Showing papers on "Herschel–Bulkley fluid published in 2001"
TL;DR: In this paper, a series of experiments on a typical thickener where these artefacts have been successfully eliminated are reported. And the flow-curves obtained show a smooth but steep transition from a very high Newtonian viscosity at low shear stress to a much lower viscousity at high shear stresses.
Abstract: The thickening properties of many commercial thickeners are difficult to measure because of wall slip artefacts. Here we report a series of experiments on a typical thickener where these artefacts have been successfully eliminated. As a result, complete, steady-state flow-curves of aqueous Carbopol 980 (the toxicologically preferred version of the older and more well-known Carbopol 940) dispersions are reported for a range of concentrations of 0.045–1.0 wt%. The vane-and-basket flow geometry was used to avoid slip problems at low shear stress, with the geometry housed in a TA AR1000-N controlled-stress rheometer, whilst a Haake RV2 viscometer with an SV2P and MV2P concentric-cylinder geometries were used at higher shear rates. The flow-curves obtained show a smooth but steep transition from a very high Newtonian viscosity at low shear stress to a much lower viscosity at high shear stress. No real yield stresses were detected, but the higher shear rate results can be fitted to the Herschel-Bulkley model, which assumes an apparent yield stress. The various model parameters are displayed as a function of Carbopol concentration.
145 citations
TL;DR: In this article, the steady flow of Herschel-Bulkley fluids in a canonical three-dimensional expansion was modeled using a regularized continuous constitutive relation, and the flow was obtained numerically using a mixed-Galerkin finite element formulation with a Newton-Raphson iteration procedure coupled to an iterative solver.
Abstract: In this paper we study steady flow of Herschel–Bulkley fluids in a canonical three-dimensional expansion. The fluid behavior was modeled using a regularized continuous constitutive relation, and the flow was obtained numerically using a mixed-Galerkin finite element formulation with a Newton–Raphson iteration procedure coupled to an iterative solver. Results for the topology of the yielded and unyielded regions, and recirculation zones as a function of the Reynolds and Bingham numbers and the power-law exponent, are presented and discussed for a 2:1 and a 4:1 expansion ratio. The results reveal the strong interplay between the Bingham and Reynolds numbers and their influence on the formation and break up of stagnant zones in the corner of the expansion and on the size and location of core regions.
124 citations
TL;DR: In this article, a stability criterion is proposed for the object in the fluid, to estimate the yield stress needed to balance buoyancy forces, and the important role of fluid-object interface effects is also highlighted.
Abstract: The drag force exerted on objects in a yield stress fluid was measured when the velocities become infinitely slow. In these quasi-static conditions, yield stress effects are predominant. Particular care was paid to determining the yield stress and checking interface conditions when characterizing these fluids from a rheometric standpoint. Drag coefficients could then be determined for interesting objects of various shapes. The important role of fluid-object interface effects was also highlighted. On the basis of these results, a stability criterion is proposed for the object in the fluid, to estimate the yield stress needed to balance buoyancy forces.
100 citations
TL;DR: In this paper, the stability of a multi-layer Poiseuille flow of two Bingham fluids is investigated and it is shown that this two-fluid flow is frequently more stable than the equivalent flow of either fluid alone.
Abstract: We consider the stability of a multi-layer plane Poiseuille flow of two Bingham fluids. It is shown that this two-fluid flow is frequently more stable than the equivalent flow of either fluid alone. This phenomenon of super-stability results only when the yield stress of the fluid next to the channel wall is larger than that of the fluid in the centre of the channel, which need not have a yield stress. Our result is in direct contrast to the stability of analogous flows of purely viscous generalised Newtonian fluids, for which short wavelength interfacial instabilities can be found at relatively low Reynolds numbers. The results imply the existence of parameter regimes where visco-plastic lubrication is possible, permitting transport of an inelastic generalised Newtonian fluid in the centre of a channel, lubricated at the walls by a visco-plastic fluid, travelling in a stable laminar flow at higher flow rates than would be possible for the single fluid alone.
68 citations
TL;DR: The hydrodynamic theory of particle movement in non-Newtonian fluids is addressed from a rheological perspective in this article, where the shear rate due to particle-to-fluid relative movement, the particle Reynolds number, and a general form of Stokes' equation for non-newtonian fluid are proposed.
50 citations
TL;DR: In this article, the relative importance of inertial, viscous and yield stress effects on the filling profile of a 2D cavity was examined using PAM-CAST/SIMULOR, which was modified by introducing a regularized Bingham fluid constitutive relation.
