Showing papers on "Herschel–Bulkley fluid published in 2009"

Macroscopic vs. local rheology of yield stress fluids

Abstract: From MRI velocimetry we measure the local flow characteristics of a Carbopol gel in a Couette geometry under different inner cylinder rotation velocities. Associated with torque data under the same flow conditions we deduce the local, steady-state, simple shear, constitutive equation of the material within a relatively wide range of sheFrom MRI velocimetry we measure the local flow characteristics of a Carbopol gel in a Couette geometry under different inner cylinder rotation velocities. Associated with torque data under the same flow conditions we deduce the local, steady-state, simple shear, constitutive equation of the material within a relatively wide range of shear rates [10−2; 100 s−1]. Then we show that in this range of shear rates this “local” behaviour is in excellent agreement with the “macroscopic” behaviour deduced from conventional rheometry with cone and plate and Couette geometries. We can conclude that this material effectively behaves as a simple yield stress fluid with a constitutive equation well represented by a Herschel–Bulkley model. This behaviour, likely due to the soft-jammed structure of the fluid, contrasts with that of aggregated systems which exhibit thixotropy and shear-banding at low shear rates.ar rates [10−2; 100 s−1]. Then we show that in this range of shear rates this “local” behaviour is in excellent agreement with the “macroscopic” behaviour deduced from conventional rheometry with cone and plate and Couette geometries. We can conclude that this material effectively behaves as a simple yield stress fluid with a constitutive equation well represented by a Herschel–Bulkley model. This behaviour, likely due to the soft-jammed structure of the fluid, contrasts with that of aggregated systems which exhibit thixotropy and shear-banding at low shear rates.

A new elastoviscoplastic model based on the Herschel–Bulkley viscoplastic model

Abstract: The aim of this paper is to introduce a new three-dimensional elastoviscoplastic model that combines both the Oldroyd viscoelastic model and the Herschel–Bulkley viscoplastic model with a power-law index n > 0 . The present model is derived to satisfy the second law of thermodynamics. Various fluids of practical interest, such as liquid foams, droplet emulsions or blood, present such elastoviscoplastic behavior: at low stress, the material behaves as a viscoelastic solid, whereas at stresses above a yield stress, the material behaves as a fluid. When n = 1 , a recently introduced elastoviscoplastic model proposed by the author is obtained. When 0 n 1 , then the plasticity criteria becomes smooth, the elongational viscosity is always well defined and the shear viscosity shows a shear thinning behavior. This is a major improvement to the previous elastoviscoplastic model. Finally, when n > 1 , the material exhibits the unusual shear thickening behavior.

Origin of apparent viscosity in yield stress fluids below yielding

Abstract: For more than 20 years it has been debated if yield stress fluids are solid below the yield stress or actually flow; whether true yield stress fluids exist or not. Advocates of the true yield stress picture have demonstrated that the effective viscosity increases very rapidly as the stress is decreased towards the yield stress. Opponents have shown that this viscosity increase levels off, and that the material behaves as a Newtonian fluid of very high viscosity below the yield stress. In this paper, we demonstrate experimentally (on four different materials, using three different rheometers, five different geometries, and two different measurement methods) that the low-stress Newtonian viscosity is an artifact that arises in non–steady-state experiments. For measurements as long as 104 seconds we find that the value of the "Newtonian viscosity" increases indefinitely. This proves that the yield stress exists and marks a sharp transition between flowing states and states where the steady-state viscosity is infinite —a solid!

Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate

Abstract: The velocity field and the adequate shear stress corresponding to the unsteady flow of a generalized Maxwell fluid are determined using Fourier sine and Laplace transforms. They are presented as a sum of the Newtonian solutions and the corresponding non-Newtonian contributions. The similar solutions for Maxwell and Newtonian fluids, performing the same motion, are obtained as limiting cases of our general results. Graphical illustrations show that the velocity profiles corresponding to a generalized Maxwell fluid are going to that for an ordinary Maxwell fluid if @a->1.

Peristaltic flow of a Maxwell fluid in a channel with compliant walls

Abstract: This paper describes the peristaltic motion of a non-Newtonian fluid in a channel having compliant boundaries. Constitutive equations for a Maxwell fluid have been used. Perturbation method has been used for the analytic solution. The influence of pertinent parameters is analyzed. Comparison of the present analysis of Maxwell fluid is made with the existing results of viscous fluid.

