Showing papers on "Herschel–Bulkley fluid published in 1997"

The hydrodynamics of non-Newtonian fluids. I

Abstract: The classical theory of the hydrodynamics of viscous fluids depends on the assumption of a particular law governing the relations between the components of stress in a fluid and those of the strain-velocity. This assumption limits its applicability to Newtonian fluids. Here, the most general possible relations between the stress and strain-velocity components, which can be obeyed by an incompressible, visco-inelastic fluid, are derived. These relations also apply to an incompressible, visco-elastic fluid in a steady state of laminar flow. It is shown how equations of motion and boundary conditions can be obtained if these relations are known. Two problems involving laminar flow are then discussed in some detail. These are: (i) the torsional motion of a cylindrical mass of fluid, produced by means of forces applied to its plane ends, and (ii) the laminar flow of a mass of fluid contained between two coaxial cylinders rotating with different angular velocities.

A nonlinear viscoelastic - plastic model for electrorheological fluids

Abstract: A nonlinear dynamic model is presented that characterizes electrorheological material behavior in terms of its shear stress versus shear strain behavior. The ER fluid model is essentially a nonlinear combination of linear shear flow mechanisms. These linear shear flow mechanisms, a three-parameter viscoelastic fluid element and a viscous fluid element, are used to describe shear flow behavior in the pre-yield and the post-yield regimes, respectively. In order to capture the material behavior in the transition through the yield point, a nonlinear combination of these linear shear flow mechanisms is used. The model, which relates the shear strain input to the shear stress output, is represented by a simple network that consists of two parallel linear mechanisms whose outputs are combined using nonlinear weighting functions. The weighting functions are dependent on the strain rate in the material. A system identification technique is developed to estimate the model parameters from experimental data, which consists of shear stress versus shear strain hysteresis loops at different levels of electric field. The results of this system identification approach indicate that the model parameters are smooth monotonic functions of the electric field. The experimental hysteresis loops are reconstructed using the estimated model parameters and the results show that the model accurately predicts material response. It is shown that the Coulomb friction-like behavior at high field strengths, which is characteristic of ER fluids, can be captured by this nonlinear mechanism-based model.

Creeping motion of a sphere in tubes filled with Herschel–Bulkley fluids

Abstract: Previous numerical simulations for the flow of Bingham plastics past a sphere contained in cylindrical tubes of different diameter ratios are extended to Herschel–Bulkley fluids with the purpose of comparing them with experiments. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coefficient as a function of the pertinent dimensionless groups. Good overall agreement is obtained between the numerical results and the experimental studies.

Molecular simulation and continuum mechanics study of simple fluids in non-isothermal planar couette flows

Abstract: The behavior of simple fluids under shear is investigated using molecular dynamics simulations. The simulated system consists of a fluid confined between two atomistic walls which are moved in opposite directions. Two approaches for shear flow simulations are compared: in one case, the sheared fluid is not thermostatted and only the confining walls are maintained at a constant temperature, while in the other, a thermostat is employed to keep the entire mass of the sheared fluid at a constant temperature. In the first case the sheared fluid undergoes significant viscous heating at the shear rates investigated, consistent with experimental observations and with theoretical predictions. Most simulations to date, however, have used the second approach which is akin to studying a fluid with infinite thermal conductivity. It is shown here that results for transport coefficients are significantly affected by the thermostat; in fact, the transport properties of the fluid determined using the two methods exhibit a qualitatively different shear rate dependence. It is also shown that the temperature profiles observed in our simulations can be described by continuum mechanics, provided the temperature dependence of the viscosity and thermal conductivity is taken into account.

