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This paper presents a lattice Boltzmann framework for the transient simulation of blood flow using biologically inspired geometries and pressure boundary conditions. The Kuang-Luo rheological model is used to represent blood as a homogeneous continuum. This model includes the two primary non-Newtonian characteristics of blood, namely viscoplasticity and pseudoplasticity. This paper makes two contributions. First, the numerical challenges associated with zero strain rates and infinite viscosity, as a consequence of the yield stress in the Kuang-Luo model, were addressed by regularising the constitutive equation so that the viscosity tends towards a finite value at low strain rates. A two-relaxation-time operator, which exhibits improved performance over the single-relaxation-time operator and lower computational overhead than the multiple-relaxation-time operator, is employed in the collision process. The recursive relationship between the local strain rate and relaxation rate was addressed by use of an implicit solver for these two quantities. The implemented model was benchmarked against analytic solutions for Poiseuille flow between parallel plates in two dimensions and in a cylindrical tube in three dimensions. More importantly, the transient performance of the implemented model was demonstrated by matching the predicted start-up flow of the Poiseuille flow of a Bingham fluid with the corresponding analytical solution. Second, the numerical developments were applied in the simulation of transient blood flow in complex configurations. The development and implementation of physically inspired pressure profiles highlighted the shortcomings of using a sinusoidal pressure profile in the prediction of velocity and stress distributions. Finally, the simulation of blood flow in a section of a carotid artery indicated a number of flow characteristics that will be of interest to future investigations of clinical problems.

Suspension culture is an important method used in the industrial preparation of pluripotent stem cells (PSCs), for regenerative therapy and drug screening. Generally, a suspension culture requires agitation to keep PSC aggregates suspended and to promote mass transfer, but agitation also causes cell damage. In this study, we investigated the use of a Bingham plastic fluid, supplemented with a polysaccharide‐based polymer, to preserve PSCs from cell damage in suspension culture. Rheometric analysis showed that the culture medium gained yield stress and became a Bingham plastic fluid, after supplementation with the polymer FP003. A growth/death analysis revealed that 2 days of aggregate formation and 2 days of suspension in the Bingham plastic medium improved cell growth and prevented cell death. After the initial aggregation step, whereas strong agitation (120 rpm) of a conventional culture medium resulted in massive cell death, in the Bingham plastic fluid we obtained the same growth as the normal culture with optimal agitation (90 rpm). This indicates that Bingham plastic fluid protected cells from shear stress in suspension culture and could be used to enhance their robustness when developing a large‐scale.

The equations describing the steady flow of Cosserat–Bingham fluids are considered, and existence of weak solution is proved for the three-dimensional boundary-value problem with the use of the Lipschitz truncation argument. In contrast to the classical Bingham fluid, the micropolar Bingham fluid supports local micro-rotations and two types of plug zones. Our approach is based on an approximation of the constitutive relation by a generalized Newtonian constitutive relation and a subsequent limiting process. Copyright © 2016 John Wiley & Sons, Ltd.

In Bingham plastic fluids, a central pre-yield or plug region exists in the middle of the concentric annular flow. In this region, the local shear stress is less than the dynamic yield stress, so the plug behaves like a rigid solid. This is the main feature that distinguishes the flow of a Bingham plastic fluid from that of a power law fluid. In this work, a simple-to-use correlation is developed to predict the boundaries of the plug of Bingham plastic fluids for laminar flow through annulus as a function of dimensionless yield stress and aspect ratio parameters for given values of the rheological constants, pressure gradient and the dimensions of the annulus. The results are found to be in excellent agreement with reported data in the literature with an average absolute deviation of less than 1.7%. The predictive tool is simple and straightforward and can be readily implemented in a standard spreadsheet program. The prime application of the method is as a quick-and-easy evaluation tool in engineering studies where plug boundaries of Bingham plastic fluids for laminar flow through annulus are being considered. The method may also serve as a benchmark in numerical and rigorous simulation studies.

The ultrasound velocity profiling technique (UVP) was used to study flow structures after a two-dimensional (2-D) 1: 11 sudden expansion of pulp fiber suspensions at varied average velocities (1-2.2 m/s) and concentrations (1.8 and 2.8 wt %). One advantage of studying jet geometry is the potential to investigate the main flow structures away from walls. Measurements done at the same percent of the total jet length, at constant concentration, show that an increase in flow rate gave a faster decrease in centerline velocity and a quicker increase in jet width. Increasing the concentration, at the same jet length, the centerline velocity was more stable and the width of the mixing layer increased more rapidly. Comparisons with CFD simulations in the laminar regime, using the Bingham plastic model, show that the main flow structures were captured if the yield stress used in the simulations is approximately 20% of the measured using a rheometer.

