Showing papers on "Herschel–Bulkley fluid published in 2008"

Homogenization approach to the behavior of suspensions of noncolloidal particles in yield stress fluids

Abstract: The behavior of suspensions of rigid particles in a non-Newtonian fluid is studied in the framework of a nonlinear homogenization method. Estimates for the overall properties of the composite material are obtained. In the case of a Herschel–Bulkley suspending fluid, it is shown that the properties of a suspension with overall isotropy can be satisfactorily modeled as that of a Herschel–Bulkley fluid with an exponent equal to that of the suspending fluid. Estimates for the yield stress and the consistency at large strain rate levels are proposed. These estimates compare well to both experimental data obtained by Mahaut et al. [J. Rheol. 52(1), 287–313 (2008)] and to experimental data found in the literature.

Integration approach of the Couette inverse problem of powder type self-compacting concrete in a wide-gap concentric cylinder rheometer

Abstract: For powder type self-compacting concrete (SCC) mixes, commonly used in Belgium, a shear thickening (Herschel–Bulkley) flow behaviour of the fresh mixes is quite often observed. A longstanding problem in rheometry is the so-called “Couette inverse problem”, where one tries to derive the flow curve τ ( γ ˙ ) from the torque measurements T(N) in a (wide-gap) concentric cylinder (Couette) rheometer, with T the torque registered at the inner, stationary cylinder and N the rotational velocity of the outer, rotating, cylinder. In this paper, the Couette inverse problem is approached by means of the integration method in order to convert T(N) into τ ( γ ˙ ) for a wide-gap (Ro/Ri = 1.45) concentric cylinder rheometer. The approach consists in the decoupling of the flow resistance and the power-law flow behaviour after exceeding the flow resistance. The integration approach is validated by experimental verification with different powder type SCC mixtures. By means of illustration, the results of one limestone powder type SCC mixture with different superplasticizer contents are shown in this paper.

Towards the zero-surface-tension limit in granular fingering instability

Abstract: The finger-like branching pattern that occurs when a less viscous fluid displaces a more viscous one confined between two parallel plates has been widely studied as a classical example of a mathematically tractable hydrodynamic instability1,2,3. Fingering in such Hele–Shaw geometries has been generated not only with newtonian fluids4,5,6 but also with various non-newtonian fluids7,8,9 including fine granular material displaced by gas, liquid or larger grains10,11,12,13,14,15. Here, we study a granular Hele–Shaw system to explore the zero-surface-tension property of granular ‘fluids’16. We demonstrate that the grain–gas interface exhibits fractal structure and sharp cusps, which are associated with the hitherto-unrealizable singular hydrodynamics predicted in the zero-surface-tension limit of normal fluid fingering2,17,18,19,20,21,22,23. Above the yield stress, the scaling for the finger width is distinct from that for ordinary fluids, reflecting unique granular properties such as friction-induced dissipation as opposed to viscous damping24,25,26,27. Despite such differences, the dimension of the global fractal structure and the shape of the singular cusps on the interface agree with the theories based on simple laplacian growth of conventional fluid fingering in the zero-surface-tension limit2,17,18,19,20,21,22,23.

Processing the Couette viscometry data using a Bingham approximation in shear rate calculation

Abstract: This paper presents an approach to computing the shear flow curve from torque–rotational velocity data in a Couette rheometer. The approximation techniques in shear rate calculation are generally dictated by the radius ratio between coaxial cylinders and the rheological behaviour of fluid tested. Here, the approach consists in analysing the sheared material as a Bingham fluid and computing an average shear rate when the fluid in the cylindrical gap is partially and fully sheared. We focus in particular on the applicability of the Bingham approximation in shear rate calculation. First, the approach is assessed by examining synthetic data generated with Newtonian, non-Newtonian and yield stress materials with known properties, varying the gap radius ratio. The results, which are compared with commonly used techniques in shear rate calculation, prove the relevance of the proposed approach. Finally, its efficiency is examined by applying it to process Couette data of yield stress fluids taken from published works.