Interstitial fluid flow in tendons or ligaments: A porous medium finite element simulation

Abstract: The purpose of this study is to describe interstitial fluid flow in axisymmetric soft connective tissue (ligaments or tendons) when they are loaded in tension. Soft hydrated tissue was modelled as a porous medium (using Darcy's Law), and the finite element method was used to solve the resulting equations governing fluid flow. A commercially available computer program (FiDAP) was used to create an axisymmetric model of a biomechanically tested rat ligament. The unknown variables at element nodes were pressure and velocity of the interstitial fluid (Newtonian and incompressible). The effect of variations in fluid viscosity and permeability of the solid matrix was parametrically explored. A transient loading state mimicking a rat ligament mechanical experiment was used in all simulations. The magnitude and distribution of pressure, stream lines, shear (stress) rate, vorticity and velocity showed regular patterns consistent with extension flow. Parametric changes of permeability and viscosity strongly affected fluid flow behaviour. When the radial permeability was 1000 times less than the axial permeability, shear rate and vorticity increased (approximately 5-fold). These effects (especially shear stress and pressure) suggested a strong interaction with the solid matrix. Computed levels of fluid flow suggested a possible load transduction mechanism for cells in the tissue.

Slip in Quantum Fluids

Abstract: In this review we describe theoretical and experimental investigations of general slip phenomena in context with the flow of the quantum liquids 3He, 4He and their mixtures at low temperatures. The phenomenon of slip is related to a boundary effect. It occurs when sufficiently dilute gases flow along the wall of an experimental cell. A fluid is said to exhibit slip when the fluid velocity at the wall is not equal to the wall’s velocity. Such a situation occurs whenever the wall reflects the fluid particles in a specular-like manner, and/or if the fluid is describable in terms of a dilute ordinary gas (classical fluid) or a dilute gas of thermal excitations (quantum fluid). The slip effect in quantum fluids is discussed theoretically on the basis of generalized Landau-Boltzmann transport equations and generalized to apply to a regime of ballistic motion of the quasiparticles in the fluid. The central result is that the transport coefficient of bulk shear viscosity, which typically enters in the Poiseuille flow resistance and the transverse acoustic impedance, has to be replaced by geometry dependent effective viscosity, which depends on the details of the interaction of the fluid particles with the cell walls. The theoretical results are compared with various experimental data obtained in different geometries and for both Bose and Fermi quantum fluids. Good agreement between experiment and theory is found particularly in the case of pure normal and superfluid 3He, with discrepancies probably arising because of deficiencies in characterization of the experimental surfaces.

Analysis of general second-order fluid flow in double cylinder rheometer

Abstract: The fractional calculus approach in the constitutive relationship model of second-order fluid is introduced and the flow characteristics of the viscoelastic fluid in double cylinder rheometer are studied. First, the analytical solution of which the derivative order is 1/2 is derived with the analytical solution and the reliability of Laplace numerical inversion based on Crump algorithm for the problem is verified, then the characteristics of second-order fluid flow in the rheometer by using Crump method is analyzed. The results indicate that the more obvious the viscoelastic properties of fluid are, the more sensitive the dependence of velocity and stress on fractional derivative order is.

Rayleigh–Taylor stability criteria for elastic-plastic solid plates and shells

Abstract: The Rayleigh–Taylor (R-T) instability theory is usually applied to the acceleration of one fluid by a lower density one, but also becomes applicable to a solid accelerated by a fluid at very high pressure. Approximate analytic R-T stability criteria are derived for both finite and infinitesimal perturbations of the driven surface of an incompressible solid plate of a given thickness, shear modulus, and von Mises yield stress uniformly accelerated by a massless fluid. The Prandtl-Reuss equations of elastic-plastic flow are assumed for the solid. A single degree of freedom, amplitude q, is assumed for the spatial dependence of the perturbation, which is approximated to be that of the semi-infinite half-plane ideal fluid linear R-T eigenfunction. The temporal dependence of q, however, is determined self-consistently from global energy balance, following a previously published model. The (significant) effect of the unperturbed solid’s stress tensor is included and related to the converging/diverging geometrie...

Flow of a viscoelastic fluid between two rotating circular cylinders subject to suction or injection

Abstract: The steady flow of an Oldroyd-B fluid between two porous concentric circular cylinders is studied. The equation of motion and the constitutive equations form a system of non-linear ODEs that is solved numerically, and in a few cases the numerical results are compared with a known analytical solution. We consider the effect of the non-Newtonian nature of the fluid on the drag and on the boundary layer structure near the walls. Numerical computations show the effect of the non-Newtonian quantities on the velocity and on the shear stress as the dimensionless parameters are varied. © by 1997 John Wiley & Sons, Ltd.

