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Showing papers on "Herschel–Bulkley fluid published in 2018"


Journal ArticleDOI
TL;DR: In this paper, the impact of three rheological parameters (τ 0, KHB and n) on the flow behavior of cuttings and H B fluid were analyzed.

48 citations


Journal ArticleDOI
TL;DR: In this paper, the peristaltic transport of a Herschel-Bulkley fluid in an axisymmetric tube was investigated and the governing equations were solved using the long wavelength and small Reynolds numbe...
Abstract: The present article investigates the peristaltic transport of a Herschel–Bulkley fluid in an axisymmetric tube. The governing equations are solved using the long wavelength and small Reynolds numbe...

38 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used the Constructal Design associated with exhaustive search to obtain the ellipse aspect ratios that maximize the Nusselt number and to minimize dimensionless pressure drop for viscoplastic fluids in cross flow around elliptical section tubes.

31 citations


Journal ArticleDOI
TL;DR: In this paper, the yield stress and other rheological parameters of gum karaya suspensions were investigated with the main objective to determine the yield-stress and other parameters using various models.
Abstract: Rheological characteristics of gum karaya suspensions which is proposed as a fracturing fluid were investigated with the main objective to determine the yield stress and other rheological parameters using various models. The flow hysteresis confirms the thixotropic behavior of fluid with increased structural breakdown at higher concentration and temperature. An empirical model developed for the studied samples accurately predicts the temperature and polymer concentration sensitivity of the apparent viscosity. The Herschel-Bulkley model showed the best fit to the experimental data; however, the yield stress obtained from some of the samples using nonlinear regression (NL) method reported physically insignificant, negative values. The proposed optimization technique, i.e., “Particle Swarm Optimization” offered the most realistic results with faster convergence over genetic algorithm making it a better choice. The oscillatory study provided more reliable yield stress values and revealed the thermogelation behavior of polymer suspensions making it suitable for high-temperature fracturing application.

24 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a new method based on the geometric average of elastic and viscous Lissajous curves to study the yielding transition of different yield stress fluids in large amplitude oscillatory shear flow.
Abstract: Large amplitude oscillation shear has been an important method to investigate the yielding and flow behavior of yield stress materials. However, there are great uncertainties in determination of the yield stress from the shear stress (or shear strain) dependence of the apparent dynamic moduli or the relative harmonic intensity using Fourier transform rheology. The yield stress from these dynamic methods is also inconsistent with the steady shear and transient shear measurements. We propose a new method, namely, stress bifurcation, based on the geometric average of elastic and viscous Lissajous curves to study the yielding transition of different yield stress fluids in large amplitude oscillatory shear flow. The results prove that typical yield stress fluids such as concentrated emulsions, polymer nanocomposites, microgels, and particulate gels all exhibit stress bifurcations, both inter and intra cyclically, in large amplitude oscillatory shear experiments. Such stress bifurcation phenomena between the average stress-strain (or strain rate) curves are independent of the type of input signal, i.e., stress-controlled versus strain-controlled. A start yield stress (strain) (related to strain) and an end yield stress (strain rate) (related to strain rate), instead of a single critical variable, were suggested to characterize yielding transitions. The frequency dependences of critical stresses, critical strain, and critical strain rate determined by the new method were also investigated systematically for the different kinds of yield stress fluids. A visco-elastic-plastic model, the Kelvin-Voigt-Herschel-Bulkley model, was also adopted to understand the stress bifurcation and frequency dependencies of critical variables in large oscillatory shear flow.Large amplitude oscillation shear has been an important method to investigate the yielding and flow behavior of yield stress materials. However, there are great uncertainties in determination of the yield stress from the shear stress (or shear strain) dependence of the apparent dynamic moduli or the relative harmonic intensity using Fourier transform rheology. The yield stress from these dynamic methods is also inconsistent with the steady shear and transient shear measurements. We propose a new method, namely, stress bifurcation, based on the geometric average of elastic and viscous Lissajous curves to study the yielding transition of different yield stress fluids in large amplitude oscillatory shear flow. The results prove that typical yield stress fluids such as concentrated emulsions, polymer nanocomposites, microgels, and particulate gels all exhibit stress bifurcations, both inter and intra cyclically, in large amplitude oscillatory shear experiments. Such stress bifurcation phenomena between the av...