SUMMARY We simulated the flow of a yield stress fluid around a gas bubble using an augmented Lagrange approach. The piecewise linear equal-order finite elements for both the velocity and the pressure approximations proposed and analyzed by Latche and Vola in 2004 were applied. A mesh adaptive strategy based on this element-pair choice was also proposed to render the yield surfaces of desired resolution. The corresponding numerical scheme was formulated for general Herschel–Bulkley fluids. Numerical results on Bingham fluid flows around a slowly rising spherical gas bubble were provided to validate the proposed algorithm. Copyright © 2011 John Wiley & Sons, Ltd.

Centrifugal pumps are widely used for transporting suspensions, but their head performance is derated when non-Newtonian fluids and/or coarse solids are present. Some head deration methods are available for high viscosity Newtonian fluids, Bingham plastic fluids and for coarse solids in water. This paper presents a modification of the Hydraulic Institute head deration method that is suitable for any homogeneous non-Newtonian rheology. A modification of the Walker and Goulas method is also considered. Possible anomalous behaviour of kaolin slurries in centrifugal pumps is discussed.

It is often desirable to operate industrial pipelines transporting non-Newtonian materials near the transition from laminar to turbulent flow. For the commonly used Bingham plastic model, the Hedstrom technique overestimates turbulent flow friction losses because it does not take account of viscous-layer thickening. In the present paper, the Wilson-Thomas model is applied to predict the transition point for Bingham plastics. Laminar and turbulent friction losses are calculated to show that conditions at transition depend only on the Hedstrom number. The results are approximated by simplified fit functions. Comparison with existing empirical correlations and experimental data from various sources shows satisfactory agreement. Il est souvent preferable d'utiliser les pipelines industriels transportant des materiaux non newtoniens pres de la transition entre l'ecoulement laminaire et l'ecoulement turbulent. Pour le modele classique des fluides de Bingham, la technique d'Hedstrom surestime les pertes de friction de l'ecoulement turbulent parce qu'elle ne prend pas en compte l'epaississement de la couche visqueuse. Dans le present article, on applique le modele de Wilson-Thomas pour predire le point de transition pour des fluides de Bingham. Les pertes de friction laminaires et turbulentes sont calculees et montrent que les conditions lors de la transition dependent uniquement du nombre d'Hedstrom. Les resultats sont exprimes sous forme approximative par des fonctions de calage simplifiees. La comparaison avec des correlations empiriques et des donnees experimentales provenant de diverses sources montre un accord satisfaisant.

Agitated-pulp chests function as low-pass filters to reduce high-frequency variability in pulp properties (mass concentration, freeness, and so on) ahead of many pulping and papermaking operations. Tests on both industrial and scale-model chests have shown that their dynamic performance is far from ideal, with a significant extent of nonideal flow (short circuiting, recirculation and stagnation) possible. The flow field of a 1:11 scale-model pulp chest was modeled using a commercial computational fluid dynamics (CFD) software package (Fluent) with the pulp suspension treated as a modified Bingham plastic. A multiple reference frame approach was used with coupling between reference frames made using a velocity transformation. The flow profiles predicted by the simulation agreed qualitatively with those observed in the experiments. The power input predicted by the simulations was slightly higher (about 12%) than that measured. The velocity field obtained from the CFD model was used to obtain the system's dynamic response to a frequency-modulated random binary input signal. These data were then used as input to a dynamic model that treated flow within the chest as following two streams: one bypassing the mixing zone and one entering it. For both streams, the fraction of suspension passing through each zone was determined and a time constant and delay time computed. These parameters were then compared to those measured experimentally under identical operating conditions. The CFD simulation provides detailed information on the velocity profile within the chest and allows the location(s) of poor mixing regions to be identified.

A polymer sheeting die design methodology is presented, which integrates finite element flow simulations, numerical optimization, and design sensitivity analyses to compute die cavity geometries capable of giving a near-uniform exit velocity. This work extends earlier die design methods to include generalized Newtonian fluid (GNF) models that represent the shear-thinning behavior of polymer melt. Melt flow computations and design sensitivity analyses are provided using the generalized Hele-Shaw flow approximation with isothermal power-law, Carreau-Yasuda, Cross, Ellis, and Bingham fluid models. The nonlinear equations for die cavity pressure are solved using the Newton-Raphson iteration method and design sensitivities are derived with the adjoint variable method. The die design method is applied to an industrial coat hanger die, in which a design parameterization is defined that allows for an arbitrary gap height distribution in the manifold of the die. In addition, die performance is assessed and compared for power-law and Carreau-Yasuda fluid flow over a range of die operating conditions. Pareto optimal die designs are also considered in this study. POLYM. ENG. SCI., 45:953–965, 2005. © 2005 Society of Plastics Engineers

