Showing papers on "Herschel–Bulkley fluid published in 1999"

On the determination of yield surfaces in Herschel-Bulkley fluids

Abstract: Herschel–Bulkley fluids are materials that behave as rigid solids when the local stress τ is lower than a finite yield stress τ0, and flow as nonlinearly viscous fluids for τ>τ0. The flow domain then is characterized by two distinct areas, τ τ0. The surface τ=τ0 is known as the yield surface. In this paper, by using analytic solutions for antiplane shear flow in a wedge between two rigid walls, we discuss the ability of regularized Herschel–Bulkley models such as the Papanastasiou, the bi-viscosity and the Bercovier and Engelman models in determining the topography of the yield surface. Results are shown for different flow parameters and compared to the exact solutions. It is concluded that regularized models with a proper choice of the regularizing parameters can be used to both predict the bulk flow and describe the unyielded zones. The Papanastasiou model predicts well the yield surface, while both the Papanastasiou and the bi-viscosity models predict well the stress field away from τ=τ0. The ...

Flow analysis of field-controllable, electro- and magneto-rheological fluids using Herschel-Bulkley model

Abstract: The Bingham plastic constitutive model has been widely used to predict the post-yield behavior of electro- and magneto-rheological fluids (ER and MR fluids). However, if these fluids experience shear thinning or shear thickening, the Bingham plastic model may not be an accurate predictor of behavior, since the post-yield plastic viscosity is assumed to be constant. In a recent study, it was theoretically and experimentally demonstrated that the Herschel-Bulkley fluid model can be successfully employed when evaluating non-Newtonian post-yield behavior of ER and MR fluids. In this paper, we extend our previous work and adopt the Herschel-Bulkley model to include a detailed analysis of ER and MR fluid dynamics through pipes and parallel plates. Simplified explicit expressions for the exact formulation are also developed. It is shown that the proposed simplified model of the Herschel-Bulkley steady flow equations for pipes and parallel plates can be used as an accurate design tool while providing a convenient...

Flow development of Herschel–Bulkley fluids in a sudden three-dimensional square expansion

Abstract: The flow development of Herschel–Bulkley fluids in a sudden three-dimensional square expansion is studied numerically. The flow is modeled using the mixed-Galerkin finite element formulation to solve the conservation of mass and momentum equations. The Herschel–Bulkley material behavior is described using a regularized model based on the Papanastasiou model. Solutions are obtained for a downstream-to-upstream expansion ratio of 2:1 and for a wide range of pressure gradient values and rheological parameters. The results show that, during the evolution of the flow, two core regions and dead zones at the corners are formed. The extent of the core regions decreases with the pressure gradient and the Reynolds number, and increases with the power-law index. It is also found that the volume flow rate at steady flow increases with the pressure gradient, power-law index, and Reynolds number.

Pushing a non-Newtonian fluid in a Hele-Shaw cell: From fingers to needles

Abstract: We make a theoretical study of the finger behavior of a simple fluid displacing a non-Newtonian fluid confined in a Hele–Shaw cell. We study the Saffman–Taylor instability when the viscosity of the displaced fluid changes with shear. Our results predict a decrease of the finger width that goes to zero for large values of the velocity. An analytical treatment allows the predictions of the dynamics in radial growth.

Wake measurements for flow around a sphere in a viscoelastic fluid

Abstract: The flow field around a sphere falling at its terminal velocity in a column of viscoelastic non-shear-thinning fluid is experimentally measured with digital particle image velocimetry. The working fluid is an extensively characterized, monodisperse, polystyrene based Boger fluid. The sphere radius relative to the radius of the column of fluid is small (a/rc=0.083). The Weissenberg number (λUt/a) ranges from 0.5 to 14 over which the sphere experiences a drag increase up to 8 times that of the Newtonian flow. The flow field is investigated in detail for We 0.5 to 2.5. A length and width scale is defined for the wake. Over this range of We the wake is found to grow linearly with We and become self-similar in a transverse cross-section of the axial component of the velocity. Streamlines along with extension and rotation rates along those streamlines are also determined.