24 citations


Journal ArticleDOI
TL;DR: In this paper, the peristaltic transport of an incompressible non-Newtonian fluid in a porous elastic tube is considered and the impacts of relevant parameters on flow rate and temperature are examined graphically.
Abstract: This paper is concerned with the peristaltic transport of an incompressible non-Newtonian fluid in a porous elastic tube. The impacts of slip and heat transfer on the Herschel-Bulkley fluid are considered. The impacts of relevant parameters on flow rate and temperature are examined graphically. The examination incorporates Newtonian, Power-law and Bingham plastic fluids. The paper aims to discuss these issues.,The administering equations are solved utilizing long wavelength and low Reynolds number approximations, and exact solutions are acquired for velocity, temperature, flux and stream functions.,It is seen that the flow rate in a Newtonian fluid is high when contrasted with the Herschel-Bulkley model, and the inlet elastic radius and outlet elastic radius have opposite effects on the flow rate.,The analysis carried out in this paper is about the peristaltic transport of an incompressible non-Newtonian fluid in a porous elastic tube. The impact of slip and heat transfer on a Herschel-Bulkley fluid is taken into account. The impacts of relevant parameters on the flow rate and temperature are examined graphically. The examination incorporates Newtonian, Power-law and Bingham plastic fluids.

24 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a pressure-driven lubrication flow of a Herschel-Bulkley fluid in a symmetric long channel of varying width, where both the consistency index and the yield stress are assumed to be pressure-dependent.
Abstract: The lubrication flow of a Herschel-Bulkley fluid in a symmetric long channel of varying width, 2h(x), is modeled extending the approach proposed by Fusi et al. [“Pressure-driven lubrication flow of a Bingham fluid in a channel: A novel approach,” J. Non-Newtonian Fluid Mech. 221, 66–75 (2015)] for a Bingham plastic. Moreover, both the consistency index and the yield stress are assumed to be pressure-dependent. Under the lubrication approximation, the pressure at zero order depends only on x and the semi-width of the unyielded core is found to be given by σ(x) = −(1 + 1/n)h(x) + C, where n is the power-law exponent and the constant C depends on the Bingham number and the consistency-index and yield-stress growth numbers. Hence, in a channel of constant width, the width of the unyielded core is also constant, despite the pressure dependence of the yield stress, and the pressure distribution is not affected by the yield-stress function. With the present model, the pressure is calculated numerically solving a...

22 citations



Journal ArticleDOI
30 Jan 2018-Water
TL;DR: In this article, the authors present a theoretically derived (with necessary approximations) law of the wall for Herschel-Bulkley fluids and implements it in a RANS solver using a specified shear approach.
Abstract: The concentration (using a lesser amount of water) of domestic slurry promotes resource recovery (nutrients and biomass) while saving water. This article is aimed at developing numerical methods to support engineering processes such as the design and implementation of sewerage for concentrated domestic slurry. The current industrial standard for computational fluid dynamics-based analyses of turbulent flows is Reynolds-averaged Navier–Stokes (RANS) modelling. This is assisted by the wall function approach proposed by Launder and Spalding, which permits the use of under-refined grids near wall boundaries while simulating a wall-bounded flow. Most RANS models combined with wall functions have been successfully validated for turbulent flows of Newtonian fluids. However, our experiments suggest that concentrated domestic slurry shows a Herschel–Bulkley-type non-Newtonian behaviour. Attempts have been made to derive wall functions and turbulence closures for non-Newtonian fluids; however, the resulting laws or equations are either inconsistent across experiments or lack relevant experimental support. Pertinent to this study, laws or equations reported in literature are restricted to a class of non-Newtonian fluids called power law fluids, which, as compared to Herschel–Bulkley fluids, yield at any amount of applied stress. An equivalent law for Herschel–Bulkley fluids that require a minimum-yield stress to flow is yet to be reported in literature. This article presents a theoretically derived (with necessary approximations) law of the wall for Herschel–Bulkley fluids and implements it in a RANS solver using a specified shear approach. This results in a more accurate prediction of the wall shear stress experienced by a circular pipe with a turbulent Herschel–Bulkley fluid flowing through it. The numerical results are compared against data from our experiments and those reported in literature for a range of Reynolds numbers and rheological parameters that are relevant to the prediction of pressure losses in a sewerage transporting non-Newtonian domestic slurry. Nonetheless, the application of this boundary condition could be extended to areas such as chemical and food engineering, wherein turbulent non-Newtonian flows can be found.