In this paper three-dimensional lubrication flow of grease is analysed numerically. The lubrication flow configuration is formed by two ellipsoid rollers. The load is assumed to be light enough for the lubrication mode to be purely hydrodynamic. The fluid behaviour is modelled using the Herschel–Bulkley model, and a two-dimensional modified Reynolds equation is derived. The numerical solutions are obtained by using a hybrid spectral/iterative technique and the Galerkin projection scheme. The effects of the material and geometrical parameters on pressure distribution are emphasized in the study. The investigation is conducted for a situation where the two ellipsoids are fully immersed in a grease lubricant. The effect of the geometry on the pressure distribution is determined by varying the ratio of the semi-axes and the minimum gap of the two rollers, respectively. The effect of the material parameters is examined by varying the power-law index and yield stress. It is found that the pressure distribution is strongly influenced by the shape of the rollers, the size of the minimum gap of the rollers and the rheological parameters. Copyright © 2005 John Wiley & Sons, Ltd.

The problem of predicting the evolution of liquefied ground, modelled as a viscoplastic material, is addressed by combining a minimum principle for the velocity field, which characterizes such an evolution, and a time step integration procedure. Two different numerical schemes are then presented for the finite element implementation of this minimum principle, namely, the regularization technique and the decomposition-co-ordination method by augmented Lagrangian. The second method, which proves more accurate and efficient than the first, is finally applied to simulate the incipient flow failure and subsequent spreading of a liquefied soil embankment subject to gravity. The strong influence of liquefied soil residual shear strength on reducing the maximum amplitude of the ground displacement is particularly emphasized in such an analysis. Copyright © 2005 John Wiley & Sons, Ltd.

The aim of this paper is to model numerically concrete flow inside formworks like the Lbox. For this purpose, we use a finite element method with Lagrangian integration points (FEMLIP). We are able to follow in time and space material motion with any type of material behaviour, including non-linear and time-dependent ones. We also can deal with free surfaces or material interfaces. Bingham's rheology is used for fresh concrete behaviour. In order to compare with experiments, we have considered three concretes (OC, HPC and SCC) with contrasted rheologies. Their yield stress is identified by experimental slump tests and also compared with the value given by a formulation concrete software. Experimental data are found to be quite close to numerical predictions. We have also made some experimental flow tests in a LBOX. We measured the flow speed and the flow shape in the final stage. The numerical modelling of these experiments is very encouraging and shows the capability of the FEMLIP using the Bingham's law to model concrete flow and filling properties. Copyright © 2005 John Wiley & Sons, Ltd.

The transport mechanisms of momentum, mass, species, and energy are investigated in detail for the rotary kiln process. The residence time prediction of the granular bed is well improved by considering different flow patterns in the tube. Introducing a mixed flow pattern of the basic slipping and slumping behavior has the most important effect on the improvement of the residence time prediction. The granular bed is assumed to behave as a Bingham fluid in the active layer of the bed. The transport mechanisms of momentum, species, and energy are modeled based on this assumption and using the kinetic gas theory. The model results of the temperature field are in very good agreement with the experimental data.

Experimental fluid velocity profiles can be readily obtained by using tomographic techniques. Combining measurements of a fluid velocity profile with a simultaneous pressure drop permits the evaluation of rheological properties. In order to control a process and to assure product quality, it is useful to monitor the rheological properties in-line or on-line. Two tomographic techniques, magnetic resonance imaging (MRI) and ultrasonic Doppler velocimetry (UDV), were used to obtain velocity profiles for a 65.7 °Brix corn syrup solution and a 4.3 °Brix tomato juice. The UDV technique provided velocity profiles that compared well with the MRI method. For the corn syrup, the shear viscosity of 1.37 Pa-s (UDV) and 1.51 Pa-s (MRI) agreed well with the offline measurement of 1.57 Pa-s. The tomato juice was best characterized as a Bingham plastic fluid. The yield stress ranged from 4.44 Pa to 4.70 Pa, which matched well with the off-line value of 4.50 Pa. The strengths and limitations of both techniques are presented.

Rheological behavior of a slurry consisting of 1- to 3-mm diced tomatoes suspended in tomato juice was evaluated by an in-line measurement method based upon ultrasonics. This technique permitted the measurements of yield stress, consistency index, and apparent wall slip. The suspension exhibited a yield stress at every flow rate studied, and its value was found to be 0.79 ±0.11 Pa. The shear viscosity at different shear rates was obtained in-line without assuming a specific constitutive equation. A comparison of Herschel-Bulkley, Power Law, Bingham Plastic, and Casson models showed that this suspension was best characterized with the Herschel-Bulkley model. The apparent wall slip region was successfully modeled as a Bingham fluid. This study shows the usefulness of this method for in-line characterization of particulate tomato products.