Laminar, transitional and turbulent flow of Herschel–Bulkley fluids in concentric annulus

Abstract: An integrated approach is presented for the flow of Herschel–Bulkley fluids in a concentric annulus, modelled as a slot, covering the full range of flow types, laminar, transitional, and turbulent flows. Prior analytical solutions for laminar flow are utilized. Turbulent flow solutions are developed using the Metzner–Reed Reynolds number after determining the local power law parameters as functions of flow geometry and the Herschel–Bulkley rheological parameters. The friction factor is estimated by modifying the pipe flow equation. Transitional flow is solved introducing transitional Reynolds numbers which are functions of the local power law index. Thus, an integrated, complete and consistent set, combining analytical, semi-analytical and empirical equations, is provided which describe fully the flow of Herschel–Bulkley fluids in concentric annuli, modelled as a slot. The comparison with experimental and simulator data from various sources shows very good agreement over the entire range of flow types.

Mathematical Model of Drum-type MR Brakes using Herschel-Bulkley Shear Model

Abstract: Most of the commercially available magnetorheological (MR) fluids are only tested up to 1200 1/s shear rates but with no magnetic field. Data are rarely available at high shear rates with magnetic field applied. In most of the applications where MR fluids are used, such as MR rotary brakes or MR translational dampers, the shear rates can be in the order of thousands and in some applications, the shear rates could be in the order of ten thousands (1/s) and higher. At these high shear rates, most MR fluids will be shear thinning and Bingham model will be inappropriate to use. The focus of this study is on the mathematical modeling of a drum-type MR rotary brake using the Herschel-Bulkey model.

Nonlocal shear stress for homogeneous fluids.

Abstract: It has been suggested that for fluids in which the rate of strain varies appreciably over length scales of the order of the intermolecular interaction range, the viscosity must be treated as a nonlocal property of the fluid. The shear stress can then be postulated to be a convolution of this nonlocal viscosity kernel with the strain rate over all space. In this Letter, we confirm that this postulate is correct by a combination of analytical and numerical methods for an atomic fluid out of equilibrium. Furthermore, we show that a gradient expansion of the nonlocal constitutive equation gives a reasonable approximation to the shear stress in the small wave vector limit.

Pulsatile flow of blood using a modified second-grade fluid model

Abstract: We study the unsteady pulsatile flow of blood in an artery, where the effects of body acceleration are included. The blood is modeled as a modified second-grade fluid where the viscosity and the normal stress coefficients depend on the shear rate. It is assumed that the blood near the wall behaves as a Newtonian fluid, and in the core as a non-Newtonian fluid. This phenomenon is also known as the Fahraeus-Lindqvist effect. The equations are made dimensionless and solved numerically.

Simulation of semidilute suspensions of non-Brownian fibers in shear flow.

Abstract: Particle-level simulations are performed to study semidilute suspensions of monodispersed non-Brownian fibers in shear flow, with a Newtonian fluid medium. The incompressible three-dimensional Navier-Stokes equations are used to describe the motion of the medium, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous drag forces. The two-way coupling between the solids and the fluid phase is taken into account by enforcing momentum conservation. The model includes long-range and short-range hydrodynamic fiber-fiber interactions, as well as mechanical interactions. The simulations rendered the time-dependent fiber orientation distribution, whose time average was found to agree with experimental data in the literature. The viscosity and first normal stress difference was calculated from the orientation distribution using the slender body theory of Batchelor [J. Fluid Mech. 46, 813 (1971)], with corrections for the finite fiber aspect ratios. The viscosity was also obtained from direct computation of the shear stresses of the suspension for comparison. These two types of predictions compared well in the semidilute regime. At higher concentrations, however, a discrepancy was seen, most likely due to mechanical interactions, which are only accounted for in the direct computation method. The simulated viscosity determined directly from shear stresses was in fair agreement with experimental data found in the literature. The first normal stress difference was found to be proportional to the square of the volume concentration of fibers in the semidilute regime. As concentrations approached the concentrated regime, the first normal stress difference became proportional to volume concentration. It was also found that the coefficient of friction has a strong influence on the tendency for flocculation as well as the apparent viscosity of the suspension in the semidilute regime.