15 citations


Journal ArticleDOI
TL;DR: In this article, a new practical and dimensional analytical model was developed for Herschel Bulkley (HB) fluid to calculate pressure surges caused by drillstring movement for non-Newtonian fluids under the fully developed flow (steady state) conditions in the laminar flow range in a slot geometry.

14 citations


01 Dec 2018
TL;DR: A mathematical model for the impact of slip velocity on peristaltic transport of blood flow has been investigated by utilizing the Herschel-Bulkley model in a flexible tube as mentioned in this paper.
Abstract: A mathematical model for the impact of slip velocity on peristaltic transport of blood flow has been investigated by utilizing the Herschel-Bulkley model in a flexible tube. The closed-form solutions are obtained for velocity, plug flow velocity, and volume flux. It is noticed that the impact of yield stress, amplitude ratio, Darcy number, velocity slip parameter, elastic parameters and fluid behavior index plays a vital role in controlling the flux in an elastic tube. The outcomes acquired from the flow quantities reveal that, the volume flux in a flexible tube decreases with an increase in the porous parameter and it increases with an increase in the slip parameter. Further, the results of Newtonian, Bingham plastic and Power-law models have been presented graphically and analysed

Journal ArticleDOI
TL;DR: In this article, the effect of shear-thinning on the stability of plan Poiseuille flow was investigated using the energy method and nonmodal stability theory, and the results showed that the shear thinning plays an important role in determining the energy growth rate and the structure of the disturbance with optimal transient growth.
Abstract: Linear stability in plane Poiseuille flow of a yield-stress shear-thinning fluid is considered. The rheological behavior of the fluid is described by the Herschel–Bulkley model. The effect of shear-thinning on the stability is investigated using the energy method and the nonmodal stability theory. The result of the energy method shows that with the increase of shear thinning, the critical energy Reynolds number decreases for both the streamwise and spanwise disturbances. For the nonmodal stability, we focus on the response to initial conditions by examining the energy growth function G(t). For a Herschel–Bulkley fluid, it is found that there can be a rather large transient growth even though the linear operator of the plan Poiseuille flow has no unstable eigenvalue. The results show that the shear thinning plays an important role in determining the energy growth rate and the structure of the disturbance with optimal transient growth.

Journal ArticleDOI
TL;DR: The theoretical values of time-mean flow rates for seminal fluid (Herschel–Bulkley fluid) have been found to be in good agreement with the experimental results.