Poly(p-phenylene) (PPP) particle-based electrorheological (ER) fluids were prepared from FeCl3-doped PPP and silicone oil. The effect of the volume fraction of PPP and applied electric field strength on ER response was investigated via measured rheological properties, including flow curve, shear viscosity, and yield stress. Furthermore, the yield stresses of the PPP-based ER fluid, which exhibit the typical characteristics of a Bingham fluid, were measured. The yield stress data collapse on a universal scaling function proposed by Choi et al. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2397–2403, 2002

The performance of a tube process viscometer was evaluated for its ability to characterize the rheological properties of pizza sauce. Tube flow was described using common rheological models (Power Law, Herschel-Bulkley, Casson and Bingham plastic) and model parameters were compared to laboratory rheometer data. Derived model parameters (tube) and measured pressure drop data were both correlated with other off-line instruments, namely the Bostwick Consistometer and Brookfield viscometer. Bingham Plastic model parameters of viscosity and yield stress as generated from the tube viscometer were found to be comparable to the rheometer generated equivalents. Measured pressure drop readings using linear and Power law regression showed good predictive capability (R 2 > 0.99 & 0.93) of Brookfield and Bostwick Consistometer readings respectively. It can be concluded that tube viscometry would result in effective real time rheological characterization of tomato-based products. Limitations of the Bostwick Consistometer are highlighted. Un viscosimetre en tube est utilise pour mesurer les proprietes rheologiques de la sauce pour pizza. Le flux a travers le tube est modelise et compare aux resultats obtenus par rheometrie. Les resultats en ligne sont compares avec ceux obtenus hors ligne avec le consistometre de Bostwick et le viscosimetre de Brookfield. La viscosimetrie en tube s'avere etre une methode efficace de mesure de rheologie et de controle dans la fabrication des sauces de pizza

We study steady miscible displacements of two visco-plastic fluids in a long plane channel. If the yield stress of the displacing fluid is less than that of the displaced fluid, uniform static residual layers can be left attached to the walls of the channel as the displacement front propagates steadily. We investigate this steady finger propagation and the problem of finger width selection. The problem is fully two-dimensional, with the two fluids separated by a sharp interface. For a given fixed interface, chosen from a wide class of physically sensible interface shapes, we show that there exists a unique solution. As well as flexibility in the exact shape of the interface, the residual static layer thickness is also non-unique. Typically layer thicknesses h ∈ (h min , h max ) admit a physically sensible static layer solution, where h min and h max are easily computable functions of the dimensionless problem parameters. The dependency of h min and h max on the dimensionless problem parameters is explained and example solutions are computed for different static residual thick-nesses.

Liquids important to the process industries sometimes have a yield stress, i.e., they only start flowing if a certain level of shear stress is reached. This can limit processes which require mass transfer to or from bubbles dispersed in the liquid, because bubbles below a certain size can get stuck in the liquid. One possibility of making such bubbles rise is investigated in this work. It consists of subjecting the liquid containing the bubbles to an oscillating external pressure. The deformation outside the bubbles causes the yield stress to be overcome and bubbles to rise which would otherwise have remained stationary. This effect has been investigated both theoretically and experimentally. An analytical model for the rise of pulsating bubbles in a Bingham medium, commonly used to model fluids with a yield stress, is derived. Experimental results for an aqueous gel show that the effect discussed does exist and is in good qualitative agreement with the model.

The main goal of this article is to discuss a novel iterative method for the numerical simulation of a steady Bingham fluid flow in a cylindrical pipe. The method is of the primal-dual type and can be interpreted as an implicit scheme of backward Euler type, applied to a well chosen time dependent variant of the problem under consideration. A key ingredient of the algorithm is a kind of dynamical Tychonoff regularization of the fixed point relation verified by the dual solution. After proving the convergence of the method, we apply it to the solution of test problems and verify its anticipated good convergence properties. Copyright © 2000 John Wiley & Sons, Ltd.

Exopolymer-producing bacteria can be used to modify soil profiles for enhanced oil recovery or bioremediation. Understanding the mechanisms associated with biomass plug development and propagation is needed for successful application of this technology. These mechanisms were determined from packed-bed and micromodel experiments that simulate plugging in porous media. Leuconostoc mesenteroides was used, because production of dextran, a water-insoluble exopolymer, can be controlled by using different carbon sources. As dextran was produced, the pressure drop across the porous media increased and began to oscillate. Three pressure phases were identified under exopolymer-producing conditions: the exopolymer-induction phase, the plugging phase, and the plug-propagation phase. The exopolymer-induction phase extended from the time that exopolymer-producing conditions were induced until there was a measurable increase in pressure drop across the porous media. The plugging phase extended from the first increase in pressure drop until a maximum pressure drop was reached. Changes in pressure drop in these two phases were directly related to biomass distribution. Specifically, flow channels within the porous media filled with biomass creating a plugged region where convective flow occurred only in water channels within the biofilm. These water channels were more restrictive to flow causing the pressure drop to increase. At a maximum pressure drop across the porous media, the biomass yielded much like a Bingham plastic, and a flow channel was formed. This behavior marked the onset of the plug-propagation phase which was characterized by sequential development and breakthrough of biomass plugs. This development and breakthrough propagated the biomass plug in the direction of nutrient flow. The dominant mechanism associated with all three phases of plugging in porous media was exopolymer production; yield stress is an additional mechanism in the plug-propagation phase.