Fluid-damping-controlled instability of tubes in crossflow

Abstract: A mathematical model for fluid damping controlled instability of tubes presented in this paper is based on the unsteady flow theory. Motion dependent fluid forces are measured in a water channel. From the measured fluid forces, fluid stiffness and fluid damping coefficients, are calculated as a function of reduced flow velocity, oscillation amplitude, and Reynolds number. Once these coefficients are known, the mathematical model can be applied to predict structural instability due to fluid damping. Many cases are considered: single tube, twin tubes, tube row, triangular array, and square arrays. The results show the instability regions based on the fluid damping coefficients and provide the answers to a series of questions on fluid elastic instability of tube arrays in crossflow.

The effective film viscosity coefficients of a thin floating fluid layer

Abstract: We derive a constitutive relation, relating the tangential stress, tangential velocity, thickness h, and viscosity μ, for a thin layer of Newtonian fluid on top of a fluid substrate. We find that the upper layer exerts a viscous tangential shear stress on the lower fluid, behaving as if it were a film with a two-dimensional shear viscosity equal to μh, and a dilatational viscosity 3μh.

Oscillatory enhancement of the squeezing flow of yield stress fluids: A novel experimental result

Abstract: The extrusion of a yield stress fluid from the space between two parallel plates is investigated experimentally. Oscillating the magnitude of the squeezing force about a mean value ( F = f [1+αcos(ω t )]) was observed to significantly enhance the flow rate of yield stress fluids, while having no effect on the flow rate of Newtonian fluids. This is a novel result. The enhancement depends on the magnitude of the force, the oscillatory frequency and amplitude, the fluid being squeezed, and the thickness of the fluid layer. Non-dimensional results for the various flow quantities have been presented by using the flow predicted for the constant-force squeezing of a Herschel–Bulkley yield stress fluid as the reference. In the limit of constant-force squeezing, the present experimental results compare very well with those of our earlier theoretical model for this situation (Zwick, Ayyaswamy & Cohen 1996). The results presented in this paper have significance, among many applications, for injection moulding, in the adhesive bonding of microelectronic chips, and in surgical procedures employed in health care.

Local similarity solutions for the stress field of an Oldroyd-B fluid in the partial-slip/slip flow

Abstract: Local similarity solutions are presented for the stress field of a fluid described by the Oldroyd-B viscoelastic constitutive equation near the singularity caused by the intersection of a planar free surface and a solid surface along which Navier’s slip law holds, the partial-slip/slip problem. For the case where the velocity field is given by Newtonian kinematics, the elastic stress field is predicted to have a logarithmic singularity as the point of attachment of the free surface is approached. Asymptotic analysis for the fully-coupled flow, where the stress and flow fields are determined simultaneously, results in a local form for the flow and elastic stress fields that is similar in form to that for the decoupled case. For both the coupled and decoupled flow problems, the strength of the singularity depends on the dimensionless solvent viscosity and the slip coefficient, but not upon the Deborah number. The asymptotic results for the coupled flow differ from the predictions with Newtonian kinematics i...

Computer Simulation of Shear-Induced Phase Separation and Rheology in Two-Component Viscoelastic Fluid

Abstract: We numerically study the dynamics of polymer solutions in two dimensions at a temperature above the equilibrium coexistence curve under shear flow. Our model is based on the Lagrangian picture of fluid dynamics. We can incorporate viscoelastic effects into the model by introducing a kind of fluid particles which have memories of their own past history. We carry out computer simulations and observe that shear-induced phase separation occur and the system shows a shear thinning rheological property. The most remarkable result is that the dependence of normal stress coefficient on shear rate changes at a shear rate which is comparable to inverse of the stress relaxation time. Our results imply that the shear-induced phase separation can change qualitative features of rheological response.

Vehicle heat generator and viscous fluid therefor

Abstract: A non-Newtonian fluid (for instance, a specific silicone oil) having a tendency that the apparent viscosity decreases as the shearing speed of a rotor (33) increases is used as a viscous fluid (F) that is contained in a vehicle heat generator provided with the rotor (33). The nominal viscosity of the viscous fluid (F) ranges from 10,000 cSt to 200,000 cSt. By using the viscous fluid, the shearing heat generating function of the viscous fluid (F) can be maintained for a long time even when the viscous fluid bears excessive shearing due to excessive rotation of the rotor (33), and the rotor (33) can be easily activated from the stationary state at a lower temperature.