Journal ArticleDOI
22 Dec 2018-Water
TL;DR: In this paper, the authors proposed a numerical approach for the analysis of concentrated domestic slurry using the Reynolds-Averaged Navier-Stokes (RANS) approach for turbulent flows.
Abstract: This article follows from a previous study by the authors on the computational fluid dynamics-based analysis of Herschel-Bulkley fluids in a pipe-bounded turbulent flow. The study aims to propose a numerical method that could support engineering processes involving the design and implementation of a waste water transport system, for concentrated domestic slurry. Concentrated domestic slurry results from the reduction in the amount of water used in domestic activities (and also the separation of black and grey water). This primarily saves water and also increases the concentration of nutrients and biomass in the slurry, facilitating efficient recovery. Experiments revealed that upon concentration, domestic slurry flows as a non-Newtonian fluid of the Herschel-Bulkley type. An analytical solution for the laminar transport of such a fluid is available in literature. However, a similar solution for the turbulent transport of a Herschel-Bulkley fluid is unavailable, which prompted the development of an appropriate wall function to aid the analysis of such flows. The wall function (called ψ1 hereafter) was developed using Launder and Spalding's standard wall function as a guide and was validated against a range of experimental test-cases, with positive results.ψ1 is assessed for its sensitivity to rheological parameters, namely the yield stress, the fluid consistency index and the behaviour index and their impact on the accuracy with which ψ1 can correctly quantify the pressure loss through a pipe. This is done while simulating the flow of concentrated domestic slurry using the Reynolds-Averaged Navier-Stokes (RANS) approach for turbulent flows. This serves to establish an operational envelope in terms of the rheological parameters and the average flow velocity within which ψ1 is a must for accuracy. One observes that, regardless of the fluid behaviour index, ψ1 is necessary to ensure accuracy with RANS models only in flow regimes where the wall shear stress is comparable to the yield stress within an order of magnitude. This is also the regime within which the concentrated slurry analysed as part of this research flows, making ψ1 a requirement. In addition, when the wall shear stress exceeds the yield stress by more than one order (either due to an inherent lower yield stress or a high flow velocity), the regular Newtonian wall function proposed by Launder and Spalding is sufficient for an accurate estimate of the pressure loss, owing to the relative reduction in non-Newtonian viscosity as compared to the turbulent viscosity.

Journal ArticleDOI
TL;DR: In this paper, a numerical solver using a multi-material level-set method is applied to track multiple interfaces simultaneously in the simulations of avalanches and subaqueous debris flows.
Abstract: . Avalanches and subaqueous debris flows are two cases of a wide range of natural hazards that have been previously modeled with non-Newtonian fluid mechanics approximating the interplay of forces associated with gravity flows of granular and solid–liquid mixtures. The complex behaviors of such flows at unsteady flow initiation (i.e., destruction of structural jamming) and flow stalling (restructuralization) imply that the representative viscosity–stress relationships should include hysteresis: there is no reason to expect the timescale of microstructure destruction is the same as the timescale of restructuralization. The non-Newtonian Herschel–Bulkley relationship that has been previously used in such models implies complete reversibility of the stress–strain relationship and thus cannot correctly represent unsteady phases. In contrast, a thixotropic non-Newtonian model allows representation of initial structural jamming and aging effects that provide hysteresis in the stress–strain relationship. In this study, a thixotropic model and a Herschel–Bulkley model are compared to each other and to prior laboratory experiments that are representative of an avalanche and a subaqueous debris flow. A numerical solver using a multi-material level-set method is applied to track multiple interfaces simultaneously in the simulations. The numerical results are validated with analytical solutions and available experimental data using parameters selected based on the experimental setup and without post hoc calibration. The thixotropic (time-dependent) fluid model shows reasonable agreement with all the experimental data. For most of the experimental conditions, the Herschel–Bulkley (time-independent) model results were similar to the thixotropic model, a critical exception being conditions with a high yield stress where the Herschel–Bulkley model did not initiate flow. These results indicate that the thixotropic relationship is promising for modeling unsteady phases of debris flows and avalanches, but there is a need for better understanding of the correct material parameters and parameters for the initial structural jamming and characteristic time of aging, which requires more detailed experimental data than presently available.