Mango pulp was tested for time-independent and time-dependent flow properties using a coaxial cylinder rheometer. Mango pulp is a pseudoplastic liquid with yield stress, and exhibits thixotropic properties. The yield stress calculated using the Casson or Bingham plastic models, had markedly higher values than those determined by stress relaxation, controlled stress experiments, or from stress-strain plots. The yield stress of mango pulp tested in this experiment was sensitive to temperature and decreased rapidly as temperature increased. The time-dependent model of Weltman was found to be most applicable (|r| ≥ 0.991, p ≤ 0.01) for mango pulp.

Landslides and their hydraulic effects are studied by numerical and experimental means. A two-dimensional model based on Navier-Stokes equations has been developed considering the sediments and water as a mixture. A Bingham law written in effective stress and an erosion-diffusion law at the water-sediment interface have been introduced into the model. Laboratory experiments consisting in the sliding of a block, a coarse gravel and a fine sand have been carried out. The results are compared with the numerical model. These experiments show the importance of sediment rheology and interstitial pressure in slide velocity and water wave generation.

A notion of a generalized solution is introduced for the one-dimensional equations of Bingham compressible flows. It makes possible to describe a joint motion of rigid and fluid zones without incorporation of free boundaries corresponding to fluid-rigid interfaces. A global unique solvability is proved. Examples are given to show the formation of fluid and rigid zones.

Electrorheological (ER) fluids are fluids that undergo changes in their rheological properties in the presence of an applied electrical field. The change in the flow properties with an applied electrical field has led to their being investigated for use as ‘smart’ lubricants. The Bingham model is currently used to describe the behaviour of these fluids. In this work, the Bingham model parameters of a commercially available ER fluid are obtained using an axial flow concentric-cylinder rheometer. Two methods are used to determine these parameters. One is the Weissenberg (—Rabinowitsch) method applied to thin annular slits, to obtain corrected stress—strain rate information. The other method involves directly fitting the velocity—pressure curve data to the axial flow rate equation of a Bingham fluid through concentric cylinders. The results obtained by these two methods differ by as much as 49.4 and 63.5% for the yield stress and viscosity, respectively. It is observed for this ER fluid that the yield stress increases according to a power law relationship with the applied electrical field. The viscosity appears to decrease linearly with an increase in the applied electrical field.

Axial flows in generalized ducts are analyzed for viscoplastic materials behaving as Bingham plastics with a yield stress. A constitutive equation proposed by Papanastasiou is used, which applies everywhere in the flow field in both yielded and practically unyielded regions. Numerical simulations are presented in several two-dimensional cross-sectional geometries, such as square and rectangular ducts (straight and concave), and eccentric annular conduits, for different flow rate and pressure drop ranges. The extent and shape of yielded/unyielded regions are shown as the dimensionless yield stress or Bingham number increases. Master curves are given for the dimensionless flow rate vs dimensionless pressure drop or vs Bingham number for quick engineering calculations useful in practical applications of materials processing. Les materiaux viscoplastiques se comportant comme des plastiques de Bingham ayant un seuil d'ecoulement sont analyses dans des ecoulement axiaux dans des conduites de section quelconque. On utilise une equation constitutive proposee par Papanastasiou qui s'applique partout dans le champ d'ecoulement, que ce soit dans les regions cisaillees ou les regions pratiquement non cisaillees. Des simulations numeriques sont presentees dans plusieurs geometries de section bidimensionnelle, telles les conduites carrees et rectangulaires (droites et concaves) et les conduites annulaires eccentriques, pour differentes gammes de debits et de pertes de charge. L'etendue et la forme des regions cisaillees et non cisaillees sont montrees en fonction de l'augmentation du seuil d'ecoulement adimensionnel ou du nombre de Bingham. On presente des courbes maitresses de debit adimensionnel en fonction de la perte de charge adimensionnelle ou du nombre de Bingham pour des calculs d'ingenierie rapides utilises dans des applications pratiques en transformation des materiaux.