Abstract: The present study concentrates on Bingham fluid filling of a 2-D cavity and examines the relative importance of inertial, viscous and yield stress effects on the filling profile. The results presented are obtained using PAM-CAST/SIMULOR, which was modified by introducing a regularized Bingham fluid constitutive relation. The results identify five different flow patterns: “mound,” “disk,” “shell,” “bubble,” and a “transition flow” between that of mound and bubble patterns. A complete map of the flow patterns as a function of the Reynolds and Bingham numbers is also presented and discussed using dimensional and physical arguments within a simplified theoretical framework.
49 citations
TL;DR: In this paper, the authors derived an analytical expression for the bulk stress of a suspension of rigid particles in a second-order fluid under the limit of dilute and creeping flow conditions.
Abstract: In this paper we study the bulk stress of a suspension of rigid particles in viscoelastic fluids. We first apply the theoretical framework provided by Batchelor [J. Fluid Mech. 41 (1970) 545] to derive an analytical expression for the bulk stress of a suspension of rigid particles in a second-order fluid under the limit of dilute and creeping flow conditions. The application of the suspension balance model using this analytical expression leads to the prediction of the migration of particles towards the centerline of the channel in pressure-driven flows. This is in agreement with experimental observations. We next examine the effects of inertia (or flow Reynolds number) on the rheology of dilute suspensions in Oldroyd-B fluids by two-dimensional direct numerical simulations. Simulation results are verified by comparing them with the analytical expression in the creeping flow limit. It is seen that the particle contribution to the first normal stress difference is positive and increases with the elasticity of the fluid and the Reynolds number. The ratio of the first normal stress coefficient of the suspension and the suspending fluid decreases as the Reynolds number is increased. The effective viscosity of the suspension shows a shear-thinning behavior (in spite of a non-shear-thinning suspending fluid) which becomes more pronounced as the fluid elasticity increases.
38 citations
TL;DR: In this paper, the free vibration of anisotropic laminated composite, as well as isotropic open or closed, cylindrical shells submerged in and subjected simultaneously to an internal and external incompressible, inviscid fluid are discussed on the basis of a refined shell theory in which transverse shear deformation and rotary inertia effects are taken into account.
36 citations
Patent•
26 Jan 2001
TL;DR: In this article, the consistency index and the power law index of a Newtonian fluid or non-Newtonian power law fluid are calculated using the Metzner and Otto concept generalized to static mixers.
Abstract: The apparatus (10) is used for determining the consistency index (k) and the power law index (n) of a Newtonian fluid or non-Newtonian power law fluid. A method is also disclosed. Accordingly, the fluid flows in a laminar manner through a first (12) and a second static mixer (14) successively connected together by means of an intermediary pipe (18). A first pressure differential (ΔP1) corresponding to a pressure drop of the fluid through the first static mixer (12) is measured. Similarly, a second pressure differential (ΔP2) corresponding to a pressure drop of the fluid through the second static mixer (14) is measured. Finally, the consistency index (k) and the power law index (n) are calculated using the Metzner and Otto concept generalized to static mixers. The apparent viscosity may also be calculated. This invention may be mounted directly on a main supply pipe (16) and allows the rheological properties of the fluid to be known in real time. It also improves the mixing of the fluid and maintains its homogeneity.
28 citations
TL;DR: The steady flow of non-Newtonian Herschel-Bulkley fluids over a one-to-two axisymmetric sudden expansion was studied numerically in this article.
Abstract: The steady flow of non-Newtonian Herschel-Bulkley fluids over a one-to-two axisymmetric sudden expansion was studied numerically Finite difference numerical solutions of the governing continuity and fully-elliptic momentum equations were obtained within the laminar flow regime for a range of Reynolds numbers, yield numbers, and power-law index values The Reynolds number, based on the upstream pipe diameter and bulk velocity, was varied between 50 and 200, while the yield number was varied between 0 and 2 The power-law index values mapped the 06-12 range, allowing for the investigation of both shear-thinning and shear-thickening effects Two distinct flow regimes are identified One is associated with a combination of low yield numbers, high Reynolds numbers, and high power-law indexes, and exhibits a recirculating flow region at the step corner which is similar to that seen in Newtonian flows The other flow regime, however, is characterized by a dead-zone behind the step corner, and is obtained for a combination of high yield numbers, low Reynolds numbers, and low power-law indexes
22 citations
TL;DR: In this article, the field-dependent Bingham and response characteristics of ER fluid under shear and flow modes were presented and two different types of electroviscometers were designed and manufactured for the shear mode and flow mode, respectively.
