Showing papers on "Herschel–Bulkley fluid published in 1986"

Yield stress: A time-dependent property and how to measure it

Abstract: This paper reviews the different aspects of the yield stress phenomenon and attempts a synthesis of knowledge. Yield stress can be probed using constant shear stress or shear rate. The magnitude of the result depends on the time allowed to determine whether the sample has developed continuous flow or has ceased flowing. It is closely associated with creep, stress growth and thixotropic breakdown and recovery, and the characteristic times of these transient responses play a part in yield stress measurement. In thixotropic fluids, yield stress is a function of structure and hence of time. In simple thixotropy, the yield stress derived from the equilibrium flow curve is the same as that for the fully built-up structure. But in many materials, the static yield stress obtained after prolonged rest is much higher than the dynamic yield stress from the equilibrium flow curve. This is associated with the phenomenon in which the equilibrium flow curve bends upwards as the shear rate is reduced to very low values. The paper also reviews the many methods that can be used to measure yield stress. It is pointed out that the choice of observation time or shear rate to use should be related to the characteristic time of the flow process to which the result is to be applied. Examples discussed are solids suspension capability of fluids, levelling and sagging, pipeline flow and start-up power requirement of mixers.

Peristaltic transport of a couple-stress fluid

Abstract: The problem of peristaltic transport of a couple-stress fluid has been investigated under a zero Reynolds number and long wavelength approximation. A comparison of the results with those for a Newtonian fluid model shows that the magnitude of the pressure rise under a given set of conditions is greater in the case of the couple-stress fluid. The pressure rise increases as the couple-stress parameter\(\bar \eta \) decreases. The difference between the pressure rise for a Newtonian and a couple-stress fluid increases with increasing amplitude ratio at zero flow rate. However, increasing the flow rate reduces this difference.

Fluid property evaluation by piezoelectric crystals operating in the thickness shear mode

Abstract: Hydrodynamic coupling between a fluid and a planar piezoelectric crystal operating in the thickness shear mode provides a powerful, yet remarkably simple means to characterize fluid properties. Equations describing hydrodynamic coupling are developed for Newtonian fluids. This analysis takes into account, for the first time, the influence of a nonuniform piezoelectric crystal surface velocity. In particular, a Gaussian velocity distribution, suggested by other work, yields a functional relationship between hydrodynamic coupling and the fluid viscosity/density product that is in agreement with experiment. Beginning with these results, analytical methods for measuring individually the fluid visocity and density are described. Finally, it is demonstrated experimentally that the automatic gain control from the piezoelectric crystal oscillation circuit provides a ready means of fluid property characterization.

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.

Hydromagnetic Stokes flow in a rotating fluid with suspended small particles

Abstract: An initial value investigation is made of the motion of an incompressible, viscous conducting fluid with embedded small spherical particles bounded by an infinite rigid non-conducting plate. Both the plate and the fluid are in a state of solid body rotation with constant angular velocity about an axis normal to the plate. The flow is generated in the fluid-particle system due to non-torsional oscillations of a given frequency superimposed on the plate in the presence of a transverse magnetic field. The operational method is used to derive exact solutions for the fluid and the particle velocities, and the wall shear stress. The small and the large time behaviour of the solutions is discussed in some detail. The ultimate steady-state solutions and the structure of the associated boundary layers are determined with physical implications. It is shown that rotation and magnetic field affect the motion of the fluid relatively earlier than that of the particles when the time is small. The motion for large times is set up through inertial oscillations of frequency equal to twice the angular velocity of rotation. The ultimate boundary layers are established through inertial oscillations. The shear stress at the plate is calculated for all values of the frequency parameter. The small and large-time behaviour of the shear stress is discussed. The exact solutions for the velocity of fluid and the wall shear stress are evaluated numerically for the case of an impulsively moved plate. It is found that the drag and the lateral stress on the plate fluctuate during the non-equilibrium process of relaxation if the rotation is large. The present analysis is very general in the sense that many known results in various configurations are found to follow as special cases.

Optimum economic pipe diameter for pumping herschel‐bulkley fluids in laminar flow

Abstract: A method for determining optimum pipe diameter, for which total pumping system cost is minimum, has been derived for the transport of Herschel-Bulkley (H-B) fluids (power-law fluids with a yield stress) in laminar flow. the method accounts for pipe system cost as a function of diameter, and pump station and operating costs as a function of power requirements. the optimum diameter can be estimated given rheological properties, fluid density, mass flow rate and economic parameters. Optimum diameter does not depend on system elevation or pressure energy difference when a linear relationship is used for pump station cost. Friction loss in fittings and valves can be ignored when the pipe length is much greater than the pipe diameter. Pump station cost has less influence than operating cost in determining the optimum diameter.

Steady Laminar Flow of Power‐Law Fluids in the Inlet Region of Rectangular Ducts

Abstract: A steady laminar flow of an incompressible non‐Newtonian fluid (inelastic power law fluid, n<1) in the inlet region of rectangular ducts was studied by the theoretical analysis using finite difference methods and the experiment on pressure drops. Theoretical predictions were compared with experimental data and analytical results available and the agreement was shown to be satisfactory. Therefore, the axial pressure distributions and the velocity profiles in the inlet region were discussed on the basis of typical computations. It was shown that the velocity in the duct center and the pressure drop of a power law fluid were smaller than those of a Newtonian fluid; the inlet length of a power law fluid was larger than that of a Newtonian fluid and increased with the decreasing power law index. Also, the additional pressure loss in the inlet region was smaller in a power law fluid than in a Newtonian fluid and decreased with the decreasing power law index. In addition, when the effect of duct shape was consid...

Dissipative instability of fluid flows with piecewise linear velocity profiles

Abstract: The viscous dissipative instability of two flows with continuous spectrum of neutrally-stable perturbations in the absence of dissipation is investigated. Ranges of wave numbers in which viscosity leads to flow destabilization are determined for a shear discontinuity in a smoothly-stratified fluid. A shear flow with a velocity in the transition layer that depends linearly on the coordinate has a continuum of neutral modes even in the case of an unstratified fluid. When viscosity is present in one of the layers with constant velocity, one of the branches of the spectrum becomes unstable. When the viscosity is the same above and below the shear layer, dissipation only leads to the damping of the perturbations.