Journal ArticleDOI
TL;DR: The magnetohydrodynamic flow through a porous medium of a second-grade fluid between two side walls induced by an infinite plate that exerts an accelerated shear stress to the fluid over an infinite Plate is examined.
Abstract: The magnetohydrodynamic flow through a porous medium of a second-grade fluid between two side walls induced by an infinite plate that exerts an accelerated shear stress to the fluid over an infinite plate is examined. Expressions for velocity and shear stress are determined with the help of integral transforms. In the absence of side walls, all the solutions that have been obtained are reduced to those corresponding to the motion over an infinite flat plate. The Newtonian solutions are also obtained as limiting case of the general solution. Finally, influence of magnetic and porosity parameter is graphically highlighted.

Journal ArticleDOI
TL;DR: In this paper, the peristaltic wall is considered to be coated with a porous lining, and the pertinent parameter effects are studied graphically for the analytical solutions of temperature profile, rate of temperature, heat transfer coefficient and mechanical efficiency.
Abstract: Heat transfer effect on the flow of Herschel Bulkley fluid moving in a non-uniform channel is analyzed. The peristaltic wall is considered to be coated with a porous lining. The pertinent parameter effects are studied graphically for the analytical solutions of temperature profile, rate of temperature, heat transfer coefficient and mechanical efficiency. The temperature profile, heat transfer coefficient and the rate of temperature decrease with increase in the Darcy number. Thickening of the porous wall coating raises the temperature profile and the rate measure of temperature. Mechanical efficiency is more in a convergent channel than in uniform and divergent channels.

Journal ArticleDOI
TL;DR: In this article, the influence of the rheological parameters of the plate material and the viscosity of the fluid on the frequency response of a hydro-viscoelastic system was investigated.
Abstract: In this paper the forced vibration of a hydro-viscoelastic system consisting of a viscoelastic plate, compressible viscous fluid and rigid wall is considered. The focus is on the investigation of the influence of the rheological parameters of the plate material and the viscosity of the fluid on the frequency response of this system. The constitutive relations for the plate material are given through the fractional-exponential operators, and the exact equations of the visco-elastodynamics in the plane-strain state are employed for describing the plate motion. The fluid motion is described through the linearized Navier–Stokes equations and it is assumed that the velocity and force vectors are continuous across the interface plane between the fluid and the plate. Numerical results on the frequency response of the normal stress acting on the interface plane and of the normal velocity of the points of this plane are presented for various values of the rheological parameters of the plate material. These results...

Proceedings ArticleDOI
09 Jul 2018
TL;DR: Genetic algorithm is used for finding Pareto fronts in MATLAB® environment for solving this multiobjective optimization problem of volume-constrained MR valve by minimizing multiple objective functions based on H-B fluid model.
Abstract: Rheological fluids find great relevance in various engineering applications. Among them, magnetorheological (MR) fluid has become popular due to its controllable rheological characteristics. It has been found that non-linear Herschel-Bulkley (H-B) fluid model is the most suitable model for characterizing MR fluids as it is able to capture shear-thinning and shear-thickening phenomena at high shear rates; the popular linear Bingham fluid model lacks this. This inadequacy of Bingham model leads to a linear approximation of hysteresis curves generated as damping force versus velocity plots and hence tends to underestimate or overestimate the behavior depending on the MR fluid used. In previous literature, authors have modeled and optimized MR valve geometry of semi-active dampers for multiple objective functions using Bingham model. In the present study, the valve is modeled using H-B fluid model and the optimization problem establishes geometric parameters of volume-constrained MR valve by minimizing multiple objective functions based on H-B fluid model; such work has not been reported till now. The proposed optimization aims at (i) maximizing dynamic range and (ii) minimizing inductive time constant with the constraints stated below. The formulation of objective functions is based on the analytical solution of a magnetic circuit such that there is a constraint on geometry for keeping magnetic flux density less than saturation limits of the valve material. All the parameters associated with H-B model of a commercially available MR fluid are determined as a function of magnetic flux density. Since there are multiple objective functions, one can go for Pareto optimal points. Therefore, for solving this multiobjective optimization problem, genetic algorithm is used for finding Pareto fronts in MATLAB® environment. Finally, the performance of the optimally designed MR valve is studied.