Abstract: This paper presents field-dependent Bingham and response characteristics of ER fluid under shear and flow modes. Two different types of electroviscometers are designed and manufactured for the shear mode and flow mode, respectively. An ER fluid consisting of soluble chemical starches (particles) and silicon oil is made and its field-dependent yield stress is experimentally distilled at two different temperatures using the electroviscometers. Time responses of the ER fluid to step electric fields are also evaluated under two operating modes. In addition, a cylindrical ER damper, which is operated under the flow mode, is adopted and its measured damping force is compared with predicted one obtained from Bingham model of the shear and flow mode, respectively.
TL;DR: In this article, the interaction between the modifications of the internal structure of a thixotropic fluid and the flow development along a pipe has been investigated and the experimental results show a progressive flatness of the velocity profiles due to the aggregation of the structural elements of the fluid.
Abstract: This paper deals with the interaction between the modifications of the internal structure of a thixotropic fluid and the flow development along a pipe. The experimental set-up consists of a pipe, where a flow of thixotropic fluid is provided from a large vessel. The axial velocity distribution was determined using particle image velocimetry technique and ultrasonic velocity profile monitor. At the entrance section, the fluid is assumed to be in a homogeneous structural state corresponding to a high shear rate. The experimental results show a progressive flatness of the velocity profiles due to the aggregation of the structural elements of the fluid. The flow evolution is governed essentially by the kinetics of aggregation and segregation since the associated time scales are longer than the relaxation time of the flow.
TL;DR: In this paper, the stability of symmetrical rotors with a cylindrical chamber partially filled with a viscous incompressible fluid is investigated and the effects of the parameters of rotor system, such as external damping ratio, fluid fill ratio, Reynolds number and mass ratio, on the unstable regions are analyzed.
Abstract: On the basis of the linearized fluid forces acting on the rotor obtained directly by using the two-dimensional Navier-Stokes equations, the stability of symmetrical rotors with a cylindrical chamber partially filled with a viscous incompressible fluid is investigated in this paper. The effects of the parameters of rotor system, such as external damping ratio, fluid fill ratio, Reynolds number and mass ratio, on the unstable regions are analyzed. It is shown that for the stability analysis of fluid filled rotor systems with external damping, the effect of the fluid viscosity on the stability should be considered. When the fluid viscosity is included, the adding external damping will make the system more stable and two unstable regions may exist even if rotors are isotropic in some casIs.
TL;DR: In this article, the authors derived Darcy's law from the theory of porous media and showed that the influence of the fluid extra stress decreases with increasing number of capillary tubes per area element.
Abstract: Usually the fluid flow through porous media is described by Darcy 's law or generalizations of it. In this contribution, Darcy 's law is derived from the theory of porous media. To archive this, the fluid extra stress (frictional stress) is neglected in comparision with the momentum exchange (drag force) between the fluid phase and the solid skeleton of a two-phase model. This common assumption is motivated by the results obtained from a microscopic capillary model in combination with a dimensional analysis of the continuum mechanical model. This analysis shows that the influence of the fluid extra stress decreases with increasing number of capillary tubes per area element.
TL;DR: The mass-detecting technique has been applied to design a capillary viscometer for viscosity measurements of both Newtonian and non-Newtonian fluids over a range of shear rates.
Abstract: The mass-detecting technique has been applied to design a capillary viscometer for viscosity measurements of both Newtonian and non-Newtonian fluids over a range of shear rates. Flow-rate and pressure-drop measurements are replaced with a measurement of liquid-mass variation with time. Using a precision balance, one can measure the variation of fluid mass collected in the receptacle, m(t), from which the test fluid viscosity and shear rate are mathematically calculated. The feasibility and accuracy of the mass-detecting technique have been demonstrated for water and non-Newtonian fluids by comparing results against established viscosity measurement techniques. The advantages of this design are simplicity (i.e., ease of operation and no moving parts), low cost, and the ability to measure viscosity over a relatively broad range of shear rates.
TL;DR: In this paper, the authors investigated diffusive corrections of this fluid dynamical model derived from a Chapman-Enskog expansion of the kinetic model, in the case where the collision time depends on the particle energy in the fluid frame.
