure dependence of the viscosity are analyzed and discussed. [ABSTRACT FROM AUTHOR]