The dam-break problem for Herschel-Bulkley viscoplastic fluids down steep flumes

Abstract: In this paper we investigate the dam-break problem for viscoplastic (Herschel–Bulkley) fluids down a sloping flume: a fixed volume of fluid initially contained in a reservoir is released onto a slope and flows driven by gravitational forces until these forces are unable to overcome the fluid’s yield stress. Like in many earlier investigations, we use lubrication theory and matched asymptotic expansions to derive the evolution equation of the flow depth, but with a different scaling for the flow variables, which makes it possible to study the flow behavior on steep slopes. The evolution equation takes on the form of a nonlinear diffusion–convection equation. To leading order, this equation simplifies into a convection equation and reflects the balance between gravitational forces and viscous forces. After presenting analytical and numerical results, we compare theory with experimental data obtained with a long flume. We explore a fairly wide range of flume inclinations from 6° to 24°, while the initial Bingham number lies in the 0.07–0.26 range. Good agreement is found at the highest slopes, where both the front position and flow-depth profiles are properly described by theory. In contrast, at the lowest slopes, theoretical predictions substantially deviate from experimental data. Discrepancies may arise from the formation of unsheared zones or lateral levees that cause slight flow acceleration.

Weakly nonlinear viscoplastic convection

Abstract: The development of thermal convection is studied for a viscoplastic fluid. If the viscosity is finite at zero shear rate, the critical Rayleigh number for linear instability takes the value given by a Newtonian fluid with that viscosity. The subsequent weakly nonlinear behaviour depends on the degree of shear thinning: with moderate shear thinning, convective overturning for a given temperature difference is amplified relative to the Newtonian case. If the reduction in viscosity is sufficiently sharp the transition becomes subcritical (the relevant situation for many regularized constitutive laws). For an infinite viscosity at zero shear rate, or a yield-stress, the critical Rayleigh number for linear instability is infinite. Nonlinear convective overturning, however, is still possible; we trace out how the finite-amplitude solution branches develop from their Newtonian counterparts as the yield stress is increased from zero for the Bingham fluid. Laboratory experiments with a layer of Carbopol fluid heated from below confirm that yield strength inhibits convection but a sufficiently strong perturbation can initiate overturning.

Experimental study of the very slow flow of a yield stress fluid around a circular cylinder

Abstract: The slow flow of a yield stress fluid around a circular cylinder was studied by Particle Image Velocimetry (PIV) technique and drag measurement. The fluid used was a Carbopol® 940 gel with shear-thinning elastoviscoplastic behaviour. The case of significant yield stress effects was examined. Special attention was paid to preparing the fluid, controlling slip and the initial stress state in the fluid. In addition to the overall field extending beyond the sheared zone, the field very near to the cylinder was examined in greater detail. Asymmetry was observed between the upstream flow and downstream flow. Examination of the very near field revealed the existence of a recirculation zone upstream of the cylinder. These effects were not predicted numerically with the Herschel–Bulkley viscoplastic model usually used. The sheared zone obtained experimentally is more extensive than that obtained numerically with the Herschel–Bulkley viscoplastic model. A static rigid zone was observed at the downstream stagnation point. Detailed analysis of the results showed that normal stresses could be the cause of this upstream recirculation.

Elongational and shear rheology of carbon nanotube suspensions

Abstract: Rheological behavior of concentrated suspensions of chemical vapor deposition carbon nanotubes in uniaxial elongation and simple shear is studied experimentally and theoretically. Nanotubes are suspended in viscous host liquids—castor oil or its blends with n-decane. The elongational measurements are performed by analyzing self-thinning (due to surface tension effect) liquid threads of nanotube suspensions. A quasi-one-dimensional model is used to describe the self-thinning process, whereas corrections accounting for thread nonuniformity and necking are introduced a posteriori. The effects of nanotube concentration and aspect ratio, viscosity of the suspending liquid, and initial diameter of the self-thinning thread in uniaxial elongation are elucidated. The results for uniaxial elongation are compared with those for simple shear. The correspondence in the results of the shear and elongational measurements is addressed and interpreted. The results conform to the Herschel–Bulkley rheological constitutive equation (i.e., power law fluids with yield stress). However, the yield stress in elongation is about 40% higher than in simple shear flow, which suggests that the original Herschel–Bulkley model need modification with the yield stress being a function of the second invariant of the deviatoric stress tensor. The present effort is the first to study capillary self-thinning of Herschel–Bulkley liquids, which are exemplified here by suspensions of carbon nanotubes.

