Herschel–Bulkley fluid

About: Herschel–Bulkley fluid is a research topic. Over the lifetime, 1946 publications have been published within this topic receiving 49318 citations.

Squeeze flow of a power-law viscoplastic solid

Abstract: A cylinder of height h is squeezed between two parallel circular plates of radius R >>h. The cylinder is assumed to behave as a generalised Newtonian material in which the stress and strain rate are coaxial: the particular cases of a rigid-plastic solid and power-law fluid are considered in detail. It is assumed that the frictional stress at the walls is a fixed fraction m of the yield stress in shear, k, in the case of the plastic material, and a fixed fraction of the effective Mises stress in the case of the power-law fluid. This boundary condition, often used in plasticity analysis, leads in both cases to a constant shear stress at the walls, rather than a no-slip boundary condition. Hoop stresses are included in an approximate analysis in which stresses and velocities are expanded as series in inverse powers of the radial coordinate r: these expansions break down near the axis r = 0 of the cylinder. The force required to compress the rigid-plastic cylinder is F= 2 3 mkϵR 3 h − + 1 2 3 kϵR 2 [(1−m 2 ) 1 2 + m − sin − m]+ O(kRh) independent of the speed of compression. The analysis can be extended to other solids and fluids characterised by a coaxial constitutive relation: by way of example, results are presented for the Bingham fluid.

Instability of a bed of particles sheared by a viscous flow

Abstract: The instability of a bed of particles sheared by a viscous fluid is investigated theoretically. The viscous flow over the wavy bed is first calculated, and the bed shear stress is derived. The particle transport rate induced by this bed shear stress is calculated from the viscous resuspension theory of Leighton & Acrivos (1986). Mass conservation of the particles then gives explicit expressions for the wave velocity and growth rate, which depend on four dimensionless parameters: the wavenumber, the fluid thickness, a viscous length and the shear stress. The mechanism of the instability is given. It appears that for high enough fluid-layer thickness, long-wave instability arises as soon as grains move, while short waves are stabilized by gravity. For smaller fluid thickness, the destabilizing effect of fluid inertia is reduced, so that the moving at bed is stable for small shear stress, and unstable for high shear stress. The most amplified wavelength scales with the viscous length, in agreement with the few available experiments for small particle Reynolds numbers. The results are also compared with related studies for turbulent flow.

Constitutive Relationships for Fluid-Solid Mixtures

Abstract: Constitutive equations are derived for the rapid shear flow of a mixture formed from granular solids in a fluid. The stress state within the mixture is considered to be created by the momentum exchange between colliding solids. The constitutive equations describe the shear and normal stresses as a function of the velocity gradient, friction and restitution coefficients of the solids, the fluid drag coefficient for the particle shape and the density of the solid and fluid constituents. The theoretical results agree well with the results obtained from numerous laboratory experiments.