Nondimensional Herschel—Bulkley Analysis of Magnetorheological and Electrorheological Dampers:

Abstract: Quasisteady modeling of linear stroke flow mode magnetorheological (MR) (or electrorheological (ER)) dampers has focused primarily on the utilization of the Bingham-plastic constitutive model to assess performance metrics such as damping capacity. In such Bingham-plastic MR (or ER) flows, the variable yield stress of the fluid, τ y , is activated by applying magnetic (or electric) field. The Bingham-plastic model assumes that the material is in either (1) a pre-yield condition where the local shear stress is less than the yield stress, τ Ty, so that the material flows with a constant post-yield viscosity. The objective of this study is to analyze the damping capacity of such a controllable MR or ER damper in the situation when the field dependent fluid exhibits post-yield shear thinning or thickening behavior, that is, the post-yield viscosity is a function of shear rate. A Herschel-Bulkley model with a field dependent yield stress is proposed, and the impact of shear rate dependent viscosity on damping capacity is assessed. Key analysis results - velocity profile, pre-yield thickness, and damping coefficient - are presented in a nondimensional formulation that is consistent with prior results for the Bingham-plastic analysis. The nondimensional analysis formulated here clearly establishes the Bingham number as the independent variable for assessing flow mode damper performance.

Modeling rheological behavior of highly flowable mortar using concepts of particle and fluid mechanics

Abstract: A particle–fluid model is developed for predicting the relationship between the shear stress and shear strain rate of highly flowable mortars. In this model, mortars are considered as a two-phase material, containing a fluid matrix (cement paste) and a group of well-graded, non-cohesive, and rigid particles (fine aggregate) that are uniformly distributed in the matrix. The mortar shear stress is assumed to be the sum of the shear stresses resulting from the paste flow, the aggregate particle movement, and the interaction between the cement paste and aggregate. The shear stress resulting from the paste flow is assessed using constitutive equations. The shear stress resulting from the aggregate particle movement is evaluated based on the probability and mechanical concepts of aggregate particle collision. The shear stress resulting from the interaction between the paste and aggregate is considered as the normal stress that the moving aggregate particles apply onto the cement paste. The shear rate of the mortar is obtained from the rheological definition of viscosity. Using this model, the effects of mortar mixture properties (such as aggregate size, volume, gradation, and friction as well as paste viscosity and yield stress) on mortar rheology are studied.

Fluid Dynamics and Behavior of Nonlinear Viscous Fluid Dampers

Abstract: Fluid dynamics in viscous fluid dampers with annular orifices was analyzed by solving the Navier–Stokes equations. The shear-thinning effect and viscoelastic behavior of silicone oil, which is often used in a viscous fluid damper, were both considered. When the solutions were compared to experimental data, it was found that both the nonlinear viscous and the restoring-force behaviors of viscous dampers can be captured. To verify the effects of fluid inertia, finite-element analysis of the fluid dynamics in the damper tested was also performed, assuming the damper was filled with a Newtonian fluid. It was found that the inertial force is not important in an annular-orificed damper moving at 10 Hz . The effect of fluid compression in a fluid damper was also discussed. The proposed equations were used to calculate the restoring forces in the annular-orificed damper. It was found that the results give a close restoring force-displacement relationship as the one given by FEMA 273.

Modeling of a clamped–clamped beam vibrating in a fluid for viscosity and density sensing regarding compressibility

Abstract: A clamped–clamped beam vibrating in a compressible fluid for the measurement of the fluid’s density and viscosity is modeled using the Bernoulli–Euler equation for the beam and the linearized Navier–Stokes equations for the fluid. The adiabatic compressibility coefficient was used to characterize the pressure–density coupling. Based on the method of moments, the flow around the beam and the associated resistance of the fluid on the beam were computed using a 2D-approximation. Hydrodynamic resistance coefficients are determined and compared to the known resistance coefficients for a cylinder vibrating in an incompressible fluid. The influence of the fluid’s compressibility on the resistance on the beam is examined and a critical value of the vibration frequency is determined, over which the beam experiences excessive damping due to the excitation of pressure waves.