Particle-based viscoplastic fluid/solid simulation

Abstract: Simulations of viscoplastic materials are traditionally governed by continuum mechanics. The viscous behavior is typically modeled as an internal force, defined by diverse quantities. This work introduces a fluid model to simulate the viscoplastic effect of solid materials, such as plastic, wax, clay and polymer. Our method consists in modeling a solid object through a non-Newtonian fluid with high viscosity. This fluid simulation uses the Smoothed Particle Hydrodynamics method and the viscosity is formulated by using the General Newtonian Fluid model. This model concentrates the viscoplasticity in a single parameter. Our results show clear effects of creep, melting, hardening and flowing.

Observation of laminar–turbulent transition of a yield stress fluid in Hagen–Poiseuille flow

Abstract: We investigate experimentally the transition to turbulence of a yield stress shear-thinning fluid in Hagen–Poiseuille flow. By combining direct high-speed imaging of the flow structures with Laser Doppler Velocimetry (LDV), we provide a systematic description of the different flow regimes from laminar to fully turbulent. Each flow regime is characterized by measurements of the radial velocity, velocity fluctuations and turbulence intensity profiles. In addition we estimate the autocorrelation, the probability distribution and the structure functions in an attempt to further characterize transition. For all cases tested, our results indicate that transition occurs only when the Reynolds stresses of the flow equal or exceed the yield stress of the fluid, i.e. the plug is broken before transition commences. Once in transition and when turbulent, the behaviour of the yield stress fluid is somewhat similar to a (simpler) shear-thinning fluid. Finally, we have observed the shape of slugs during transition and found their leading edges to be highly elongated and located off the central axis of the pipe, for the non-Newtonian fluids examined.

Slumps of viscoplastic fluids on slopes

Abstract: Free-surface slumps of viscoplastic fluid, modelled using a Herschel–Bulkley constitutive law, are studied as they flow from rest, behind a rapidly removed dam, along an inclined two-dimensional channel. These dam-break flows are eventually arrested and attain a final, static state in which the streamwise pressure gradient and the along-slope component of gravitational acceleration are balanced by the yield stress. The shapes of the arrested free surfaces are compactly represented as Lambert- W functions and are characterised by two dimensionless parameters that measure the magnitude of the slope relative to the initial aspect ratio of the release and the magnitude of the yield stress relative to the weight of fluid layer. These states are only attained asymptotically for long times after the release and perturbations to the final profiles are shown to decay as 1 / t n , where n is the power index in the Herschel–Bulkley model. This analysis requires careful formulation, because, formally, within a diminishing boundary layer close to the front of the motion, the size of the perturbation exceeds the arrested state. Thus, while straightforward linearisation of the governing equation is possible within the bulk of the flow outside of the boundary layer, this must be matched asymptotically to the solutions within the boundary layer close to the front. The presence of this region does not obviate computation of the rate of approach to the arrested state, but is required to permit complete calculation of the evolving shape of the free surface.

Effects of Radiation and Variable Fluid Viscosity on Flow and Heat Transfer along a Symmetric Wedge

Abstract: Radiation effects on boundary layer flow and heat transfer of a fluid with variable viscosity along a symmetric wedge is presented here. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. A third order and a second order coupled ordinary differential equation system corresponding to the momentum and the energy equations are obtained. These equations are then solved numerically. With the increase of temperature-dependent fluid viscosity parameter (i.e. with decreasing viscosity), the fluid velocity increases up to the cross-over point ( 0 η η = ) ( 90 . 0 0 ≈ η is the nearest numerical value of the cross-over point) and after the crossing over point the fluid velocity is found to decrease but the temperature increases at a particular point. The significant finding of this study is that, due to variable fluid viscosity, flow separation is controlled. The temperature decreases with increasing value of radiation parameter and Prandtl number.