Journal ArticleDOI
TL;DR: In this article, the rheological parameters of an environmentally friendly drilling fluid formulated based on an Algerian bentonite and two polymers (hydroxyethyl cellulose and polyethylene glycol) have been optimized using a genetic algorithm.
Abstract: The Herschel–Bulkley rheological parameters of an environmentally friendly drilling fluid formulated based on an Algerian bentonite and two polymers—hydroxyethyl cellulose and polyethylene glycol—have been optimized using a genetic algorithm. The effect of hydroxyethyl cellulose, temperature, pH and sodium chloride (NaCl) on the three-parameter Herschel-Bulkley model was also studied. The genetic algorithm technique provided improved rheological parameter characterization compared to the nonlinear regression, especially in the case of drilling fluids formulated with sodium chloride making it a better choice. Furthermore, the oscillatory test offered more reliable yield stress values. The rheological parameters were found to be very sensitive to different conditions. Yield stress and consistency index increased with increasing the hydroxyethyl cellulose concentration, reaching maximum at a temperature of 65 °C and decreased with decreasing pH and also when adding sodium chloride to the drilling fluid. The flow index changed inversely to yield stress and consistency index. The physical origins of these changes in rheological parameters were discussed and correlation between variation in rheological parameters and bentonite suspension properties were concluded. Based on these results, it is recommended to use the proposed formulation of drilling fluid at high temperature and when the formation of alkaline pH is encountered due to the gelation mechanism and to select the optimum concentration of NaCl to avoid degradation of the rheological parameters.

Journal ArticleDOI
TL;DR: In this article, a grid-shaped probe was used for semi-liquid products like mayonnaise, which was simplified in a CFD simulation which provided a correlation from which the rheological parameters could be extracted.

Journal ArticleDOI
TL;DR: In this article, an analytical analysis of axisymmetric pulsatile blood flow through an inclined stenosed artery of a periodically accelerated body under the influence of a magnetic field has been done.
Abstract: Analytical investigation of Herschel-Bulkley model for axisymmetric pulsatile blood flow through an inclined stenosed artery of a periodically accelerated body under the influence of a magnetic field has been done. Invoking suitable transformations, the flow governing partial differential equations are non-dimensionalized. For these non–dimensionalized equations, an exact solution representing the different flow characteristic has been derived by employing the perturbation method. Flow rate and impedance analysis of the Herschel-Bulkley fluid has been done graphically by varying the yield stress, pressure gradient. Some important results are obtained pertaining to the medical interest.

Journal ArticleDOI
TL;DR: In this article, the authors exploited the concept of work and energy to analyze the oscillatory shear stress and showed that a rheological behavior such as strain thinning can be originated by various origin in the perspective of energy.
Abstract: Two methods are widely used to quantitatively analyze the nonlinear stress in large amplitude oscillatory shear (LAOS) flow; one is to analyze the stress in time domain and the other in strain or strain rate domain. Distinguished from these two methods, this paper exploits the concept of work and energy to analyze the oscillatory shear stress. The inner area in the strain-stress Lissajous curve after one cycle is known to be related with work, and that of the strain rate-stress Lissajous with energy. To precisely analyze the nonlinear stress, it helps to consider work and energy not only after a complete cycle but also during the cycle. In this paper, we trace the work and energy during the oscillation, together with their derivatives. We apply this concept to perfectly elastic solid, purely viscous liquid, and viscoelastic fluid. By this approach, it is shown that a rheological behavior such as strain thinning can be originated by various origin in the perspective of work and energy, which means that the rheological behavior can be subclassified in terms of work and energy. This approach is useful because it can analyze nonlinear stress without mathematically intriguing higher harmonics and it can be easily applied to any type of material with different stress shape.