Tomographic signal processing has been added to a conventional electromagnetic flowmeter. The result is a new method for measuring rheological parameters of viscous, non-Newtonian fluids. The practical realization requires only minor changes to existing instruments. Hence their main advantages are maintained, such as non-invasive, in-litre measurement without pressure drop. The basic idea is to generate two different magnetic fields with the flowmeter by switching the current direction in one of the magnetic coils. The flowmeter measures two signals depending on the flow profile. Using simple parametric models for both the flow profile and the rheology, the flow prolile can be calculated from the flowmeter signals, and from the flow profile the rheological behaviour is determined. The theory and experimental results with a slightly modified industrial flowmeter are presented

SUMMARY The duct flow of Bingham plastic fluids is analysed with the variational inequality-based finite element method. The problem of tracking the yield surface is solvable through the regularization technique which can be easily incorporated into the existing finite element code. The existence theorem of this method was established through the theory of variational inequalities. A small positive constant is added to the second shear rate invariant, resulting in an apparent viscosity of finite magnitude in the unyielding plug zone. This makes the minimization of the non-differential variational integral possible. In order to achieve convergence at small regularization parameter, a zero-order continuation is employed. It is also shown that a fine tessellation of the flow domain is necessary for tracking the yield surfaces unambiguously. Two classes of duct flow, namely axial flows in eccentric annuli and in an L-shaped duct, were investigated. In both cases it was easy to show the presence of the mobile plugs around the duct centres from the axial velocity profiles; however, the stagnant plugs at the narrow side in eccentric annuli with large eccentricity and near the apex of right-angled corners in an L-shaped duct could only be identified from the calculation of the distributions of the second shear rate or shear stress invariant. # 1997 John Wiley & Sons, Ltd.

Slurries of finely milled Irish peat in Shell White Spirit (100F) were prepared and their rheological behaviour was evaluated in terms of shear rate, solids concentration, moisture content and particle size distribution of the solids. The moisture content of the peat was found to be of crucial significance in determining both the effective solids concentration and the stability of the suspensions. The viscosity of slurries composed of 7% moisture peat solids were almost independent of solids concentration and displayed Newtonian rheological behaviour, with a viscosity of approximately 0.012 N s m -2 . The viscosity of the suspending medium was 1.006 x 10 -3 N s m -2 at 20 ± 1°C. The viscosity of the slurries composed of 55% moisture peat solids was observed to rise sharply, up to about 0.10 N s m -2 with solids concentration. The shear rate dependence of these suspensions was more complex and their flow characteristics were evaluated in terms of empirical non-Newtonian models. It proved difficult to confidently distinguish between the Bingham Plastic and Casson models as each gave best fit regression curves which were almost identical. Particle size distribution analysis of the suspensions indicates the formation of peat aggregates in the 55% moisture samples which exhibited more rapid settling of the solid.

The flow of a Bingham fluid in a concentric cylinder viscometer can be give rise to free boundary problems. In the region between the two rotating cylinders the fluid behaves like a viscous fluid if the shear stress, expressed as a linear function of the shear rate, exceeds a yield value, and like a rigid body otherwise. The surfaces dividing fluid and rigid zones are the free boundaries, where we assume that the shear rate is zero. Starting from a model proposed in a previous work, where just one fluid and one rigid zone were present, here we study the physical problem taking into account the possible formation of further rigid zones inside the fluid. We introduce a kind of “regularization” of the problem, pointing out the existence of a unilateral constraint to which the formation of new rigid zones is related. Each time the constraint comes into play, the problem must be reformulated by letting new free boundaries appear bounding the newly created rigid region. Moreover we analyse the possible collapsing of the rigid zones.

The present numerical study concentrates on the effects of moderate and high Reynolds numbers on the laminar flow of a non-Newtonian rigid viscoplastic (Bingham) fluid through a sudden contraction in a pipe. The flow is assumed to be steady, incompressible, and isothermal. Results are presented for a wide range of the governing Reynolds and yield numbers and the significant effects of these two parameters both on the integral and local kinematic properties of the flow field are established. Low yield numbers result in the disappearance of the recirculating flow region at the corner replacing it with a region of very low rates of deformation. The evolution of the centerline velocity in the vicinity of the contraction plane is shown to be independent of the yield number and dependent on the Reynolds number, while the concavities in the streamwise velocity profiles appearing at high Reynolds numbers are independent of the yield number. The pressure losses through the contraction increase with yield number with the effect being more pronounced at lower Reynolds numbers. La presente etude numerique porte sur les effets de nombres de Reynolds moderes ou eleves sur l'ecoulement laminaire d'un fluide viscoplastique rigide non newtonien (Bingham) a travers une contraction soudaine dans un tube. On suppose l'ecoulement stationnaire, incompressible et isotherme. Des resultats sont presentes pour un large eventail des nombres de Reynolds et de nombre de seuil et les effets significatifs de ces deux parametres sur les proprietes cinematiques locales et integrales du champ d'ecoulement sont demontres. De faibles nombres de seuil entraǐnent la disparition de la region d'ecoulement en recirculation dans le coin ou elle est remplacee par une region a tres faibles vitesses de deformation. On montre que l'evolution de la vitesse le long de l'axe central a proximite du plan de contraction est independante du nombre de seuil et dependante du nombre de Reynolds, tandis que les concavites des profils de vitesse dans la direction du courant apparaissant a des nombres de Reynolds eleves sont independantes du nombre de seuil. Les pertes de charge a travers la contraction augmentent avec le nombre de seuil, l'effet etant plus prononce aux petits nombres de Reynolds.

