Showing papers on "Herschel–Bulkley fluid published in 1998"

A Herschel–Bulkley model for mud flow down a slope

Abstract: The spreading and sediment deposit of a two-dimensional, unsteady, laminar mud flow from a constant-volume source on a relatively steep slope is studied theoretically and experimentally. The mud under consideration has the rheological properties of a Herschel–Bulkley fluid. The flow is of low-Reynolds-number type and has a well-formed wave front moving a substantial distance downslope. Due to the nonlinear rheological characteristics, a set of nonlinear partial differential equations is needed for this transient problem. Depth-integrated continuity and momentum equations are derived by applying von Karman's momentum integral method. A matched-asymptotic perturbation method is implemented analytically to get asymptotic solutions for both the outer region away from, and the inner region near, the wave front. The outer solution gives accurate results for spreading characteristics, while the inner solution, which is shown to agree well with experimental results of Liu & Mei (1989) for a Bingham fluid, predicts fairly well the free-surface profile near the wave front. A composite solution uniformly valid over the whole spreading length is then achieved through a matching of the inner and outer solutions in an overlapping region. The range of accuracy of the solution and the size of the inner and overlapping regions are quantified by physical scaling analyses. Rheological and dynamic measurements are obtained through laboratory experiments. Theoretical predictions are compared with experimental results, showing reasonable agreement. The impact of shear thinning on the runout characteristics, free-surface profiles and final deposit of the mud flow is examined. A mud flow with shear thinning spreads beyond the runout distance estimated by a Bingham model, and has a long and thin deposit.

Fresh concrete: A Herschel-Bulkley material

Abstract: Some preliminary results of an experimental program on the rheological behavior of fresh concrete are presented. In the rheological tests, performed with a plane-to-plane rheometer, it appears tha the relationship between torque and rotation speed is not exactly linear. The fresh concrete behavior is better described by the Herschel-Bulkley model: $$\tau = \tau \prime _0 + a \dot \gamma ^b $$ ; τ and $$\dot \gamma $$ are the shear stress and the strain gradient applied to the specimen, respectively. τ′0,a andb are three material parameters describing the concrete behavior. Among other advantages, this new description avoids the problem of negative yield stress encountered with the Bingham model.

Squeeze-flow of a Herschel–Bulkley fluid

Abstract: Squeeze-flow experiments of a Herschel–Bulkley material between two rigid plates, investigated both experimentally and computationally by Adams et al. (J. Non-Newtonian Fluid Mech. 71 (1997) 41) are compared against an approximate analysis for generalised Newtonian fluids presented by Sherwood and Durban (J. Non-Newtonian Fluid Mech. 62 (1996) 35), for the case in which the interface between the material and the plates is lubricated. The analysis presented here assumes a rigid-viscoplastic material, rather than the elastic-viscoplastic material of Adams et al., but the viscoplastic model for flow is identical. However, the shear stress boundary condition at the plates differs from the Coulomb friction law of Adams et al.: the shear stress is here assumed to be a constant fraction of the effective stress (and consequently turns out to be independent of position). A simple expression for the total force required to push the plates together is obtained for the case when friction at the plates is small. Agreement between this expression and the experimentally-measured force is good at high strain, though the elastic deformation observed prior to yield is not captured by the rigid-viscoplastic analysis.

Numerical and experimental investigation of thermal convection for a thermodependent Herschel-Bulkley fluid in an annular duct with rotating inner cylinder

Abstract: This paper presents an experimental and numerical investigation of the thermal convection for a Herschel-Bulkley fluid, in an annular duct, with rotating inner cylinder. The outer cylinder is heated at constant heat flux density (φ) p and the inner one is adiabatic. This work has two main motivations. First, it seeks to determine the angular velocity Ω c for which the plug zone is reduced to zero. Second, to arrive at a better comprehension and better description of the effect of the variation of the consistency K with temperature T on heat transfer. In the case of slot approximation, Bittleston and Hassager (1992) presented for a Bingham fluid an analytical expression of Ω c .

Hydromagnetic flow of a second-grade fluid in a channel — some applications to physiological systems

Abstract: An asymptotic series solution for steady flow of an incompressible, second-grade electrically conducting fluid in a channel permeated by a uniform transverse magnetic field is presented. The depth of the channel is assumed to vary slowly in the axial direction. Analytical expressions are derived for the vorticity and pressure drop along the channel as well as the wall shear stress. It is found that for fixed values of the Reynolds number R and the non-Newtonian parameter K1, the wall shear stress increases with increasing value of magnetic parameter M. Numerical computations carried out for a specific slowly varying channel show that flow separation occurs for both second-grade (K1 0) fluids when |K1|<0.15. The analysis also reveals the interesting result that while flow separation takes place for a second-order fluid for K1≥0.15, no separation occurs at all for |K1|≥0.15 for a second-grade fluid.