Journal ArticleDOI
TL;DR: In this paper, a three-dimensional computational fluid dynamics simulation of a controlled low-strength material (CLSM) slurry filling with piping transportation is presented to study and predict the flowing behavior of controlled low strength material (SLM) slurps.
Abstract: In order to study and predict the flowing behaviour of controlled low-strength material (CLSM) slurry filling with piping transportation, a three-dimensional computational fluid dynamics simulation...

Journal ArticleDOI
TL;DR: In this article, a numerical study of flow and heat transfer convection inside a lid-driven square cavity filled with a shear-thinning Herschel-Bulkley fluid is presented.
Abstract: The present numerical study, based on the finite volume method, deals with the characterization of flow and heat transfer convection inside a lid-driven square cavity filled with a shear-thinning Herschel–Bulkley fluid. The upper and bottom walls of the enclosure are thermally insulated, while the vertical ones are mobile and differentially heated. The study focuses on the effect of the fluid’s rheological properties, i.e., the fluid’s viscoplasticity (0.50 ≤ Bng ≤ 5000) and the flow index (0.2 ≤ n ≤ 1.0), on both flow and heat transfer within the cavity on one hand and on the modifications involved by the introduction of viscous dissipation (0 ≤ Br ≤ 10) on the other hand. The results show that the increase of the generalized Bingham number leads to the increase of the unyielded regions inside the enclosure. In addition, heat transfer is more pronounced for weak values of the generalized Bingham number and great values of the fluid’s flow index. Viscous dissipation modifies significantly both flow and heat transfer structures, especially for mixed and dominant natural convection. To sum up the obtained results, useful abacuses predicting the heat exchange within the enclosure are given.

Journal ArticleDOI
TL;DR: In this article, an extension of authors' previous model for a 3D hydraulic fracture with Newtonian fluid, which aims to account for the Herschel-Bulkley fluid rheology and to study the associated effects, is presented.
Abstract: The paper presents an extension of authors’ previous model for a 3D hydraulic fracture with Newtonian fluid, which aims to account for the Herschel–Bulkley fluid rheology and to study the associated effects. This fluid rheology model is the most suitable for description of modern complex fracturing fluids, in particular, for description of foamed fluids that have been successfully utilized recently as fracturing fluids in tight and ultra-tight unconventional formations with high clay contents. Another advantage of using Herschel–Bulkley rheological law in the hydraulic fracture model consists in its generality as its particular cases allow describing the behavior of the majority of non-Newtonian fluids employed in hydraulic fracturing. Except the Herschel–Bulkley fluid flow model the considered model of hydraulic fracturing includes the model of the rock stress state. It is based on the elastic equilibrium equations that are solved by the dual boundary element method. Also the hydraulic fracturing model contains the new mixed mode propagation criterion, which states that the fracture should propagate in the direction in which mode $${{\mathrm{\mathrm {II}}}}$$ and mode $${{\mathrm{\mathrm {III}}}}$$ stress intensity factors both vanish. Since it is not possible to make both modes zero simultaneously the criterion proposes a functional that depends on both modes and is minimized along the fracture front in order to obtain the direction of propagation. Solution for Herschel–Bulkley fluid flow in a channel is presented in detail, and the numerical algorithm is described. The developed model has been verified against some reference solutions and sensitivity of fracture geometry to rheological fluid parameters has been studied to some extent.

Journal ArticleDOI
TL;DR: In this article, the inclination of the artery has been developed to understand the effect on blood flow, and the results are shown numerically and graphically, as well as comparative studies have been presented in addition to the current results.
Abstract: In the current mathematical model magnetic field, the inclination of the artery has been developed to understand the effect on blood flow. This model also reveals the effect of core velocity, wall shear stress and volumetric flow rate on the wall of the artery under the stenotic conditions. Blood has been taken as a Herschel-Bulkley fluid in which several stenoses are taken at equal distances in an inclined artery. Using appropriate boundary conditions, analytical expressions have been fulfilled for all these flow characteristics. The results are shown numerically and graphically, as well as comparative studies have been presented in addition to the current results. This information can be valuable in developing the latest diagnosis for the treatment of atherosclerotic artery, the progress of equipment and the development of medicines.

