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Recently, Zou et al. (2020a) published a theoretical analysis on the radial flow of a Bingham fluid, where they argued that the classical analysis by Dai and Bird (1981) violates the mass conservation. The present discussion aims to clarify this conflict between those two studies. It is noted that Zou et al. (2020a) presumed the gap-wise mass flux is negligible in the mass conservation equation, while Dai and Bird (1981) did not require so in their model, and this is found to be the origin of the conflict. In fact, Dai and Bird (1981)’s model is shown to not violate the mass conservation. Therefore, those two models should be viewed as separate models derived from different perspectives. Details of the major difference between the two models are discussed.

In this work, the momentum and heat transfer characteristics of a time-dependent flow of Bingham plastic fluid over a heated isothermal sphere have been investigated numerically over wide ranges of conditions: Reynolds number, 5 ≤ Re ≤ 120, Bingham number, 0.1 ≤ Bn ≤ 100, Prandtl number, 0.7 ≤ Pr ≤ 100, frequency, π/4 ≤ ω* ≤ π and amplitude, 0 ≤ A ≤ 0.8. The influence of the fluid yield stress and inertia due to the imposed flow pulsations on the flow and thermal fields have been examined in detail. Detailed structure of the flow and temperature fields are analysed in terms of the instantaneous streamlines, isothermal contours, yielded/unyielded zones, surface pressure profiles, time-average drag coefficient and surface- and time-average Nusselt number. The influence of the frequency and amplitude of pulsations on the size of yielded (fluid-like) and unyielded (solid-like) zones is considered in order to understand convective heat transport. The size of yielded zones is seen to be in phase with the imposed pulsating velocity. However, the yield stress effects suppress the influence of flow pulsations. The temporal evolution of the drag coefficient and Nusselt number lag the imposed pulsating flow by different degrees thereby indicating the inherently different evolution of the momentum and thermal boundary layers. Broadly, the pulsating flow conditions may lead to up to 20% augmentation in heat transfer provided there is a moderate degree of advection and/or when the fluid yield stress effects are weak, i.e., small Bingham numbers. Thus, the maximum benefits of pulsating flow accrue in Newtonian fluids only. Finally, the present values of the time-average Nusselt number have been consolidated in the form of a predictive expression.

Grouting is a commonly used technique in rock engineering to enhance the joint strength and improve the stability of surrounding rock. Grout penetration characteristic is controlled by grouting parameters and has a significant role on practice. In the study, a numerical manifold method (NMM) for grout penetration process simulation in fractured rock mass is firstly proposed. The fluid flow behaviour of the grout is assumed to be a Bingham fluid and control equations are established using discrete fracture network model. The global discretization equation, element sub-matrixes and NMM simulation algorithm for grouting are presented. Then, numerical tests for grouting process in a single fracture and a regular fracture network are conducted firstly to verify the proposed NMM grouting model by comparing with analytical solutions and experimental results. Furthermore, the effects of mesh size, fracture and slurry parameters on the grouting performance are systematically investigated using a random fracture network example. The numerical results indicate that the grouted zone and propagation depth decrease as the mesh size of numerical model and yield strength increases, while it increases as initial fracture aperture and grouting pressure increases.

In this paper, experimental experiments were conducted using advanced computerized rheometer. The lean solid slurry (10 to 40 percent by weight) requires an immense amount of water and requires high-energy pumping power. The rheological properties are highly dependent on shear strength, solid density and particle size distribution. The plastic viscosity and yield stress enhanced with a solid concentration. At higher concentrations of solids, the experimental results fitted well with the Bingham plastic model. The results reveal that the plastic viscosity and yield stress of the slurry samples are increased due to finer particles. Bingham plastic viscosity depends primarily on solid concentration and particle size.

Ice-containing cemented paste backfill (ICPB) is a novel type of backfill material that has both the advantages of traditional CPB and the underground cooling function. The pipeline transport characteristics of ICPB need to be investigated to promote its application, which are influenced by the rheological properties. The objective of this study is to investigate the rheological properties of ICPB by means of experimental and computational fluid dynamics (CFD) methods. The rheological parameters were measured using a rheometer and the slump test was performed in a cylinder slump. A calculation model that considered the slump mold lifting and the ice particle phase change was established to simulate the cylindrical slump. The results indicate that the ICPB behaved as a Bingham fluid. The yield stress, plastic viscosity, and thixotropy increased with an increase in the ice/water ratio and concentration, while the cylindrical slump decreased under the same variation. The simulation results of the cylindrical slump were compatible with the experimental results. Furthermore, the numerical study indicates the slump increased when the test temperature was increased from 285 K to 305 K. The results found in this study can be used as a reference for the pipe design of ICPB.