Flow of viscous fluid

Abstract: All fluids are viscous. In the case where the viscous effect is minimal, the flow can be treated as an ideal fluid; otherwise the fluid is treated as a viscous fluid. If the movement of fluid is not affected by its viscosity, it could be treated as the flow of ideal fluid and the viscosity term could be omitted. The flow around a solid, however, cannot be treated in such a manner because of viscous friction. Nevertheless, only this friction affects the very thin region near the wall. Prandtl identified this phenomenon and had the idea to divide the flow into two regions : the region near the wall where the movement of flow is controlled by the frictional resistance, and the other region outside the above not affected by the friction and therefore assumed to be an ideal fluid flow. The former is called the boundary layer and the latter the main flow.

Peristaltic Motion of Generalized Newtonian Fluid in a Non-Uniform Channel

Abstract: The problem of peristaltic transport of a non-Newtonian (Carreau) fluid in a non-uniform channel has been investigated under zero Reynolds number with long wavelength approximation. The problem is formulated using a perturbation expansion in terms of a variant of Weissenberg number. It is assumed that chyme in the male small intestine behave like Carreau fluid since most of the physiological fluid behave like a non-Newtonian fluid. Pressure rise and friction force, in the case of non-uniform geometry, are found much smaller than the corresponding values in the case of uniform geometry. Furthermore, the pressure rise and the friction force are smaller in the case of Carreau fluid than Newtonian fluid. A comparison between Carreau fluid, couple-stress fluid and Casson fluid is given. The pressure rise and friction force are discussed for various of the physical parameters of interest.

Examination of flow behaviour of electrorheological fluids in the flow mode

Abstract: The use of electrorheological (ER) fluids in hydraulic systems has been demonstrated in detailed investigations at the Institute of Fluid Power Transmission and Control (IFAS) [1]. The flow behaviour of this fluid cannot be described reliably. A detailed knowledge of this flow behaviour would enable better ER component design and produce basic information for simulation models. It is therefore important for the practical applications of ER fluids.A detailed comparison is made between existing rheological models, e.g. the Bingham model, and measured values in flow mode to confirm these models and, if possible, to define a material property constant. In addition, a simple model describing the flow behaviour of an ER fluid in the flow mode with the help of a geometrical dependent variable is presented. This variable is derived from measured values and reflects the influence of the gap height and the gap length. A comparison between this function and real measured values gives a very good agreement wi...

Exact solution for compressive flow of viscoplastic fluids under perfect slip wall boundary conditions

Abstract: Based on the perfect slip condition between rigid walls and fluids, the compressive flow of Herschel-Bulkley fluids and biviscous fluids was studied. The explicit expressions of stresses and fluid velocity were given. To move the rigid walls for a Herschel-Bulkley fluid with the yield stress (τ0), the mean pressure applied onto the rigid wall should be larger than 2τ0/ . No yield surface exists in the interior of the fluids when flow occurs. For a biviscous fluid, a critical load was given. The fluid behaves like the Bingham fluid when the external applied load onto the wall is larger than the critical load, otherwise the fluid is Newtonian.

Surface Roughness Effects in Hydrodynamic Lubrication Involving the Mixture of Two Fluids

Abstract: In this paper, the relations expressing the effects of surface roughness and homogeneous mixture (the mixture of power-law fluid inserted into a Newtonian fluid) on the roughness-induced flow factor are derived. A coordinate transformation is utilized to simplify the derivation. By using the perturbation approach incorporated with Green function technique, the flow factors and shear stress factors are derived and expressed as functions of the volume fraction of the power-law fluid in the mixture (v p ), the viscosity ratio of the power-law fluid to that of the Newtonian fluid (N or μ p * ), the flow behavior index of the power-law fluid (n), the Peklenik numbers (γ i ) and the standard deviations (σ i ) of each surface. A form of the average Reynolds equation is then obtained. It is shown that a number of currently available models are special cases of the theory presented here. Finally, the performance of a journal bearing is discussed.

A finite element solution procedure for porous medium with fluid flow and electromechanical coupling

Abstract: We consider a coupled problem of the deformation of a porous solid, flow of a compressible fluid and the electrical field in the mixture. The governing equations consist of balance of the linear momentum of solid and of fluid, continuity equations of the fluid and current density, and a generalized form of Darcy's law which includes electrokinetic coupling. The compressibility of the solid and the fluid are taken into account. We transform these equations to the corresponding finite element relations by employing the principle of virtual work and the Galerkin procedure. The nodal point variables in our general formulation are displacements of solid, fluid pore pressure, relative velocity of the fluid and electrical potential. Derivation of the FE equations is presented for small displacements and elastic solid, which can further be generalized to large displacements and inelastic behaviour of the solid skeleton. According to this formulation we can include general boundary conditions for the solid, relative velocity of the fluid, fluid pressure, current density and electrical potential. The dynamic-type non-symmetric system of equations is solved through the Newmark procedure, while in the case of neglect of inertial terms we use the Euler method. Numerical examples, solved by our general-purpose FE package PAK, are taken from biomechanics. The results are compared with those available in the literature, demonstrating the correctness and generality of the procedure presented. © 1998 John Wiley & Sons, Ltd.