Journal ArticleDOI
TL;DR: In this article, a steady, laminar, incompressible, Poiseuille flow of a Herschel-Bulkley fluid between two horizontal parallel elastic walls is modeled.
Abstract: In order to model the blood flow through an artery in presence of catheter, we considered a steady, laminar, incompressible, Poiseuille flow of a Herschel-Bulkley fluid between two horizontal parallel elastic walls. The power law index ( ) and yield stress ( ) are the two parameters of the Herschel - Bulkley fluid. By giving different values for the above mentioned parameters, we get the Newtonian, Bingham and Power-law fluids as special cases. The exact solutions for the flow quantities such as velocity, plug flow velocity and flux are derived. The flux is determined as a function of inlet, outlet, external pressures and the elastic property of the channel. The effect of elastic parameters on flux variation is analyzed. Further when and our results qualitatively agree with those of Rubinow and Keller [2]. In addition, velocity of the Herschel- Bulkley fluid flow is expressed in terms of elastic parameters.

Dissertation
01 Jan 2018
TL;DR: In this paper, a new magnetorheological (MR) fluid which contains Maghemite (γ-Fe2O3) nanoparticles was developed to improve its performance in terms of physical and rheological properties and its application in MR device.
Abstract: This research is focused on the development of a new magnetorheological (MR) fluid which contains maghemite (γ-Fe2O3) nanoparticles so as to improve its performance. The performance of MR fluid is presented in terms of physical and rheological properties and its application in MR device. In this work, the γ-Fe2O3 has been synthesized using co-precipitation method and coated with oleic acid. Two types of MR fluids were prepared, bidisperse MR fluid containing carbonyl iron (CI) microparticles substituted with γ-Fe2O3 and MR fluid utilizing γ-Fe2O3 additive. MR fluid containing γ-Fe2O3 showed great improvement exhibiting reduced sedimentation rate and enhanced re-dispersibility. During the period of 50 hours, the bidisperse MR fluid with 5 wt% of γ-Fe2O3 reduced 15% of sedimentation rate and MR fluid with 1 wt% of γ-Fe2O3 additive reduced 9.6% of sedimentation rate compared to pure CI MR fluid. The rheological properties of the MR fluid were analyzed with respect to the rheological models of Bingham Plastic, Herschel Bulkley and Casson models. The rheological properties of bidisperse MR fluid revealed that the substitution of 5 wt% γ-Fe2O3 increased the yield stress by 8.5% but further substitution of γ-Fe2O3 would slightly decrease the yield stress. On the other hand, the MR fluid added with γ-Fe2O3 additive showed improvement in yield stress over the entire range of magnetic field applied. The results indicated that the addition of 1 wt% of γ-Fe2O3 in MR fluid increased the yield stress by 11.7%. The performance of MR fluid using MR valve equipped with a hydraulic bypass damper resulted in improvement of damping force when γ-Fe2O3 is added. The MR fluid with 1 wt% γ-Fe2O3 additive improved the maximum damping force up to 11.1% compared to the pure MR fluid. Therefore, the substitution and addition of γ-Fe2O3 nanoparticles in the MR fluid improved both its physical and rheological properties, hence it can potentially be used in commercial application as a simple and reliable damping device.

Journal ArticleDOI
Youquan Bao1, Jinjun Zhang1, Xinyi Wang1, Xueyi Li1, Hao Hou1, Bo Yu1 
TL;DR: In this paper, the authors defined a dimensionless number Ut for the start-up of weakly compressible Herschel-Bulkley fluids in pipelines and showed that the effect of these five parameters on the applicability of the quasi-steady assumption depends only on the value of Ut.