Bio-mimicking the natural structure is one of the important aspects which have been developed with various inventions in the fields of engineering. There has been a subsequent effort to mimic the branched structure that can be seen in the leaves of trees and also in the branched structure of veins and arteries in the human body. This is done on the Lifting plate Hele-Shaw Cell (LHSC) setup. In LHSC, Bingham plastic fluid is squeezed between two parallel plates and then one of the plates is lifted up. This leads to some indefinite branched pattern commonly known as viscous fingers or micro fractals. Viscous fingering can be obtained using Newtonian fluid, Bingham plastic fluid. In this paper Bingham plastic fluid is used to study. Saffman-Taylor instability explains the formation of these viscous fingers. The main part of this paper is to control the formation of the viscous fingers and to get it in the desired shape. This can be done by providing some anisotropies on the surface of the plate in the form of pits or holes. The experiments are conducted under wide range of lifting velocities in Hele-Shaw cell. The geometrical dimensions of the viscous fingers are measured and their variation with the lifting velocity is plotted.

This study examined the magnetorheological (MR) behavior of magnetite-based MR fluids according to the magnetite concentration, magnetic field strength, and different viscosity of silicone oil as the carrier fluid. To this end, an experimental design was chosen to decrease the experimental error and provide a better rheological interpretation. The flow behavior parameters increased remarkably with increasing medium viscosity and nanoparticles (NPs) concentration, whereas the magnetic field strength had a milder effect, exhibiting a saturation value above which its effect became almost negligible. Moreover, both the Bingham plastic and power law models were found to fit their flow behaviors well. Almost all the critical rheological parameters of the aforementioned models experienced remarkable improvement after increasing the magnetic field strength, NPs concentration and carried fluid viscosity. In addition, mathematical correlations were derived to model each of the rheological parameters such as plastic viscosity and yield stress (for Bingham fluid model) and the consistency and power-law indices (for power-law model).

The aiding-buoyancy mixed convection heat transfer in Bingham plastic fluids from an isothermal cylinder of elliptical and circular shape in a vertical adiabatic channel is numerically investigated. For a fixed shape of the elliptical cylinder E = 2 (ratio of major to minor axes), the effect of confinement is studied for three values of blockage ratio, B, defined as the ratio of the channel width to the circumference of the cylinder/π, as 6.5, 2.17 and 1.3. In order to delineate the role of cross-section of the cylinder, results are also presented here for a circular cylinder of the same heat transfer area as the elliptical cylinder. The results presented herein span the range of conditions as: Bingham number, 0 ≤ Bn ≤ 100, Reynolds number, 1 ≤ Re ≤ 40, and Prandtl number, 1 ≤ Pr ≤ 100 over the range of Richardson number Ri = 0 (pure forced convection) to Ri = 10. Extensive results on drag coefficient, local and surface averaged values of the Nusselt number and yield surfaces are presented herein to elucidate the combined effects of buoyancy, blockage ratio and fluid yield stress. The morphology of the yield surfaces shows that the unyielded plug regions formed upstream and downstream of the cylinder grow faster at low Reynolds numbers with the increasing yield stress effects under the weak buoyancy forces, i.e., small values of Grashof or Richardson number. The heat transfer enhancement is observed with the increasing channel-confinement due to the sharpening of the temperature gradients near the surface of the cylinder. The average Nusselt number shows a positive dependence on the Reynolds number, Prandtl number and Richardson number irrespective of the shape of the cylinder or the type of fluid. By employing the modified definitions of the dimensionless parameters (based on the two choices of the overall effective fluid velocity), predictive correlations have been established for estimating the value of the average Nusselt number in a new application.

During well drilling operations, unexpected gas influx may take place when the bottom hole pressure falls below the pore pressure. The conventional procedure to control the influx consists of shutting-in the well and waiting for pressure stabilization. The pressures measured at the surface after the well closure and the pit gain are used to estimate the pore pressure, the gas density, and the kick magnitude. However, the drilling fluid compressibility and rheology can undermine pore pressure transmission to the surface, which can affect the pit gain and the well closing pressure. The current work presents a transient compressible isothermal mathematical model to predict pit gain and pressure transmission along the well during gas kicks. The model is based on the balance equations of mass and momentum that are solved by the method of characteristics. Three types of drilling fluids are analyzed: Newtonian, Bingham Plastic and thixotropic. The Darcy's law is used to represent the gas influx through the rock formation. The results indicate that the usual pressure balance used to estimate the pore pressure may lead to mistaken values and also that the drilling fluid compressibility and rheology have considerable effect on the pit gain and on the gas volume that invades the well. In all cases investigated, the gas volume within the well is at least 50% higher than the pit gain. Therefore, drilling fluid compressibility cannot be neglected on the estimation of the formation fluid volume within the well.

