Showing papers on "Herschel–Bulkley fluid published in 2000"

Conditions for Similitude between the Fluid Velocity and Electric Field in Electroosmotic Flow

Abstract: Electroosmotic flow is fluid motion driven by an electric field acting on the net fluid charge produced by charge separation at a fluid−solid interface. Under many conditions of practical interest, the resulting fluid velocity is proportional to the local electric field, and the constant of proportionality is everywhere the same. Here we show that the main conditions necessary for this similitude are a steady electric field, uniform fluid and electric properties, an electric Debye layer that is thin compared to any physical dimension, and fluid velocities on all inlet and outlet boundaries that satisfy the Helmholtz−Smoluchowski relation normally applicable to fluid−solid boundaries. Under these conditions, the velocity field can be determined directly from the Laplace equation governing the electric potential, without solving either the continuity or momentum equations. Three important consequences of these conditions are that the fluid motion is everywhere irrotational, that fluid velocities in two-dime...

Analysis of electro- and magneto-rheological flow mode dampers using Herschel-Bulkley model

Abstract: Electrorheological (ER) and magnetorheological (MR) fluid- based dampers are typically analyzed using Bingham-plastic shear flow analysis under quasi-steady fully developed flow conditions. An alternative perspective, supported by measurements reported in the literature, is to allow for post- yield shear thinning and shear thickening. To model these, the constant post-yield plastic viscosity in Bingham model can be replaced with a power law model dependent on shear strain rate that is known as the Herschel-Bulkley fluid model. Depending on the value of the flow behavior index number, varying degrees of post-yield shear thickening or thinning behavior can be analyzed. A nominal ER bypass damper is considered. Damping forces in the damper are analyzed by approximate parallel plate geometry. The impacts of flow behavior index on shear stress-strain relationship and velocity profile for variable electric field are also examined numerically. Then, analytical damping predictions of ER/MR flow mode dampers are compared using the nonlinear Bingham-plastic and nonlinear Herschel-Bulkley analyses.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Field-controllable electro- and magneto-rheological fluid dampers in flow mode using Herschel-Bulkley theory

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, the Herschel-Bulkley model is employed 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 and generalized mathematical form for modeling ER and MR fluids. Theoretical and experimental analyses are presented for a MR fluid damper, which is designed, developed, and tested at the University of Nevada, Reno (UNR).

The effect of fluid pressure on wave speeds in a cracked solid

Abstract: In a porous or cracked elastic solid, the effective stress (defined in terms of the loads applied to the solid part of the outer boundary) and effective strain (defined in terms of the displacements at the solid part of the outer boundary) occurring in small-amplitude deformations are connected by a linear relation along with the pressure within the fluid occupying the pores and cracks. We derive here a formula of this kind for a static system in which enough time is allowed for pressure to be equalized throughout the fluid (on the assumption that all pockets of fluid are connected in some way). The formula depends on the overall stiffnesses relating stress to strain for the same material with the fluid removed (dry or empty cracks and pores). For undrained conditions where no fluid is allowed to enter or leave the body, the pressure is directly related to the effective stress and strain, and the Gassmann relations are obtained relating the stiffnesses for an isotropic material in dry and undrained conditions. For an anisotropic material, the Brown–Korringa relations are recovered. Externally imposed stresses and fluid pressure distort the material structure and influence the wave speeds of elastic waves. The main way in which this occurs is in changing the aspect ratios of flat cracks, the most compliant part of the microstructural geometry. This effect on the wave speeds is studied here both in terms of crack closure, with corresponding changes in crack number density, and in variations in crack aspect ratios. The principal way in which the latter influences the wave speeds is through the fluid incompressibility factor in the formula for the properties of materials with connected cracks. An increase in aspect ratio of the cracks is equivalent to a reduction in the bulk modulus of the fluid. This effect is apparent in the limits of both high frequencies, when the material behaves as if the cracks were isolated, and low frequencies, when undrained conditions apply.

Lagrangian viscoelastic flow computations using the Rivlin-Sawyers constitutive model

Abstract: A new finite element technique for the numerical simulation of 3D time-dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematics description of the fluid flow. It represents a further development of the 3D Lagrangian integral method (3D-LIM) from an upper convected Maxwell fluid to a fluid described by an integral constitutive equation of the Rivlin–Sawyers type. This includes the K-BKZ model. The convergence of the method is demonstrated on the axisymmetric problem of the inflation of a polymeric membrane only restricted by a clamping ring.