Pressure drops of non-newtonian purely viscous fluid flow through synthetic foams

Abstract: This work aims at giving a first insight of non-Newtonian fluid flow through synthetic foams. At first, a review of experimental pressure drops measured with Newtonian fluids through various foams is proposed as well as a recall of a capillary-type flow model used to determine structural parameters. In this particular case of Newtonian fluid flow, a single equation is shown to correlate experimental data whatever the grade of the foam. Results of an image analysis study are also given; they allow to give a physical sense to the value of the equivalent diameter of pore given by the flow model. In a second part, results of pressure drops measured with a non-Newtonian fluid are reported. A model allowing the determination of the pressure drops for non-Newtonian purely viscous fluid flow through packed beds of particles, based on the same capillary representation of porous media, is tested in the case of fluid flow through synthetic foams. The model predictions are acceptable for foams of high grades, but a d...

Internal Damper Characteristics of Rotor System withSubmerged ER Fluid Journal Bearing

Abstract: Electro-Rheological (ER) fluid behavior is similar to Bingham fluid’ s. Only when the shear stress magnitude of ER fluid exceeds the yield stress, Newtonian flow results. Continuous shear strain rate equation about shear stress which simulates Bingham-like fluid shows viscosity variations. Shear yield stress is controlled by electric fields. Electric fields in circumferential direction around the journal are also changeable because of gap distance. These values make changes of spring and damping coefficients of journal bearings compared to Newtonian flow case. Implicit viscosity variation effects according to shear strain rates of fluid are included in generalized Reynolds' equation for submerged journal bearing. Fluid film pressure and perturbation pressures are solved using switch function of Elord's algorithm for cavitation boundary condition. Spring and damping coefficients are obtained for several parameters that determine the characteristics of ER fluids under a certain electric field. From these values stability region for simple rotor-bearing system is computed. It is found that there are no big differences in load capacities with the selected electric field parameters at low eccentric region and higher electric field can support more load with stability at low eccentric region.

On the Generation of Discontinuous Shearing Motions of a Non-Newtonian Fluid

Abstract: The system under study models unsteady, one-dimensional shear flow of a highly elastic and viscous incompressible non-Newtonian fluid with fading memory under isothermal conditions. The flow, in a channel, is driven by a constant pressure gradient, is symmetric about the center line, and satisfies a no-slip boundary condition at the wall. The non-Newtonian contribution to the stress is assumed to obey a differential constitutive law (due to Oldroyd, Johnson & Segalman), the key feature of which is a non-monotone relation between the total steady shear stress and strain rate. In a regime in which the Reynolds number is much smaller than the Deborah (or Weissenberg) number, one obtains a degenerate, singularly perturbed system of nonlinear reaction-diffusion equations. It is shown that if the driving pressure gradient exceeds a critical value (the local shear stress maximum of the steady stress vs. strain rate relation), then the solution to the governing system, starting from rest at , tends as to a particular discontinuous steady state solution (the “top-jumping” steady state), except in a small neighborhood of the discontinuity. This discontinuous steady state is shown to be nonlinearly stable in a precise sense with respect to perturbations yielding smooth initial data. Such discontinuous steady states have been proposed to explain “spurting” flows, which exhibit a large increase in mean flow rate when the driving pressure is raised above a critical value.

Fluid Inertia Effects on the Performance of Short and Long Squeeze Film Dampers Executing Periodic Vibration

Abstract: A comprehensive study is made to examine effects of fluid inertia on pressure distribution, load capacity, wall shear stress differences (defined in Nomenclature), and velocity variation of flow in short and long Squeeze Film Dampers (SFDs). The SFD is assumed to execute a small excursion around an arbitrary static position. Exact solutions, in the form of a Fourier series, for fluid pressure and velocity are obtained for periodic motions of the SFD journal. An example of a horizontal motion, with various static positions in bearing clearance, is studied in detail for both short and long bearing configurations. It is found that the existence of fluid inertia generally increases the peak pressure value, and hence the load capacity. Wall shear stress differences and velocity distribution are also altered by the presence of the fluid inertia compared with inertialess flow, but the parabolic shape of the velocity may be maintained. Insight on how the fluid inertia effect is internally related to the viscous effects is also gained from this study.