Stability of plane Couette–Poiseuille flow of shear-thinning fluid

Abstract: A linear stability analysis of the combined plane Couette and Poiseuille flow of shear-thinning fluid is investigated. The rheological behavior of the fluid is described using the Carreau model. The linearized stability equations and their boundary conditions result in an eigenvalue problem that is solved numerically using a Chebyshev collocation method. A parametric study is performed in order to assess the roles of viscosity stratification and the Couette component. First of all, it is shown that for shear-thinning fluid, the critical Reynolds number for a two-dimensional perturbation is less than for a three dimensional. Therefore, it is sufficient to deal only with a modified Orr–Sommerfeld equation for the normal velocity component. The influence of the velocity of the moving wall on the critical conditions is qualitatively similar to that for a Newtonian fluid. Concerning the effect of the shear thinning, the computational results indicate that this behavior leads to a decrease in the phase velocity of the traveling waves and an increase in stability, when an appropriate viscosity is used in the definition of the Reynolds number. Using a long-wave version of the Orr–Sommerfeld equation, the cutoff velocity is derived. The mechanisms responsible for the changes in the flow stability are discussed in terms of the location of the critical layers, Reynolds stress distribution, and the exchange of energy between the base flow and the disturbance.

Some accelerated flows for a generalized Oldroyd-B fluid

Abstract: In this paper, we construct the exact solutions for the accelerated flows of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of a viscoelastic fluid. The velocity field and the adequate tangential stress that is induced by the flow due to constantly accelerating plate and flow due to variable accelerating plate are determined by means of discrete Laplace transform. In the special cases when α = β = 1 , as it was to be expected, our solutions tend to the similar solutions for an Oldroyd-B fluid. Moreover, the corresponding solutions for a Maxwell, second grade and Newtonian fluids appear as the limiting cases of the presented results.

Magnetohydrodynamic flow of a Sisko fluid in annular pipe : A numerical study

Abstract: This paper presents a numerical study for the unsteady flow of a magnetohydrodynamic (MHD) Sisko fluid in annular pipe. The fluid is assumed to be electrically conducting in the presence of a uniform magnetic field. Based on the constitutive relationship of a Sisko fluid, the non-linear equation governing the flow is first modelled and then numerically solved. The effects of the various parameters especially the power index n, the material parameter of the non-Newtonian fluid b and the magnetic parameter B on the flow characteristics are explored numerically and presented through several graphs. Moreover, the shear-thinning and shear-thickening characteristics of the non-Newtonian Sisko fluid are investigated and a comparison is also made with the Newtonian fluid. Copyright © 2009 John Wiley & Sons, Ltd.

Shear rejuvenation, aging and shear banding in yield stress fluids

Abstract: The purpose of this work is to simulate shear rejuvenation and aging effects in shear thinning yield stress fluids in a typical rotational rheometer and to provide a common framework to describe the behavior of yield stress materials in general. This is particularly important in the determination of material constants under both steady and unsteady conditions. The breakdown and buildup of structure are studied using a theory based on the Herschel–Bulkley flow model that it is consistent with experimental data. The theory is implemented using a novel computational method. Interestingly, the simulations reveal the existence of time-dependent shear banding that occurs within the gap when the macroscopically imposed shear rate is below a certain critical value. Shear banding is analyzed in detail and results showing the effects of major parameters on the phenomenon are presented.

An Investigation of Squeeze Flow as a Viable Technique for Determining the Yield Stress

Abstract: A systematic study of squeeze flow (SF) was performed on different concentrations of Carbopol with varying yield stresses. A sample of constant volume was placed between two parallel plates and a series of constant force steps applied, following the plate separation as a function of time. Precise rheological measurements of the model yield stress fluids were performed in addition to the well-controlled SF tests. These rheological measurements were used in conjunction with the SF equations to determine the time-dependent plate separation, allowing a direct comparison of theory and experiment throughout the entire test. The limiting height achieved during constant force SF reveals information about the yield stress of the fluid as predicted by the theory. It appears that by carefully controlling the experimental conditions of the squeeze test one can obtain yield stress values that agree with the rheological measurements within 10%. Additionally, the validity of the lubricational theory was tested; not only for the determination of the yield stress but throughout the flow as well.

Axial couette flow of an oldroyd-b fluid due to a time-dependent shear stress

Abstract: The velocity field and the shear stress corresponding to the motion of an OldroydB fluid due to an infinite circular cylinder subject to a longitudinal time-dependent shear stress are established by means of Hankel transforms. The exact solutions, presented under series form, can be easy specialized to give the similar solutions for Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material parameters on the behavior of the fluid are shown by graphical illustrations. AMS 2000 Subject Classification: 76A05.