The hydromagnetic flow of a dusty visco-elastic fluid between two infinite parallel plates

Abstract: An initial value investigation is made on the motion of an incompressible visco-elastic (Rivlin-Ericksen) fluid with small particles between two infinite moving parallel plates in the presence of a transverse magnetic field. The flow is generated in the fluid particle system due to time dependent pressure gradient and also the motion of the plates in the presence of an external imposed transverse magnetic field. By Laplace transform technique, the velocity distribution and wall shear stress have been obtained for four different cases, when the pressure gradient and both the plate velocities are 1. (i) decreasing exponentially with time, 2. (ii) varying periodically with time, 3. (iii) impulsive type, and 4. (iv) acting for a finite time. In each case, shear stresses at the boundary plates are also calculated.

Flow Characteristics of a ``Multiconfigurational'', Shear Thinning Viscoelastic Fluid with Particular Reference to the Orthogonal Rheometer

Abstract: This paper deals with the flow characteristics of a class of nonsimple viscoelastic fluid models developed by Rajagopal and Srinivasa (1999). The central feature of these models is that the stress response is lastic from a changing natural configuration with the viscous dissipation occurring due to changes in the natural state. The class of models considered are characterized by three independent parameters that represent respectively the elasticity, the viscosity and the shear thinning index.

Steady vortex in a uniform shear flow of an ideal fluid

Abstract: This paper is concerned with the existence of maximizers for a certain non-convex energy functional, relative to a class of rearrangements of a given function. Physically, the solution represents a uniform shear flow containing a bounded vortex anomaly, in R2. The prescribed data are the rearrangement class of the vorticity field.

Simulation of Lubricated Squeezing Flow of a Herschel-Bulkley Fluid Under Constant Force

Abstract: Abstract Lubricated squeezing flow (LSF) of a Herschel-Bulkley fluid between parallel disks under constant force was theoretically analyzed. An analytical expression for the fluid thickness as a function of time was obtained in terms of a hypergeometric function. The fluid thickness profiles in LSF were simulated for a range of each of the model parameters (n, K, τo). The solution obtained in this study reduces to the corresponding analytical equations previously derived for LSF of Newtonian and power-law fluids. The simulations for Herschel-Bulkley fluid were compared with the response of Newtonian and power-law fluids. The dependence of the limiting fluid thickness (i.e. H(t)/H0 at 180 s) on model parameters is presented.

Collapse of a cylinder of Bingham fluid

Abstract: The ``Slump Test" is a simple method of measuring the yield stress of certain materials such as concrete and concentrated suspensions. In this procedure a cylindrical test sample is allowed to deform under its own weight, and the yield stress is obtained from the change in height (slump height) of the sample using an empirical calibration curve. In this paper the slump height/yield stress relationship of the material, considered as a Bingham fluid, is investigated numerically using a finite volume procedure applied to a homogeneous two-fluid (liquid-air) model representing flow of an equivalent single phase with variable properties. Advection is approximated using a van Leer flux limiter to reduce interface smearing without the occurrence of spurious oscillations. Predictions are in reasonable agreement with published experimental data for high yield stress materials, but are less satisfactory when the yield stress is low.

Hiemenz magnetic flow of a non-Newtonian fluid of second grade with heat transfer

Abstract: The steady laminar flow of an incompressible viscous electrically conducting non-Newtonian fluid of second grade impinging normal to a plane wall with heat transfer is investigated. An externally applied uniform magnetic field is applied normal to the wall, which is maintained at a constant temperature. A numerical solution for the governing momentum and energy equations is obtained. The effect of the characteristics of the non-Newtonian fluid and the magnetic field on both the flow and heat transfer is outlined. PACS Nos.: 47.50 and 47.15

Correspondence Relation Between Linear Elastic Problem and Newtonian Fluid Problem

Abstract: The correspondence relation between a linear elastic problem and a Newtonian fluid problem is discussed in the paper. It is shown that, to establish the correspondence relation between the two problems, it is not enough to consider the constitutive equations only. On the basis of a comparison of all basic equations between the two problems, it is proved that a Newtonian fluid problem satisfying the three conditions of (1)incompressible; (2)small Reynolds number; (3) temperature-independent viscosity, is equivalent to a quasi-static incompressible linear elastic problem. Applying this equivalence relation to the numerical simulation of the tectonic stress field, the computer programs for elastic problems can be used to solve the viscous flow of the lithosphere.