Theoretical Study on Equation of Motion and Yield Stress of Electrorheological Fluid.

Abstract: The flow of electrorheological(ER)fluids has been analyzed theoretically based on the constitutive equation for Bingham fluids. However, it is necessary to take account of internal rotation in ER fluids, because they are suspensions of particles. The equation of motion of an ER fluid is derived based on not only the constitutive equation of stress for a Bingham fluid but also on the theory of micropolar electrically conducting fluids, assuming the equilibrium equation of angular momentum. With respect to the yield stress, which is a characteristic of ER fluids, we consider that the interaction of particles, which are polarized by an applied electric field, is based on a two-body problem at the cutting surface of a cluster of particles. As a result, a new equation is derived based on the theory of dipole-dipole interaction. Yield stress in this study is not dynamic yield stress but static yield stress.

Creeping flow of generalized Newtonian fluid through a fixed and a fluidized bed of spherical particles

Abstract: The modified Rabinowitsch-Mooney equation, together with the corresponding relations for consistency variables has been employed to the flow solution of generalized Newtonian fluid through a fixed and a fluidized bed of spherical particles. The usefulness of the proposed equations has been verified for a power-law fluid, using both the published and original experimental results

Comparative evaluation of some existing rate-type constitutive equations for a viscoelastic fluid undergoing wiggle flow

Abstract: A comparative evaluation of existing rate-type constitutive equations is provided for a viscoelastic fluid undergoing accelerated flow. To this end, accurate point velocity and stress birefringence data previously obtained by laser Doppler anemometry and stress birefringence are utilized. For each constitutive equation, the numerical values of constants which yield the best fit with experimental data are determined via non-linear regression analysis. The best agreement between experimental and calculated normal stress differences is obtained with the White-Metzner equation. The success of this equation is attributed to the deformation rate dependence of its viscosity and time constant.

Vehicular heat generators and viscous fluids for the same

Abstract: As a viscous fluid (F) contained in a vehicular heat generator provided with a rotor (33), a non-Newtonian fluid having an apparent viscosity that decreases as the shear rate of the rotor (33) increases (e.g., a kind of silicone oil) is employed. The nominal viscosity of the viscous fluid (F) is in the range of 10,000 cSt to 200,000 cSt. If such viscous fluid is employed, the viscous fluid (F) maintains its shear heat generating function over an extended period even under circumstances where the fluid (F) is subjected to over-shearing by over-rotation of the rotor (33). In addition, low-temperature starting of the rotor is facilitated.

球・バネマクロモデルによる粘弾性流体の直接数値シミュレーション : モデル化と解析方法

Abstract: We propose a new bead-spring model for direct numerical simulation of viscoelastic fluid flow. The present bead-spring macromodel, which has a tetrahedral structure, models a gathering of interwined polymer chain, and is used to investigate the interference between fluid and particles. In this paper, the method of analysis is presented and characteristics of two-dimensional Poiseuille flow are examined. As a result, the following was clarified. Fluid which contains bead-spring macromodels has a non-Newtonian viscosity and shear-thinning characteristics. The cause of the shear thinning characteristics is the interaction of rotation and the transformation of the bead-spring macromodel.

Effects of Ekman layer on flows and temperature of viscoelastic fluid in a rotating frame

Abstract: An experimental analysis of the hydrodynamic flow of a fluid and the temperature distribution in a porous medium is presented. The experiment has been carried out using viscoelastic fluid in a rotating channel, bounded by two impermeable infinite plates at a constant temperature, under the action of a uniform pressure gradient in the direction of the flow. The primary and secondary flow velocities, the temperature distribution and heat transfer in terms of the Nusselt number of the fluid are studied in the model due to the effects of the Ekman layer on the fluid for various values of the viscoelastic parameter (Ve) in the channel height h=-1 to +1.