To understand the effect of particle size on magnetorheological effect two magnetorheological (MR) fluids, composed of nano-hollow spheres (NHSs), of diameters 250 nm (MRF250) and 700 nm (MRF700), are studied. The results are compared with their solid counterpart with Fe3O4 nanoparticles (NPs) based MR fluid of 100 nm diameter (MRF100). To understand the MR mechanism the flow curves (shear stress vs shear rate) are fitted with different established models and our samples are found to follow the Bingham Plastic model. The yielding behavior of the MR fluids is found to be morphology dependent. The MR fluid with larger particles show maximum yield stress ∼830 Pa at an applied field 0.4 T, due to the combined effect of larger surface area and higher magnetism. Hollow nano spheres show better stability than that of NPs due to compatible density with the carrier fluid.

In this paper, thermosolutal natural convection in an open porous cavity filled with Bingham fluids has been simulated numerically. Fluid flow, heat and mass transfer, and yielded/unyielded parts have been conducted for certain pertinent parameters of Rayleigh number (Ra = 104-106), Darcy number (Da = 10-2-10-6), porosity (e = 0.1-0.9), Lewis number (Le = 2.5-100), the Buoyancy ratio (N = 0.1-20), and Prandtl number (Pr = 1-100). Moreover, the Bingham number (Bn) is studied in a wide range of different studied parameters. Results indicate that the heat and mass transfer increases and the unyielded section diminishes as Rayleigh number rises. For specific Rayleigh and Darcy numbers, the increase in the Bingham number decreases the heat and mass transfer. However, the decreases in heat and mass transfer due to Bingham number becomes stronger as Darcy number drops from Da = 10-2 to 10-6. The growth of the Bingham number expands the unyielded sections in the cavity generally in different Darcy numbers and porosities. The increases in Darcy number changes the size and shape of the unyielded section while heat and mass transfer drop gradually. For fixed Rayleigh, Darcy and Bingham numbers, the unyielded region is decreased by the augmentation of the porosity. In addition, heat and mass transfer augments gradually as the porosity increases. The enhancement of buoyancy ratio increases heat and mass transfer for the studied parameter. The rise of Lewis number has a marginal effect on heat transfer, but the mass transfer rises considerably.

It is well known that the Non-Newtonian Bingham fluid flow in porous media does not obey the conventional linear Darcy’s law due to the yield stress for the Bingham fluid: There exists a threshold pressure gradient, which means that the seepage flow only happens when the threshold pressure gradient is overcome. The principle of non-Darcy seepage flow with the threshold pressure gradient is also applicable into the situation of the fluid flow in the low-permeable porous media. Here, a nonlinear moving-boundary mathematical model is built for the semispherical centripetal non-Darcy seepage flow with the threshold pressure gradient in a three-dimensional infinite heavy oil reservoir with the type of Bingham fluid; wherein the moving boundary conditions are incorporated for describing the effect of the threshold pressure gradient. In consideration of the strong nonlinearity of the model, the similarity transformation method is applied into obtaining the exact analytical solution of the model. In order to keep full self-similarity for the model, the inner boundary condition is set as variable flow rate that increases linearly with the time. As a result, an exact analytical solution for the nonlinear moving-boundary mathematical model of semispherical centripetal non-Darcy seepage flow with the threshold pressure gradient is obtained. The existence and the uniqueness of the exact analytical solution are also strictly proved. It is also theoretically proved that as the threshold pressure gradient tends to zero, the exact analytical solution can be reduced to that of a mathematical model of semispherical centripetal Darcy’s seepage flow. The presented exact analytical solution can be used for strictly verifying the validity of the numerical methods for solving the three-dimensional moving boundary models of non-Darcy seepage flow with the threshold pressure gradient in the actual engineering problems. From the exact analytical solution, it is also revealed that when the threshold pressure gradient exists, the spatial pressure distribution exhibits an instructive feature of compact support; as the threshold pressure gradient tends to zero, the sensitivity of its effect on the transient distance of the moving boundary and the transient pressure will grow, which reveals the difficulty in accurately determining the position of the moving boundary by the numerical methods and the serious uncertainty problem in the interpretation of the threshold pressure gradient by the pressure transient analysis method in engineering as the threshold pressure gradient is rather small. Through the comparison of the two different exact analytical solutions that corresponds to the two different models with and without incorporating the moving boundary conditions for describing the effect of the threshold pressure gradient, it is demonstrated that when the moving boundary conditions are not incorporated in the modeling, the effect of the threshold pressure gradient on the spatial pressure distribution, the transient pressure and the productivity index can be overestimated largely. Therefore, it is very necessary to incorporate the moving boundary conditions in the modeling of non-Darcy seepage flow with the threshold pressure gradient. The study in the paper definitely provides solid theoretical basis of fluid mechanics for the relevant engineering applications in the development of heavy oil reservoirs and low-permeable reservoirs in petroleum engineering and in the development of water resources in low-permeable formations in hydraulic engineering.

