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.

Laminar, unidirectional flow of a thixotropic fluid in a circular pipe

Abstract: In this paper we study the unidirectional, axisymmetric flow of a bentonite mud in a circular pipe. Bentonite mud is an inelastic, thixotropic, generalised-Newtonian fluid. We use a rheological model that characterises this behaviour in terms of a single parameter Λ which is a measure of the amount of structure in the fluid. The behaviour of Λ is determined by a single rate equation which models the tendency of fluid structure to increase whilst being limited by the imposed shear rate. We find that, for certain parameter ranges, the model is not structurally stable, but that this problem can be eliminated by including diffusion of fluid structure. A graph of the equilibrium shear stress for a given shear rate (the rheogram) is not monotonic, yet no mechanical instability occurs in pipe flow. We contrast this with recent work on the pipe flow of a Johnson-Segalman-Oldroyd fluid which displays spurting and oscillatory behaviour. The difference lies in the relative magnitude of normal stress effects in the two fluids. There appear to be no grounds for discarding the constitutive model studied here simply because of the non-monotonicity of the equilibrium rheogram.

The significant influence of internal stresses on the dynamics of bubbles in a yield stress fluid

Abstract: The shape and trajectory of bubbles in Carbopol gels were accurately observed over long periods. As the concentration increases, the trajectories are observed to evolve from vertical and rectilinear to three-dimensional shapes. Local strain and velocity fields have been determined. Bubble injection is quasi-static in order to obtain a separation governed by the equilibrium among surface tension, buoyancy and stresses applied to the bubble. Internal stresses in the fluid, of structural origin and induced by the mechanical history in the fluid volume, remain in the fluid for at least several months. They play a major role in bubble formation and propagation.

The effects of stress and fluid pressure on the anisotropy of interconnected cracks

Abstract: SUMMARY The cracks in a porous matrix that is subjected to a change in the applied stress or fluid pressure will undergo a distortion related to their orientation relative to the principal directions of the applied stress. Both the crack distribution and the fluid-flow properties of the aggregate will be altered as a consequence, of a change in either the applied stress or fluid pressure, resulting in a change in the effective elastic parameters of the material. An effective medium theory, based on the method of smoothing and incorporating a transfer of fluid between connected cracks via non-compliant pores, is used to derive an expression for the effective elastic parameters of the material, to first order in the crack density � . This expression involves a dependence on both the applied stress and the fluid pressure, and is used to determine the effects on the anisotropy of the effective medium of the applied stress and the fluid pressure. A number of azimuthally symmetric compressive stresses are applied to an isotropic crack distribution to determine the material properties of the resulting transversely isotropic effective medium, as a function of the excess in compressive stress over fluid pressure. As a result of competing processes, the theory predicts that, for a non-hydrostatic stress, there is a pressure at which the anisotropy reaches a maximum value before the properties of the effective medium decay, under increasing stress, to those of the uncracked matrix. The theory does not, however, account for the material failure that will occur at large compressive stresses. Finally, the theory predicts that S waves are more sensitive to changes in the applied stress or fluid pressure than P waves.

Rheopexy and tunable yield stress of carbon black suspensions

Abstract: We show that besides simple or thixotropic yield stress fluids there exists a third class of yield stress fluids. This is illustrated through the rheological behavior of a carbon black suspension, which is shown to exhibit a viscosity bifurcation effect around a critical stress along with rheopectic trends, i.e., after a preshear at a given stress the fluid tends to accelerate when it is submitted to a lower stress. Viscosity bifurcation displays here original features: the yield stress and the critical shear rate depend on the previous flow history. The most spectacular property due to these specificities is that the material structure can be adjusted at will through an appropriate flow history. In particular it is possible to tune the material yield stress to arbitrary low values. A simple model assuming that the stress is the sum of one component due to structure deformation and one component due to hydrodynamic interactions predicts all rheological trends observed and appears to well represent quantitatively the data.

Rheological Properties of Rodlike Particles in a Newtonian and a Non‐Newtonian Fluid

Abstract: The macroscopic rheological behavior of suspensions of nearly monodisperse glass fibers having a mean aspect ratio, ār, of 24.3 and a mean length, L, of 267 μm, and commercial ground glass fibers, ār=7.6 and L=84 μm, were studied. Volume fractions of 0.02, 0.05, and 0.08 were used. For Newtonian suspending fluids, the shear viscosities and the dynamic linear viscoelastic properties of the suspension showed Newtonian behavior. In a stress growth experiment, the shear stress obtained a maximum value before reaching steady state. Upon reversal of shearing, a similar stress growth pattern was retraced. The non‐Newtonian suspending fluid, a polyisobutylene in cetane solution, was found to behave as a second‐order fluid at low shear‐rates and frequencies and shear‐thinned at higher values. Suspensions in this fluid also behaved as second‐order fluids at low shear‐rates and frequencies. The dependency of two of the second‐order fluid constants upon the volume fraction of particles was determined.