Chapter 1 – Non-Newtonian fluid behaviour

Abstract: Fluids can be classified in two different ways, either according to their response to the externally applied pressure or according to the effects produced under the action of a shear stress. The first scheme of classification leads to the so called “compressible” and “incompressible” fluids, depending upon whether the volume of an element of fluid is dependent on its pressure. While compressibility influences the flow characteristics of gases, liquids can normally be regarded as incompressible and what is of greater importance is their response to shearing. This chapter explores the flow characteristics of single phase liquids, solutions, and pseudo-homogeneous mixtures (such as slurries, emulsions, gas-liquid dispersions), which may be treated as a continuum if they are stable in the absence of turbulent eddies, depending upon their response to externally imposed shearing action. A non-Newtonian fluid is one whose flow curve (shear stress versus shear rate) is either non-linear or does not pass through the origin, i.e. where the apparent viscosity, shear stress divided by shear rate, is not constant at a given temperature and pressure, but is dependent on flow conditions such as flow geometry, shear rate, and sometimes even on the kinematics history of the fluid element under consideration. The most common type of time-independent non-Newtonian fluid behavior observed is pseudoplasticity or shear-thinning, characterized by an apparent viscosity that decreases with increasing shear rate.

Comparison of a quasi-Newtonian fluid with a viscoelastic fluid in planar contraction flow

Abstract: The flow of a 5.0 wt.% solution of polyisobutylene in tetradecane through a planar 4 : 1 contraction exhibiting a shear thinning viscosity is simulated using the flow-type sensitive quasi-Newtonian fluid model. The shear viscosity is fitted by the Giesekus model, which, with the chosen parameters, leads to an extension thickening elongational viscosity. The stress and velocity fields of the numerical simulations are compared with the experimental results of Quinzani et al. [J. Non-Newtonian Fluid Mech. 52 (1994) 1–36] and the numerical results of the viscoelastic simulation using the Giesekus model of Azaiez et al. [J. Non-Newtonian Fluid Mech. 62 (1996) 253–277]. It can be shown that the quasi-Newtonian fluid qualitatively predicts the essential features of the flow in the vicinity of the contraction.

Thermal boundary layer flow of a micropolar fluid past a wedge with constant wall temperature

Abstract: The steady laminar flow of micropolar fluids past a wedge has been examined with constant surface temperature. The similarity variables found by Falkner and Skan are employed to reduce the streamwise-dependence in the coupled nonlinear boundary layer equation. Numerical solutions are presented for the heat transfer characteristics with Pr=1 using the fourth-order Runge-Kutta method, and their dependence on the material parameters is discussed. The distributions of dimensionless temperature and Nusselt number across the boundary layer are compared with the corresponding flow problems for a Newtonian fluid over wedges. Numerical results show that for a constant wedge angle with a given Prandtl number Pr=1, the effect of increasing values ofK results in an increasing thermal boundary thickness for a micropolar fluid, as compared with a Newtonian fluid. For the case of the constant material parameterK, however, the heat transfer rate for a micropolar fluid is lower than that of a Newtonian fluid.

Laminar Flow of a Nonlinear Viscoplastic Fluid Through an Axisymmetric Sudden Expansion

Abstract: A combined experimental and computational study was carried out to investigate the laminar flow of a nonlinear viscoplastic fluid through an axisymmetric sudden expansion. The yield-stress, power-law index, and the consistency index of the yield shear-thinning test fluid were 0.733 Pa, 0.68, and 0.33 Pa · s0.68 , respectively, resulting in a Hedstrom number of 1.65. The Reynolds number ranged between 1.8 and 58.7. In addition, the flow of a Newtonian fluid through the same expansion was also studied to form a baseline for comparison. Velocity vectors were obtained on the vertical center plane using a digital particle image velocimeter (PIV). From these measurements. two-dimensional distributions of axial and radial velocity as well as the stream function were calculated covering the separated, reattached and redeveloping flow regions. These results were compared to finite difference numerical solutions of the governing continuity and fully-elliptic momentum equations. The calculations were found to be in good agreement with the experimental results. Both computational and experimental results indicate the existence of two distinct flow regimes. For low Reynolds numbers, a region of nonmoving fluid is observed immediately downstream of the step and no separated flow zone exists. For the higher Reynolds numbers, a recirculating flow zone forms downstream of the expansion step, which is followed by a zone of stagnant fluid adjacent to pipe wall characterizing reattachment.

