Showing papers on "Herschel–Bulkley fluid published in 1976"

Useful Non-Newtonian Models

Abstract: Here 1t is the total momentum flux (or stress tensor), defined in such a way that the force transmitted from the negative side of a surface element of unit area and normal vector n is [n· 1t] (Bird, Stewart & Lightfoot 1960). The symbol b stands for the unit tensor, , is the extra stress tensor, p is the isotropic pressure, and y = (Vv) + (Vv)t is the rate-of-strain tensor; the viscosity Il depends on temperature, pressure, and concentration, but not on the time t or on any kinematic quantities such as y. It is well known that liquids with complex structure, such as macromolecular fluids, soap solutions, and two-phase fluids are not described by (1). The following are some of the "non-Newtonian" effects that have been observed:

The slow motion of a sphere in a second-order fluid

Abstract: The slow motion of a rigid sphere in a viscoelastic fluid is studied. Variations of the velocity gradient of the undisturbed fluid motion over the dimension of the sphere are neglected. Considering only rheologically slow flows the equations of a second-order fluid are employed. The resulting hydrodynamic force and couple are calculated and shown to be fundamentally different from the corresponding results in a Newtonian fluid: for the force a coupling is found not only for translation and rotation but also for translation and a pure straining motion. For the torque only a coupling between rotation and a pure straining motion exists. It is demonstrated that by means of this coupling the two material parameters can be obtained individually. Furthermore any lateral migration of a sphere in a vertical Poiseuille flow would immediately unmask the fluid as a non-Weissenberg fluid.

Some viscous fluid cosmological models of plane symmetry

Abstract: Two plane-symmetric cosmological models representing viscous fluid with free gravitational field of type D have been obtained. The effect of viscosity on various kinematical parameters has been discussed.

Entrance flow of a yield-power law fluid

Abstract: In the present work we have obtained the numerical solution of the momentum equation for a Yield-Pseudoplastic power-law fluid flowing in the entrance region of a tube. The accuracy of the numerical results is checked by comparing the asymptotic values of friction coefficients and velocity profiles with the corresponding results from the analytical solutions for the fully-developed region. The results of the entrance flow solution for the power-law exponent equal to unity (Bingham fluid) are also in agreement with the numerical solution for a Bingham fluid. Detailed results are presented for wide ranges of yield numbers and power law exponents.

Numerical investigation of the tangential twist of an incompressible viscous fluid jet

Abstract: The problem of the formation of eddy flow of tangential twist is examined. The fluid flow mode is laminar. The flow parameters are found by the numerical solution of the complete system of Navier-Stokes equations.

Structured fluid theory

Abstract: The simplest case of structured fluid theory is shown to correspond to a type of Maxwell fluid which exhibits normal stress differences. A nonlinear problem related to the deformation of suspended liquid drops as induced by inertial effects is solved and the influence of structured fluid parameters investigated.

Expansion of a high‐pressure gas sphere in a porous medium II: Fluid compressible

Abstract: The work presented in an earlier paper [D. Epstein, J. Geophyos. Res. 72, 3701–3710 (1967)] on the expansion of a high‐pressure gas bubble in a fluid‐saturated porous medium, with the fluid treated as incompressible, is extended by treating the fluid as slightly compressible. Two limiting cases are considered: If the particulate matter is carried along with the fluid, the porous medium acts as a dense liquid, with parameters determined by simple functions of the density and compressibility of the fluid and solid particles, and the usual equations of motion apply. However, if the relative velocity of the fluid with respect to the solid is essentially equal to the fluid velocity, the motion is assumed to be governed by a compressible, generalized Darcy equation. From this equation a pair of integrodifferential equations for the bubble radius as a function of time are derived. The form of the radius‐time curve depends on a nondimensional resistance factor m? = (1/2) β?/c, a combination of quantities characte...

First-order approximation in a steady fluid flow problem with surface forces taken into account

Abstract: The plane problem of finding the shape of the free surface of an ideal incompressible fluid is considered for a fully developed discharge from an infinite layer through a point sink. The gravitational and surface stress forces are taken into account.

Flow of a viscous fluid in a deformable valved tube in the presence of gravity

Abstract: The problem of the flow of a viscous incompressible fluid in a tube of finite length with valves at the ends is solved numerically with allowance for gravity and elastic wall properties that vary periodically with time.

Effect of a radial temperature gradient on the stability of the flow of a second-order fluid between two co-axial cylinders

Abstract: It has been found that the effect of a radial temperature gradient on the Taylor stability problem for a viscoelastic fluid and for a Newtonian fluid is the same.

Nonisothermal flow of a non-Newtonian fluid in the slowly converging channel of a belt worm-conveyor pump under conditions of complex shear

Abstract: The flow of an anomalously viscous fluid with an exponential rheological equation in the converging channel of the screw of a belt worm-conveyor pump is examined taking into account the circulatory flow of the fluid, the dissipation of mechanical energy, and the exchange of heat with the environment.