The flow rate of a com starch-kerosene ERF through a narrow channel formed by a pair of electrodes has been measured over a range of electric fields between 0 and 2.8 kV/mm. The effect of the entrance shape and various electrode configurations on the flow rate of the ERF has been examined. The relationship between the flow rate and applied voltage is theoretically analysed on the assumption that the ERF is a Bingham fluid and compared with the observed values. It has been illustrated that the theoretically derived relationship is in good agreement with the observed values if a correction term or adjustable parameters are incorporated. Le debit d'un fluide electro-rheologique (ERF) d'amidon de mais-kerosene circulant dans un canal etroit forme par une paire d'electrodes a ete mesure dans une gamme de champs electriques de 0 a 2,8 kV/mm. On a etudie l'effet de la forme de l'entree et des differentes configurations d'electrodes sur le debit de l'ERF. La relation entre le debit et le voltage applique est analysee de facon theorique en posant comme hypothese que l'ERF est un fluide de Bingham, puis cette relation est comparee avec les valeurs observees. On montre que cette relation calculee theoriquement montre un bon accord avec les valeurs observees si un terme de correction ou des parametres ajustables sont introduits.

This paper demonstrates the use of the nuclear magnetic resonance (NMR) velocity spectrum to rheologically characterize a fluid-like material in steady tube flow. The velocity spectra for four different materials, an oil-water solution, a polyacrylamide solution, tomato juice and a paper pulp suspension are measured and qualitative agreement with theory based upon simple constitutive models is demonstrated. These materials exhibit Newtonian, power law and Bingham plastic behavior. Homogeneous and heterogeneous samples are used and the applicability to each discussed. The velocity spectra from NMR experiments allows for a nonin-vasive method of monitoring flow behavior and as such has applications to online process monitoring of rheological properties.

The shear-rate/shear-stress data of cooked maine flour suspensions were obtained using a concentric cylinder viscometer in the shear rate range of 3 and 1326 s −1 . The effects of concentration of maize flour (2-10%) in the cooked suspensions on yield stress, flow behavior index, consistency index and apparent viscosity, were investigated. Cooked maize flour suspensions were pseudoplastic in nature with yield stress. At flour concentrations above 6 %, the experimentally determined yield stresses were lower than those calculated from different rheological models. The shear-rate/shear-stress data were examined using the rheological models: the power law, Bingham plastic, Casson, Costell-Duran, Herschel-Bulkley and Mizrahi-Berk models. The last two models were found to provide the best fit (r ≥ 0.991, p ≤ 0.01)

In this article we propose a new equation that combines behaviors of Bingham and Williamson pseudoplastic materials. We compare this equation with other ones, and in the Appendix, we consider its theoretical foundation. © 1993 John Wiley & Sons, Inc.

Developing flows of generalized Bingham (Herschel-Bulkley) fluids in concentric annuli were studied numerically. A control volume approach based upon an upwinding finite difference technique was used to solve the equation of motion. The results in terms of velocity and pressure drop profiles are shown graphically. Radius ratios of 0.02, 0.2, 0.4 and 0.6; power-law indices (n) of 0.7, 1.0 and 1.2; generalized Bingham numbers of 5, 10 and 15 were investigated. At present, there are no experimental results with which to make comparisons. However, there are results for fully developed flows and comparison has been made with these. In all cases the agreement was good. On a etudie numeriquement le developpement ďecoulements de fluides de Bingham (Herschel-Bulkley) generalises. Une methode des volumes de contrǒle basee sur une technique de differences finies avec decentrage amont a ete utilisee pour resoudre ľequation de deplacement. Les resultats portant sur les profils de vitesse et les pertes de charge sont illustres par des graphiques. On a etudie des rapports de rayons de 0,02, 0,2, 0,4 et 0,6, des indices de lois de puissance (n) de 0,7, 1,0 et 1,2 et des nombres de Bingham generalises de 5, 10 et 15. A ľheure actuelle, il 'existe pas de resultats experimentaux avec lesquels etablir des comparaisons. Cependant, on dispose de resultats pour des ecoulements completement developpes, qui nous ont permis ďetablir une comparaison. Dans tous les cas traites, ľaccord est satisfaisant.