Lattice Boltzmann simulations of complex fluids: viscoelastic effects under oscillatory shear

Abstract: We incorporate viscous coupling between components into a numerical model of fluid mixtures. This leads to a memory effect and a frequency-dependent response to applied perturbations. For example, when oscillatory shear is applied to one of the fluid components the viscous drag results in phase segregation if the components have sufficiently different viscosities. Such a situation could occur in dilute polymer solutions where the viscosity is strongly concentration dependent and we present results both for this case and for a symmetric binary fluid mixture.

Flow of a quasi-Newtonian fluid through a planar contraction

Abstract: Flows through abrupt contractions are dominated by the rapid extension experienced in passing through the contraction. Thus, it is useful to employ a fluid model which considers the extensional viscosity explicitly in its constitutive equation. In this paper, the quasi-Newtonian fluid model, which admits shear thinning and extension thickening of the viscosity depending on the local type of flow as proposed by Schunk and Scriven [P. Schunk, L. Scriven, J, Rheol 34 (1990) 1085], is applied to the numerical simulation of the flow of a dilute polyacrylamide solution through a planar 4 : 1 contraction. In this theory the extra stress tensor does not only depend on the rate of strain tensor but also on the relative rate of rotation of the fluid. The material function – the viscosity function – is allowed to depend on the invariants of these two kinematic tensors yielding a local distinction between extensional, shear or rotation dominated flow. The governing equations are discretized using a finite volume method. Different model parameters are varied and the simulation results are compared with the generalized Newtonian fluid and experimental data.

Flow past a sphere moving towards a wall in micropolar fluid

Abstract: The paper presents the first ''exact'' solution to the problem of creeping flow past a sphere moving towards a wall in micropolar fluid. The analytical-numerical method is presented, that is a development of the boundary collocation technique previously used for solving many corresponding problems for a Newtonian fluid. The initial study of the method has been carried out and the results for a force acting on a sphere compared with their counterparts for a Newtonian fluid are presented. It is worth while to note that the drag force on a sphere depends on material constants of the micropolar fluid and the distance from the wall.

Dynamics of a Radial Electrorheological Clutch

Abstract: Time dependent solutions to the equations of motion for flow in an enclosed radial electro-rheological clutch are developed and discussed in relation to the speed of operation. The method follows a procedure previously developed for cylindrical clutch geometry but in this case analytical solutions are obtained. The fluid is treated as a homogeneous continuum obeying the Bingham plastic constitutive equation incorporating a yield stress and viscous component. The results show that the acceleration expected from a consideration of yield stress and inertia is not always achieved. The viscous component places fluid dynamic restriction on the maximum acceleration of the output rotor. However, this limit is only approached if the output load inertia is very low. The results have a bearing on the choice of fluid for high speed operation.

The Singularities Near the Corner of a Viscoelastic Fluid in a 2D Cavity

Abstract: In this article finite differences are used to study viscoelastic incompressible flow of a Criminale Erickson Filbey fluid in a square cavity flow domain. In this case, the nature of corner singularities is examined in which the fluid is contained and the flow generated by the motion of one or more walls. The governing equations are formulated in terms of stream function and vorticity equation and the corresponding radial parts are defined by a fourth-order non-linear differential equations for Stokes flow. In recent years that mathematical formulations of viscoelastic flows often remain very complex velocity and stress field and then stress singularities are known to occur in several flows as in this article. Therefore, singularity behaviour became a very important current issue in fluid dynamics. However, this article is set up with the aim of examining the corner singularities for cavity driven flow in 2D for viscoelastic flow despite the Newtonian flow being well known. Then we show that the viscoelastic fluid has different singularity behaviour than the viscous fluid near the corner with respect to the shear-rate.