Abstract: This work is concerned with an extension of the classical compressible Euler model of fluid dynamics in which the fluid internal energy is a measure-valued quantity. This model can be derived from the hydrodynamic limit of a kinetic model involving a specific class of collision operators. In the present paper, we investigate diffusive corrections of this fluid dynamical model derived from a Chapman–Enskog expansion of the kinetic model, in the case where the collision time depends on the particle energy in the fluid frame. We show that the closure relations for the stress tensor and heat flux vector differ from their expression in the usual Navier–Stokes model. We argue why such a feature could be used as a tool towards an understanding of fluid turbulence from kinetic theory.
TL;DR: In this article, an analytical scheme for the evaluation of the compressibility factor of a simple fluid is presented based on the clasical perturbation theory and on a recent (analytical) approximation for the radial distribution function of the hard-sphere fluid.
Abstract: An analytical scheme for the evaluation of the compressibility factor of a simple fluid is presented. It is based on the clasical perturbation theory and on a recent (analytical) approximation for the radial distribution function of the hard-sphere fluid. The scheme, which provides, in the case of the Lennard-Jones fluid, explicit expressions for both structural and thermodynamic quantities in a closed form, requires the hard-sphere fluid equation of state as the sole input. Using the Carnahan–Starling equation of state for the hard-sphere reference fluid, the prediction of the critical point as well as the behavior of the pressure of the Lennard-Jones fluid are an improvement in relation to previous work and compare rather well with recent numerical simulations. The same applies to the radial distribution function computed with the present scheme and the Weeks–Chandler–Andersen approach. From a knowledge of the freezing and melting transitions in
the hard-sphere system, the liquid and solid branches of the reduced temperature vs. reduced density curve at coexistence for the Lennard-Jones fluid are simply obtained.
TL;DR: In this article, the authors investigated a well-known model representing a basic system of conservation laws for a one-dimensional flow with temperature-dependent viscosity using a combination of analytical and numerical tools.
TL;DR: In this article, momentum and energy equations describing the heat and fluid flow of Herschel-Bulkley fluids within concentric annular ducts are analyzed using the classical integral transform technique, which permits accurate determination of parameters of practical interest in engineering such as friction factors and Nusselt numbers for the duct length.
Abstract: Related momentum and energy equations describing the heat and fluid flow of Herschel-Bulkley fluids within concentric annular ducts are analytically solved using the classical integral transform technique, which permits accurate determination of parameters of practical interest in engineering such as friction factors and Nusselt numbers for the duct length. In analyzing the problem, thermally developing flow is assumed and the duct walls are subjected to boundary conditions of first kind. Results are computed for the velocity and temperature fields as well as for the parameters cited above with different power-law indices, yield numbers and aspect ratios. Comparisons are also made with previous work available in the literature, providing direct validation of the results and showing that they are consistent.
TL;DR: In this paper, the effect of the Weissenberg (which is a measure of the elasticity of the fluid), Rayleigh and Biot numbers on the temperature and streamline profiles are delineated and this has been documented first time for viscoelastic fluid.
TL;DR: In this article, a finite volume method for solving the Navier-Stokes equations and using a power-law model exhibiting shear thinning viscosity and Casson's model as the constitutive equations for the non-Newtonian fluid was presented.
Abstract: Non-Newtonian effects in a channel with moving wall indentations are assessed numerically by a finite volume method for solving the unsteady incompressible Navier-Stokes equations and using a power-law model exhibiting shear thinning viscosity and Casson's model as the constitutive equations for the non-Newtonian fluid. The computations show that for a non-Newtonian fluid, there are differences in the velocity profiles and in the structure and size of the reversed flow regions as compared with the corresponding Newtonian fluid. The comparison of non-Newtonian and Newtonian wall shear stress reveals a slight decrease in the magnitude on the average for the non-Newtonian case, eventually resulting in the strength of the “wave train” being slightly weaker than those corresponding to a Newtonian fluid.
Journal Article•
TL;DR: In this article, the authors investigated theoretically whether fluid elasticity is responsible for the formation of circulating cells near the corner, which has been observed experimentally in various polymer processes, and they used series expansions proposed by Strauss (1974) for the stream function and stress components.