Fluid dynamics of the sliding plate

Abstract: A fluid with viscosity which depends on temperature and concentration is placed between two infinite parallel plates moving relative to each other with constant velocity. On the basis of certain simplifying assumptions, the fluid equations of continuity, momentum, energy and concentration are obtained and solved analytically. A non-linear integro-differential equation is derived which governs the fluid velocity component parallel to the walls and a parameter perturbation technique is suggested and utilized for its solution. Using the Padé approximants technique, the series summation and improvement is performed. The effect of viscosity variation due to variation in temperature and concentration on the fluid flow is discussed quantitatively. Quaestiones Mathematicae 23(2000), 59–66

Behaviors of anisotropic fluids in the vicinity of a wedge

Abstract: The laminar boundary layer flow and heat transfer of anisotropic fluids in the vicinity of a wedge have 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 equations. The numerical solutions are presented using the fourth-order Runge-Kutta method and the distribution of velocity, micro-rotation, shear and couple stresses and temperature across the boundary layer are plotted. These results are also compared with the corresponding flow problems for Newtonian fluid over wedges. It is found that for a constant wedge angle, the skin friction coefficient is lower for micropolar fluid, as compared to Newtonian fluid. For the case of the constant material parameterK, however, the magnitude of velocity for anisotropic fluid is greater than that of Newtonian fluid. The numerical results also show that for a constant wedge angle with a given Prandtl number,Pγ=1, the effect of increasing values ofK results in increasing thermal boundary layer thickness for anisotropic fluid, as compared with Newtonian fluid. For the case of the constant material parameterK, however, the heat transfer rate for anisotropic fluid is lower than that of Newtonian fluid.

Using shear impedance reflection factor models for simulation of viscosity measurements

Abstract: Viscosity of a fluid is known to affect the reflection of shear waves from a solid/fluid interface. In this paper, we will discuss an impedance plane wave model to explain the influence of the change in density and viscosity of a fluid which is in contact with a solid. This modeled is used in the development of sensors for measuring the viscosity of the fluid. Newtonian and Non-Newtonian fluids were considered. The experimental results is compared with model simulated data to provide insight into the melting of glass. The sensitivity and precision of the measurements as well as the range/limitation of measurements will be interpreted through the use of the shear impedance model.

Theoretical analysis of the hydrodynamic characteristics of electrorheological fluid in a parallel duct flow

Abstract: An experimental investigation is conducted to clarify the hydrodynamic characteristics of ERF with elastic particles of smectite in a two-dimensional parallel duct of various widths. Experimental data on pressure difference to a volumetric flow rate in a supplying D.C. electric field are measured. These data are arranged to obtain the apparent viscosit by using the integral method of rheology. From the data of apparent viscosity, the wall friction coefficient is obtained. The increment of the apparent viscosity caused by the applying electric field is a function of shear rate as well as the electric field strength and the width of the duct. However, the wall friction coefficient is not a function of elecric field strength and the width of the parallel duct, but only of shear rate. The yield stress is a function of the width of the parallel duct as well as of electric field strength. The ratio of Non-Newtonian viscosity in the apparent viscosity is varied by the intensity of the shear rate.

Dynamic yield stress of electrorheological fluid

Abstract: Combining the microstructure and the interaction between two particles in an electrorheological fluid that is calculated by the modified dipole model and the conductivity model respectively, the shear stress strain relationships of the electrorheological fluid were set up. On this basis, and considering the fracture and reconfiguration process in the post yield state of this material, its dynamic yield stress was obtained. The calculation indicates that the dynamic yield stress lower than static yield stress by about 25%. In addition, the dynamic yield stress of the electrorheological fluid increases nearly linearly with the volume fraction at the small volume fraction and gets their maximums at rather large volume fractions, 0.4～0.5.

X-fluid and viscous fluid in D-dimensional anisotropic integrable cosmology

Abstract: D-dimensional cosmological model describing the evolution of a perfect fluid with negative pressure (x-fluid) and a fluid possessing both shear 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 the exact solutions are studied. It is shown the possibility to resolve the cosmic coincidence problem when the x-fluid plays role of quintessence and the viscous fluid is used as cold dark matter.

Characteristics for generalized hermomechanical fields in viscous fluid media

Abstract: In the context of a general theory of characteristics, thermomechanical processes are considered in fluid media with the final heat-propagation velocity. The equations of propagation of characteristics for two variants of the theory of a viscous fluid medium are derived, and ways of applying them for determining displacement velocities are indicated.