On some generalizations of the second grade fluid model

Abstract: In this article, we provide a brief review of some generalizations of the second grade fluid model. We discuss certain similarities between these fluids and fluids of higher grades, while also describing certain limitations of these models. The new models that we put forth are based upon some interesting experimental results which suggest that not only can normal stress coefficients depend upon the shear rate, but that this dependency is in fact not the same rate as that of shear viscosity variation with shear rate. We then discuss some steady flows of these generalized second grade fluid models.

Transient response of fluid pressure in a poroelastic material under uniaxial cyclic loading

Abstract: Poroelasticity is a theory that quantifies the time-dependent mechanical behavior of a fluid-saturated porous medium induced by the interaction between matrix deformation and interstitial fluid flow. Based on this theory, we present an analytical solution of interstitial fluid pressure in poroelastic materials under uniaxial cyclic loading. The solution contains transient and steady-state responses. Both responses depend on two dimensionless parameters: the dimensionless frequency Ω that stands for the ratio of the characteristic time of the fluid pressure relaxation to that of applied forces, and the dimensionless stress coefficient H governing the solid–fluid coupling behavior in poroelastic materials. When the phase shift between the applied cyclic loading and the corresponding fluid pressure evolution in steady-state is pronounced, the transient response is comparable in magnitude to the steady-state one and an increase in the rate of change of fluid pressure is observed immediately after loading. The transient response of fluid pressure may have a significant effect on the mechanical behavior of poroelastic materials in various fields.

Flow of Herschel–Bulkley fluid through an inclined tube of non-uniform cross-section with multiple stenoses

Abstract: The steady flow of Herschel–Bulkley fluid through an inclined tube of non-uniform cross-section with multiple stenoses has been investigated. Assuming the stenoses to be mild, the flow equations have been linearised and the expressions for resistance to the flow and wall shear stress have been derived. The effects of various parameters on these flow variables have been studied. It is found that the flow resistance increases with the heights of the stenoses, yield stress, power law index, but decreases with inclination. Further, the shear stress increases with plug core region radius.

Using Computational Fluid Dynamics To Study the Dynamic Behavior of the Continuous Mixing of Herschel-Bulkley Fluids

Abstract: A continuous-flow mixer was designed and built to study the mixing of xanthan gum solution, a pseudoplastic fluid possessing yield stress. The extent of flow nonideality was quantified using a dynamic model that incorporated two parameters: channeling and fully mixed volume in the vessel. Dynamic experiments were made using the frequency-modulated random binary input of a brine solution to determine the magnitude of nonideal flow parameters. The same experiments were simulated using a computational fluid dynamics (CFD) package (Fluent 6.2). CFD flow fields were used to obtain the system dynamic response to a tracer injection applied at conditions identical to the experimental ones. The extents of channeling and effective mixed volume were determined using the CFD model and then compared with the parameters obtained experimentally. Validated CFD flow fields enabled us to effectively monitor the effect of various operating conditions on flow nonideality, to relate flow pattern and cavern dimension to flow n...

Two-Fluid Herschel-Bulkley Model for Blood Flow in Catheterized Arteries

Abstract: The steady flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the core region of suspension of all the erythrocytes as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is observed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases when all the other parameters held constant. It is noticed that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly much smaller for the present two-fluid model than those of the single-fluid model.