Rheological characteristics of stirred yoghurt, varying in dry matter content, fermentation temperature and composition of bacteria cultures, were evaluated using a Bohlin VOR Rheometer. Flow curves, covering the shear rate range 29–920 s−1, generally indicated the presence of a yield point and pseudoplastic behaviour, but also Bingham plastic behaviour was observed for some of the specimens. Systematic variations in the profile of the flow curves were observed as a result of the applied manufacturing conditions. Flow curves exhibiting pseudoplastic behaviour with a yield stress could not, over this broad shear rate interval, be described satisfactorily by the often applied Casson or Herschel-Bulkley models, and consequently a new one, the QRS-model was introduced. This model contains three parameters and gave a significantly better fit, with R2 values generally above 0.99.

The rate of dissolution of rock salt in drilling mud was measured as a function of flow rate and temperature under conditions simulating those in a well. A water based drilling mud, containing about 10% solids and additives was used, as well as a polymer “mud” composed of a Xanthan gum polymer solution and 5% salt, but no solids. The non-Newtonian muds were pumped through a “slit” flow cell, with a slab of rock salt flush with one side of the cell wall. The data (including water over the same range of conditions) were described by a mass transfer coefficient, and were correlated in dimensionless form based on the theoretical solution of the analogous heat transfer problem, adapted to non-Newtonian fluids. The non-Newtonian properties were described by an effective viscosity, which is consistent with either the power law or Bingham plastic viscosity model. On a mesure la vitesse de dissolution de sel de roche dans des boues de forage en fonction du debit et de la temperature dans des conditions simulant celles d'un puits. Une boue de forage a base d'eau contenant environ 10% de solides et d'additifs a ete utilisee ainsi qu'une «boue» de polymeres composee d'une solution de polymeres de gomme de xanthane et de 5% de sel sans solides. Les boues non newtoniennes ont ete pompees dans une cellule d'eoulement a «fente», avec un panneau de sel de roche tangent a une paroi de la capteur. Les donnees (incluant l'eau dans la meme gamme de conditions) sont decrites par un coefficient de transfert de matiere et correlees sous une forme adimensionnelle basee sur la solution theorique du probleme analogue de transfert de chaleur, adaptee aux fluides non newtoniens. Les proprietes non newtoniennes sont decrites par une viscosite effective, qui concorde avec la loi de puissance ou le modele de viscosite plastique de Bingham.

In this paper, we present a rheological study of a compact layer of highly swollen gel beads. The flow regimes of these systems are modelled by an elastic sinusoid moving in a Newtonian fluid. This model predicts a yield stress varying with the square root of the elastic modulus of the gel bead. The slope at the origin (at zero velocity) of the flow curve is expected to depend only on geometrical parameters and on the solvent viscosity. The experimental data are in qualitative agreement with the theoretical predictions.

A finite element analysis of the dip coating process with Bingham fluids is presented. The solution method for the viscoplastic flow problem was based on the augmented Lagrangian method allowing a rigorous treatment of the stress discontinuity. To compute the location of the free surface at equilibrium, an iterative method was used based on the arbitrary Eulerian-Lagrangian approach in conjunction with mesh smoothing. Numerical predictions were validated against experimental data for the Newtonian limit case. Computations were then performed with Bingham fluids. The influence of yield stress on the meniscus flow Is discussed.

Some rheological materials, such as melting polymers, cosmetic creams, ketchup, toothpaste, can be modeled as non-NEWTONian fluids by using a non-linear constitutive relation. An incompressible flow of this kind of amorphous matter can be considered as a thermodynamic process, and a solution for the pressure, velocity and temperature fields describe it fully. Since such flow processes are generally irreversible, entropy is produced leading to dissipation in the system. This energy loss can be measured indirectly in a cone/plate viscometer which is used to determine viscosity of a BINGHAM fluid. While dissipation is an observable quantity we also want to be able to calculate it. Thus the goal of this work is to explain briefly how to compute a transient flow of a viscous fluid in two-dimensional channel under a sinusoidal traction and calculate the dissipated energy for non-NEWTONian fluids. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Friction losses of the laminar flow of a Bingham plastic fluid through a pipe is characterised by a friction factor, f, which depends on two dimensionless parameters, the Reynolds and the Bingham numbers. The relationship is a fourth degree equation for f, named after Buckingham (1921). In this short communication, we present a novel expression for its only physically meaningful solution, which is easier to handle than those presented previously by other authors.

SUMMARY We model the forming process as a fluid flow. A finite element program, FIDAP, which analyses flow problems, was used to calculate velocity and strain rates at points throughout the material during the deformation process. This allows predictions to be made on the shape and quality of the resulting part. The stress-strain relation we used models the plastic flow of metals (Bingham fluids). The FEM approximation of such a fluid is tested by comparing results for a simple analytical example. In forming processes provision must be made for friction between dye and workpiece, and the program was modified accordingly. Two classical ring forming simulations are compared to published results.