Permanent Waves in Slow Free-Surface Flow of a Herschel–Bulkley fluid

Abstract: Unsteady flow of a viscoplastic fluid on an inclined plane is examined. The fluid is described by the three-parameter Herschel–Bulkley constitutive equation. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid and steady uniform motion. A permanent wave solution is then derived, and the relation between wave speed and flow depth is discussed. It is shown that more types of gravity currents are possible than in a Newtonian fluid; these include some cases of flows propagating up a slope. The speed of permanent waves is derived and the possible surface profiles are illustrated as functions of the flow behavior index.

Comparison of Lorenz type and plasma fluid models for nonlinear-interchange-mode generation of shear flow

Abstract: By solving nonlinear fluid model equations, it is shown that the nonlinear interchange mode generates shear flow through Reynolds stress, which suppresses fluctuation amplitude substantially. The nonlinear interaction between vortex motion and shear flow produces a relaxation oscillation. This behaviour is also confirmed by a Lorenz type model with five ordinary differential equations. However, for the same Rayleigh number and Prandtl number , the period of relaxation oscillation becomes shorter and the amplitude of vortex motion becomes smaller.

Rotating rigid rods or incompressible fluids: How to determine the stress?

Abstract: When a fluid fills up a rotating box, the pressure inside the fluid is easily obtained by solving a closed set of equations. However, if the fluid is incompressible, the mass conservation equation is trivially satisfied and the pressure remains undetermined. After a preliminary analysis of the similar problem of a rotating rigid rod, this paradox is removed by giving the fluid a small value of the compressibility χ and taking χ→0 at the end of the calculation.

Steady non-swirling axisymmetric flows: flow classification and rheological consequences

Abstract: For steady non-swirling axisymmetric flow ( $u_{\varphi} = 0$ ) of an incompressible fluid two invariants of the rate of strain dyadic D are introduced, which directly enter into the expression for D. This being the case they - in conjunction with the vorticity - allow a flow classification into strong and weak flows. For a generalized Newtonian fluid an expression for the viscosity function $\eta$ is listed, which reduces for model fluids to correct results in shearing and, respectively, extensional flow. A possible modification of $\eta$ is proposed, which involves the relative vorticity as well (quasi-Newtonian fluid), since this allows $\eta$ to adjust itself to the local nature of the flow. As such it should prove useful for numerical calculation.

Second-order constitutive equation for the surface stress tensor of a fluid–fluid interface

Abstract: In this paper a constitutive equation is derived for the surface stress tensor of a simple fluid–fluid interface. The equation is an extension of the linear Boussinesq surface fluid model, and is correct up to second order in the rate of deformation tensor. It is valid for simple fluid–fluid interfaces, without memory effects and yield stresses.

Nonsteady flow of viscous fluid in a tube of triangular cross-section

Abstract: By superposing of one-dimensional solutions an exact solution is obtained for the nonsteady two-dimensional problem of the motion of an incompressible viscous fluid in a rigid tube whose cross-section is a regular triangle. The fluid is driven by a time-dependent pressure gradient. The fluid particles may have a nonuniform initial velocity distribution over the tube cross-section. Solutions are obtained in the form of series for the cases in which the fluid is accelerated from rest by a varying pressure gradient and also in the stationary oscillating regime under the action of a periodically pulsating pressure gradient.

Characteristics of a fluid

Abstract: This chapter provides an overview of fluids and their characteristics. Fluids are divided into liquids and gases. Gas is easy to compress and it fully expands to fill its container. There is thus no free surface. Consequently, an important characteristic of a fluid from the viewpoint of fluid mechanics is its compressibility. Another characteristic is its viscosity. Whereas a solid shows its elasticity in tension, compression, or shearing stress, a fluid does so only for compression. In other words, a fluid increases its pressure against compression, trying to retain its original volume. This characteristic is called compressibility. Furthermore, a fluid shows resistance whenever two layers slide over each other. This characteristic is called viscosity. For liquids, compressibility must be taken into account whenever they are highly pressurized, and for gases, compressibility may be disregarded whenever the change in pressure is small. Although a fluid is an aggregate of molecules in constant motion, the mean free path of these molecules is 0.06 μm even for air of normal temperature and pressure; therefore, a fluid is treated as a continuous isotropic substance. A non-existent, assumed fluid without either viscosity or compressibility is called an ideal fluid or perfect fluid. A fluid with compressibility but without viscosity is occasionally discriminated and called a perfect fluid, too.

Inertia effects of the fluid and cylinder in coaxial cylindrical rheometer

Abstract: The inertias of the fluid and the inner cylinder in coaxial cylinder rheometer (CACR) have great influence on the unsteady flow of non-Newtonian fluid. Even for the Newtonian fluid there exist the so called “stress overshoot” phenomenon. In the present article this phenomenon was studied in detail and a method correcting the measured results for an unsteady flow in the rheometer was proposed. It is found that the inertia effect of the fluid can be ignored when the gap between cylinders is small.

Rayleigh-Bernard Convection Of Non-Newtonian Fluid

Abstract: The main purpose of this work is to present the use of boundary-domain integral method to analyse the flow behaviour of non-Newtonian fluid, ie. power law fluid. The available parametric model is applied representing a non-linear dependence between shear rate and deformation velocity. To evaluate the presented approach the Rayleigh-Benard natural convection of the Newtonian and non-Newtonian fluid has been solved.