Peristaltic Flow of a Third-Grade Fluid in a Planar Channel

Abstract: The problem of peristaltic transport of a non-Newtonian fluid represented by the constituve equation for a third grad fluid was analysed for the case of planar channel with harmonically undulating extensible wall, under zero Reynolds number and long wavelength approximation. New exact analytical solution of the non-linear equation resulting from the momentum equation was given when γ2 + γ3(which are the dimensionless material constants)>0 and under some conditions when γ2 + γ3 0 and γ2+ γ3<0. Finally, we have shown that pumping rate of a third-grade fluid can be greater or less than for a Newtonian fluid having a shear viscosity same as the lower-limiting viscosity of non-Newtonian material depending on the value of the material constants, amplitude ratio and flow rate.n/a

Mathematical Models and Feature Parameters of Non Newtonian Liquid Flows in Porous Media

Abstract: The nonuniform capillary the group model is used to establish the generalized Darcy′s law and a general equation of the power law fluid and Bingham fluid flow through porous media. The relationships are derived between the effective permeability and the effective viscosity of power law fluid versus the feature parameters of the fluids and formation media and between the starting pressure gradient of Bingham fluid and fluid feature parameters versus the feature parameters of the fluids and formation media.

Integration of Complete System of Dynamic Equations for Ideal Fluid

Abstract: The Eulerian system of dynamic equations for the ideal fluid is closed but incomplete The complete system of dynamic equations arises after appending Lin constraints which describe motion of fluid particles in a given velocity field The complete system of dynamic equations for the ideal fluid can be integrated Description in terms of hydrodynamic potentials (DTHP) arises as a result of this integration The integrated system contains indefinite functions of three arguments, which can be expressed via initial and boundary conditions The remaining initial and boundary conditions for the integrated system can be made universal (ie the same for all fluid flows), and the resulting system of equations contains full information about the fluid flow including initial and boundary conditions for the fluid flow Some hydrodynamic potentials appear to be frozen into the fluid, and the Kelvin's theorem on the velocity circulation can be formulated in a contour-free form Description in terms of the wave function (DTWF) appears to be a kind of DTHP Calculation of slightly rotational flows can be carried out on the basis of DTHP, or DTWF Such a description of a rotational flow appears to be effective

Fluid dynamics of fine suspension flow

Abstract: Publisher Summary This chapter discusses the fluid dynamics of fine suspension flow. Various equations and constitutive rheological equations for the phases of a suspension at neglect of random particle and fluid fluctuations are discussed. The influence of thermal particle fluctuations on the rheology of Brownian suspensions with the help of a specific thermodynamic constituent of the interphase interaction force is explained. An alternative way to describe this influence by means of specifying appropriate contributions to the effective stress tensors that affect flow of the suspension phases is considered. The hydrodynamically induced particle and fluid fluctuations may be obtained as a result of two possible physical mechanisms. The first mechanism bears upon random displacements of particles caused by relative motion of neighboring particle layers in shear flow. The second mechanism is due to the relative fluid flow working at random fluctuations of the suspension concentration, and thus originating peculiar pseudoturbulent fluctuations. The impact of both shear-induced and pseudoturbulent fluctuations on suspension flow is also described by introducing pertinent contributions to the effective stress tensors.

The Stress-State in a Torsion Shear Cell Filled With a Newtonian Fluid

Abstract: The flow in a torsional shear cell is investigated with the purpose of finding a measure for the wall effect due to strongly nonuniform flow in the vicinity of the edge of the top platen. Various laminar flow problems are analysed that are relevant to this set-up. These include pure shearing flow of a single fluid in a both an infinite and finite cell, as well as pure shear of a two-fluid system in a finite cell. For pure shearing flow it is found that the extent of the wall effect is of the order of magnitude of the depth of the fluid layer. For piston flow the wall effect is entirely determined by boundary conditions at the bottom of the cell

Validity of the first‐order fluid model

Abstract: The general validity of the first-order fluid model is considered. Conditions are established for which a first-order fluid represents an acceptable approximation to the integral viscoelastic fluid from which it was derived as a Taylor series approximation. The results are applied to two flow problems: generation of flow by the application of a pressure gradient and the growth or dissolution of bubbles in viscoelastic liquids.