The viscoplastic Stokes layer

Abstract: A theoretical and experimental study is presented of the viscoplastic version of the Stokes problem, in which a oscillating wall sets an overlying fluid layer into one-dimensional motion. For the theory, the fluid is taken to be described by the Herschel–Bulkley constitutive law, and the flow problem is analogous to an unusual type of Stefan problem. In the theory, when the driving oscillations are relatively weak, the overlying viscoplastic layer moves rigidly with the plate. For sufficiently strong oscillations, the fluid yields and numerical solutions illustrate how localized plug regions coexist with sheared regions and migrate vertically through the fluid layer. For the experiments, a layer of kaolin slurry in a rectangular tank is driven sinusoidally back and forth. The experiments confirm the threshold for shearing flow, equivalent to a balance between inertia and yield-stress. However, although kaolin is well described by a Herschel–Bulkley rheology, the layer dynamics notably differs between theory and experiments, revealing rheological behaviour not captured by the steady flow rule.

Exact solutions for a viscoelastic fluid with the generalized Oldroyd-B model

Abstract: In this paper, the generalized Oldroyd-B model with the fractional calculus approach is used. Exact analytic solutions for the velocity and the stress fields in term of the Fox H-function are obtained by using the discrete Laplace transform for two types of flows of a viscoelastic fluid, namely, (i) flow due to impulsive motion in the presence of a constant pressure gradient and (ii) flow induced by an impulsive pressure gradient. The influence of various parameters of interest on the velocity and shear stress has been shown and discussed through several graphs. Moreover, a comparison between Oldroyd-B and generalized Oldroyd-B fluids is also made.

Determination of rheological properties of whole blood with a scanning capillary-tube rheometer using constitutive models

Abstract: We examine the applicability of three different non-Newtonian constitutive models (power-law, Casson, and Herschel-Bulkley models) to the determination of blood viscosity and yield stress with a scanning capillary-tube rheometer. For a Newtonian fluid (distilled water), all three models produced excellent viscosity results, and the measured values of the yield stress with each model were zero. For unadulterated human blood, the Casson and Herschel-Bulkley models produced much stronger shear-thinning viscosity results than the power-law model. The yield stress values for the human blood obtained with the Casson and Herschel-Bulkley models were 13.8 and 17.5 mPa, respectively. The two models showed a small discrepancy in the yield stress values, but with the current data analysis method for the scanning capillary-tube rheometer, the Casson model seemed to be more suitable in determining the yield stress of blood than the Herschel-Bulkley model.

Exact solutions for generalized Burgers’ fluid in an annular pipe

Abstract: This paper deals with some unsteady unidirectional transient flows of generalized Burgers’ fluid in an annular pipe. Exact solutions of some unsteady flows of generalized Burgers’ fluid in an annular pipe are obtained by using Hankel transform and Laplace transform. The following two problems have been studied: (1) Poiseuille flow due to a constant pressure gradient; (2) axial Couette flow in a annulus. The well known solutions for Navier-Stokes fluid, as well as those corresponding to a Maxwell fluid, a second grade fluid and an Oldroyd-B fluid appear as limiting cases of our solutions.

Rheological analysis of water clay compositions in order to investigate mudflows developing in canals

Abstract: This paper describes the physical and rheological property mixtures of water and kaolinitic clay that form the interstitial fluid found in muds from inundations or torrential lava. Several compositions with varying volume concentrations (Cv) were tested in a high-precision R/S rheometer (shear rate x shear stress). The rheometric parameters such as critical stress, apparent viscosity and outflow curves were established. A detailed analysis of the possible thixotropic fluid (shear thinning) and preparation of the mixtures were carried out. Such mud-type mixtures were well adjusted to the Herschel-Bulkley rheologic model at 03 parameters namely τ =τ=τc + Kγn , where τ is the shear stress; τc the yield stress (or initial rigidity); k is the consistency term; n the flow index; and γ= du dy the deformation rate or shear rates. Considering that this is a thorough research that seeks to infer laws of friction on a canal taking into account the non-Newtonian rheology of the flowing material, it is observed that the tested mixturesspecifically keep away from the Newton model, though less for the Bingham model, and adjusted well to the Herschel-Bulkley model, especially for lower deformation rates. Finally, from a refined literature review on the subject, it was appropriate to describe in detail a wider range of deformation rates and overall behavior laws of the various parameters of the Herschel Bulkley as a function of the concentration by volume (Cv).