Towards a continuous microfluidic rheometer

Abstract: In a previous paper we presented a way to measure the rheological properties of complex fluids on a microfluidic chip (Guillot et al., Langmuir 22:6438, 2006). The principle of our method is to use parallel flows between two immiscible fluids as a pressure sensor. In fact, in a such flow, both fluids flow side by side and the size occupied by each fluid stream depends only on both flow rates and on both viscosities. We use this property to measure the viscosity of one fluid knowing the viscosity of the other one, both flow rates and the relative size of both streams in a cross-section. We showed that using a less viscous fluid as a reference fluid allows to define a mean shear rate with a low standard deviation in the other fluid. This method allows us to measure the flow curve of a fluid with less than 250 μL of fluid. In this paper we implement this principle in a fully automated set up which controls the flow rate, analyzes the picture and calculates the mean shear rate and the viscosity of the studied fluid. We present results obtained for Newtonian fluids and complex fluids using this set up and we compare our data with cone and plate rheometer measurements. By adding a mixing stage in the fluidic network we show how this set up can be used to characterize in a continuous way the evolution of the rheological properties as a function of the formulation composition. We illustrate this by measuring the rheological curve of four formulations of polyethylene oxide solution with only 1.3 mL of concentrated polyethylene oxide solution. This method could be very useful in screening processes where the viscosity range and the behavior of the fluid to an applied stress must be evaluated.

Non-Newtonian Fluid Behaviour

Abstract: This chapter focuses on the flow characteristics of single-phase liquids, solutions, and pseudo-homogeneous mixtures such as slurries, emulsions, and gas–liquid dispersions, which are considered as a continuum when 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 is nonlinear 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, etc., and sometimes even on the kinematic history of the fluid element under consideration. The most common type of time-independent non-Newtonian fluid behavior observed is pseudoplasticity or shear-thinning which is characterized by an apparent viscosity that decreases with increasing shear rate. Many mathematical expressions of varying complexity and form have been proposed in the literature to model shear-thinning characteristics and some of them are straightforward attempts at curve fitting, giving empirical relationships for the shear stress or apparent viscosity while others are theoretically based on statistical mechanics, as an extension of the application of the kinetic theory to the liquid state or the theory of rate processes, etc. Viscoplastic fluid behavior is characterized by the existence of a yield stress ( τ 0 ) which has to be exceeded before the fluid deforms or flows and such a material deforms elastically or flows en masse like a rigid body when the externally applied stress is smaller than the yield stress. Three commonly used models used for viscoplastic fluids include Bingham plastic model, Herschel-Bulkley fluid model, and Casson fluid model.

A Unifying Perspective on the Quasi-steady Analysis of Magnetorheological Dampers

Abstract: A magnetorheological (MR) fluid, modeled as a Bingham plastic (BP) material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Based on viscom...

Particle segregation by Stokes number for small neutrally buoyant spheres in a fluid

Abstract: It is a commonly observed phenomenon that spherical particles with inertia in an incompressible fluid do not behave as ideal tracers. Due to the inertia of the particle, the planar dynamics are described in a four-dimensional phase space and thus can differ considerably from the ideal tracer dynamics. Using finite-time Lyapunov exponents, we compute the sensitivity of the final position of a particle with respect to its initial velocity, relative to the fluid, and thus partition the relative velocity subspace at each point in configuration space. The computations are done at every point in the relative velocity subspace, thus giving a sensitivity field. The Stokes number, being a measure of the independence of the particle from the underlying fluid flow, acts as a parameter in determining the variation in these partitions. We demonstrate how this partition framework can be used to segregate particles by Stokes number in a fluid. The fluid model used for demonstration is a two-dimensional cellular flow.

Non-Newtonian Fluid Flow on a Flat Plate Part 1: Boundary Layer

Abstract: A modified power-law viscosity for non-Newtonian fluids based on actual measurements is proposed. This realistic model allows removal of the singularities at the leading edge of a flat-plate boundary layer for either shear-thinning or shear-thickening fluids. Under this condition, the boundary-layer equations can be solved numerically by simple finite difference methods that march downstream from the leading edge, as is usually done for Newtonian fluids. Numerical results are presented for the case of a shear-thinning fluid; applying the model to a shear-thickening fluid is straightforward. The effects of this new variable viscosity are explicitly demonstrated by comparing plots of isolines of viscosity and shear rate, the velocity distribution, and the wall shear stress for non-Newtonian and Newtonian fluids.