Showing papers on "Herschel–Bulkley fluid published in 1989"

Slow spreading of a sheet of Bingham fluid on an inclined plane

Abstract: To study the dynamics of fluid mud with a high concentration of cohesive clay particles, we present a theory for a thin sheet of Bingham-plastic fluid flowing slowly on an inclined plane. The physics is discussed on the approximate basis of the lubrication theory. Because of the yield stress, the free surface need not be horizontal when the Bingham fluid is in static equilibrium, nor parallel to the plane bed when in steady flow. We then show that there is a variety of gravity currents that can advance at a constant speed and with the same profile. Experimental confirmation of one type is presented. By solving a nonlinear partial differential equation, transient flows due either to a steady upstream discharge or to the sudden release of a finite fluid mass on another fluid layer are studied. In the first case there is a mud front which ultimately propagates as a constant speed as a steady gravity current. In the second case, when the ambient layer is sufficiently shallow that there is no initial motion, the flow induced by the new fluid can terminate after the disturbance has travelled a finite distance. The extent of the final spread is examined. Disturbances due to an external pressure travelling parallel to the free surface are also examined. It is found in particular that a travelling localized pulse of pressure gradient not only generates a localized mud disturbance which travels along with the forcing pressure, but further leaves behind a permanent footprint.

The Measurement of Wall Shear Stress

Abstract: Knowledge of the wall shear stress is of both fundamental and practical importance The mean stress is indicative of the overall state of the flow over a given surface while the fluctuating stress is a “footprint” of the individual processes that transfer momentum to the wall The measurement techniques can be divided into two main categories: direct and indirect The indirect techniques can be further divided into momentum balance methods and correlation methods

A finite element analysis of laminar unsteady flow of viscoelastic fluids through channels with non-uniform cross-sections

Abstract: The effects of non-Newtonian behaviour of a fluid and unsteadiness on flow in a channel with non-uniform cross-section have been investigated. The rheological behaviour of the fluid is assumed to be described by the constitutive equation of a viscoelastic fluid obeying the Oldroyd-B model. The finite element method is used to analyse the flow. The novel features of the present method are the adoption of the velocity correction technique for the momentum equations and of the two-step explicit scheme for the extra stress equations. This approach makes the computational scheme simple in algorithmic structure, which therefore implies that the present technique is capable of handling large-scale problems. The scheme is completed by the introduction of balancing tensor diffusivity (wherever necessary) in the momentum equations. It is important to mention that the proper boundary condition for pressure (at the outlet) has been developed to solve the pressure Poisson equation, and then the results for velocity, pressure and extra stress fields have been computed for different values of the Weissenberg number, viscosity due to elasticity, etc. Finally, it is pertinent to point out that the present numerical scheme, along with the proper boundary condition for pressure developed here, demonstrates its versatility and suitability for analysing the unsteady flow of viscoelastic fluid through a channel with non-uniform cross-section.

Analytical solutions for equations of unsteady flow of non-newtonian fluids in tube

Abstract: This paper presents analytical solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse the behaviour of axial velocity and shear stress for unsteady flow of non-Newtonian visco-elastic fluids in tube, and to provide a theoretical base for the projection of pipe-line engineering.

Radial oscillations of gas bubbles in viscoelastic materials

Abstract: Most previous studies of acoustic cavitation in biological tissue have treated the material surrounding the bubble as a Newtonian fluid with sometimes increased viscosity. The present work describes the derivation of a generalized Rayleigh‐Plesset equation for a gas bubble in a continuous viscoelastic material. Viscoelasticity is modeled to include either stress relaxation (Maxwell fluid) or aftereffect (Voigt fluid). Several cases are considered: (1) a bubble with a (a) viscous shell suspended in a Newtonian fluid, (b) viscoelastic shell suspended in a Newtonian fluid, (c) viscoelastic shell suspended in a viscoelastic fluid; and (2) a “clean” bubble suspended in a (a) viscous or (b) viscoelastic fluid. In general, the effect of viscoelasticity is to decrease the resonance frequency and increase the threshold for transient cavitation. Preliminary measurements of cavitation thresholds in a liquid seeded with Albunex® stabilized microbubbles are presented and interpreted in light of the theory. [Work suppo...

The hydrodynamics of a bent cylinder in a viscoelastic fluid

Abstract: The hydrodynamics of a bent cylinder specimen moving in a viscoelastic fluid and a Newtonian fluid has been studied experimentally by observing the falling motion of the specimen with different initial orientations. The effect of the end-to-end distance on the terminal velocity of the specimen was also investigated in both fluids. In the Newtonian fluid, no matter what the initial position or the bend angle of the specimen was, it always reoriented to the open-end-up position and kept this shape while it fell. In the viscoelastic fluid, however, the open-end-up specimen always fell down as it was, while open-end-down specimen did not always flip to the open-end-up position as in the Newtonian fluid, but, if the bend angle was smaller than a critical value, it fell down with open-end-down shape. The effect of the end-to-end distance on the specimen terminal velocity was found to be significantly different between the Newtonian and the viscoelastic fluid. These observations represent new experimental findings, unique to a viscoelastic fluid, and may be attributed to the existence of a polymer network in viscoelastic solutions created by high molecular-weight polymer chains.

An asymptotic theory for laminar pipe flow of a non-Newtonian fluid

Abstract: For a generalized Newtonian fluid the viscosity η* varies with the shear rate\(\dot \gamma *\). Instead of assuming a certain dependence like rheological models do, the viscosity is expanded in a Taylor serie with respect to\(\dot \gamma *\). Based on this expansion a perturbation approach to laminar pipe flow withqw = const. and viscous heating included is formulated. The basic flow (zero order solution) is that of a Newtonian fluid. Higher order terms successively account for the influence of a non-Newtonian fluid. — The asymptotic results compare reasonably well with those of specific rheological models like power law or Ellis model. — The influence of temperature dependent properties (including the viscosity) can be accounted for by the same kind of asymptotic approach. The influence of shear rate as well as temperature dependence thus can be combined in general results valid for all generalized Newtonian fluids.

Study of nonstationary problems for a compressible viscous fluid

Abstract: i. :Statement of the Problem and Method of Solution. We consider the propagation of a plane nonstationary wave of pressure in a compressible viscous fluid. We describe motion of the fluid by means of the linearized Navier-Stokes equations [2]. We write the vector velocity field of the fluid in the form

Turbulence of a non-newtonian fluid

Abstract: This paper presents a simple theory for a non-Newtonian fluid, especially the corotational Jeffreys model. Particular attention is paid to the frequency spectrum of the strain fluctuations, and through this article it is found that the Jeffreys fluid will exhibit an “onset” Reynolds number, above which the effects of the non-Newtonian nature of this fluid are felt. Because time dependent behavior of the strain-strain correlation is emphasized, this study is complementary to the molecular theory.