Abstract: The analysis of the flow of a viscoelastic fluid near a corner point finds its application in the design of extrusion dies of technological importance. This paper discusses a problem of this type corresponding to the steady flow of a viscoelastic fluid simulated by the Oldroyd 4-constant fluid model in a corner region formed by two planes. The aim of this study is to investigate theoretically whether or not fluid elasticity is responsible for the formation of circulating cells near the corner, which has been observed experimentally in various polymer processes. Since such circulating cells are detrimental in equipment for polymer processing, it is important to understand and be able to predict the conditions under which circulating cells appear. Using series expansions proposed by Strauss (1974) for the stream function and stress components, the governing equations of the problem are reduced to ordinary differential equations. These equations have been solved by employing a numerical technique. The effects of the viscoelastic parameters on the flow pattern are carefully delineated. There is, unlike the case of Newtonian fluid, a secondary flow near the corner point.
Journal Article•
TL;DR: In this paper, a D-dimensional cosmological model describing the evolution of a perfect fluid with negative pressure (x-fluid) and a fluid possessing bothsh ear and bulk viscosity in n Ricci-flat spaces is investigated.
Abstract: A D -dimensional cosmological model describing the evolution of a perfect fluid with negative pressure (x-fluid) and a fluid possessing bothsh ear and bulk viscosity in n Ricci-flat spaces is investigated. The second equations of state are chosen in some special form of metric dependence of the shear and bulk viscosity coefficients. The equations of motion are integrated, and the dynamical properties of exact solutions are studied. It is shown that the 2-component model, where the x-fluid plays the role of a quintessence and the viscous fluid is used as cold dark matter, is free from the cosmic coincidence problem.
Journal Article•
TL;DR: In this article, a servo-driving system was set-up by assembling a microstepping motor, a ball screw and a linear motion guide for the particle motion in a non-Newtonian fluid.
Abstract: In this research, experimental studies have been performed on the hydrodynamic interaction between a spherical particle and a plane wall by measuring the force between the particle and wall. To approach the system as a resistance problem, a servo-driving system was set-up by assembling a microstepping motor, a ball screw and a linear motion guide for the particle motion. Glycerin and dilute solution of polyacrylamide in glycerin were used as Newtonian and non-Newtonian fluids, respectively. The polymer solution behaves like a Boger fluid when the concentration is 1,000 ppm or less. The experimental results were compared with the asymptotic solution of Stokes equation. The result shows that fluid inertia plays an important role in the particle-wall interaction in Newtonian fluid. This implies that the motion of two particles in suspension is not reversible even in Newtonian fluid. In non-Newtonian fluid, normal stress difference and viscoelasticity play important roles as expected. In the dilute solution weak shear thinning and the migration of polymer molecules in the inhomogeneous flow field also affect the physics of the problem.
TL;DR: In this article, a new type of rheometer has been designed based on hydrodynamic principle, which consists of a rotating inner cylinder (shaft) in a fixed hollow outer cylinder.
TL;DR: The flow between two plates in the phase of establishment for the case of a viscoelastic fluid in comparison with a Newtonian fluid is investigated numerically and analytically.
Abstract: The flow between two plates in the phase of establishment for the case of a viscoelastic fluid in comparison with a Newtonian fluid is investigated numerically and analytically The quantitative and qualitative features of the flow are analyzed It is noted that in a number of cases this flow has wave features, and it is determined that the presence of viscoelasticity usually increases the time of establishment of the flow It is pointed out that some of the revealed features of the flow can be used in experimental investigations of non‐Newtonian fluids
TL;DR: The exact solutions for the unsteady flow of an elastico-viscous fluid caused by general periodic oscillations are obtained because the plate is assumed to be rigid as well as porous executing periodic rotary oscillations.
01 Jan 2001
TL;DR: In this article, the authors considered the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with pstructure.
Abstract: We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with pstructure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case p = 1 are covered by this analysis.
Patent•
27 Sep 2001
TL;DR: In this article, the authors calculate the viscosity and shear stress of a fluid from the performance curve, power consumption, heat loss quantity, or measurement power dissipation density of a flow through device with thermal sensors.
Abstract: The measurement method involves calculating the viscosity and shear stress of a fluid from the performance curve, power consumption, heat loss quantity, or measurement power dissipation density of a flow through device with thermal sensors The device generates a flow relative to its measurement organ in context with the passing speed of a fluid and a fluid with identified viscosity and shear stress The viscosity and shear stress of the fluid is calculated based on the performance curve of the device when the measured fluid is passing through, and the performance curve of the device when a predetermined fluid with identified viscosity and shear stress is passing throughAn Independent claim is also included for a viscosity and a thrust measurement device