The main aim of this paper is to measure the induced torque needed to rotate a steel fiber, hence an experimental and parametrical analysis of factors governing steel fiber alignment in cement pastes and mortar, rotating from static position and rotating in a dynamic fluid is here presented. To aim this objective, a set of rheological tests has been conducted to assess the torque necessary to rotate steel fibers immersed into different fresh cement paste and mortar mixes with Bingham fluid behaviour. Fibers of different aspect ratios (length/width) and different geometry, straight and hooked-end, have been evaluated as they are the more commonly used. On the other hand, different parameters (type of mixture, size of aggregates, volume fraction of aggregates) affecting cement mixtures are also analysed and their influence in fiber orientation discussed. Fiber alignment depends on external torques applied to fibers, immersed into a cement-water-aggregate viscous system, that can be produced during or after casting. The flowability of the fresh suspension with fibers produces a load/pressure that generates a torque that can align them. Fiber alignment is a main goal to pump the fresh material. Hence, the factors that govern fiber alignment are studied which increase the post-cracking strength of cement-based composites under load along its life service due to casting or pumping. To that end, a set of tests has been conducted to assess the torque necessary to rotate steel fibers immersed into different fresh cement paste and mortar mixes with Bingham fluid behaviour. Fibers of different aspect ratios(length/width) and different geometry (straight and hooked-end) have been evaluated. On the other hand, different parameters (type of mixture, size of aggregates, volume fraction of aggregates) affecting cement mixtures are also analysed and their influence on fiber orientation is discussed. The values obtained here are between 1 and 14 N . mm min of dynamic yield torque and 0.1 and 0.5 N . mm min for viscoplastic torque per fiber, depending on fiber geometry, are helpful to improve the fiber alignment in cement-based composites reinforced with fibers through a design and production based on these parameters., Special acknowledgment, appreciation and recognition to the IETcc-CSIC collaboration using the Viskomat™ NT rheometer within the framework of the Excellence Project MINECO BIA2013-47876-C2-1P. The authors want also acknowledge the laboratory of Materials of Architecture, Universidad Poiltécnica de Madrid.

This article evaluates the slurry viscosity of radioactive waste. Hanford waste is a motley mixture of particle sizes and densities composed of metal and oxide particles with constituents spanning much of the periodic table stored at high ionic strength and high pH. Hanford wastes have traditionally been represented as simply an ideal Bingham plastic, but this rheological approximation often provides a poor fit from 0 to 200 1/s, precisely the range of interest for engineering design of waste transport and mixing systems. A modified Cross formulation inclusive of a yield stress is used to fit stress-strain rate data for reconstituted Hanford REDOX sludge waste, measured by increasing shear-rate (up-ramp) and decreasing shear-rate (down-ramp) sweeps. This continuous single equation formulation quantitatively matches experimental data better than other rheological models including the Bingham plastic and Herschel-Bulkley approximations. The increase of viscosity and yield stress from up ramp to down ramp suggests the formation of particle microstructure during shear due to attractive forces.

The aim of this experimental study is to determine the jet breakup of non-Newtonian, Bingham plastic slurries in air, notably to obtain an experimentally verified formula for the breakup length. The ash-to-water concentration varies between appr. 9% and 57% resulting in Ohnesorge-numbers between 0.0215 and 0.0476 . The Bingham plastic fluid discharge from a circular orifice and the jet exit Weber-numbers were varied between 983 and 46866 . The Hedstrom-numbers are between 172 and 235, the Reynolds-numbers were in the range of 906–7169 and the tested Froude-numbers are between 7.06 and 42.13 at standard temperature and ambient pressure. Most of our experiments fall into the second wind-induced regime. A linearly increasing correlation was found for the dimensionless breakup length as a function of We , the Reynolds-, and the Froude-number. The rheology and the particle size distribution of the (fly and bottom) ash were measured and are reported, respectively.

Effects of the orientation and apex angle on the settling velocity of conical particles in Bingham plastic fluids are numerically investigated over a Reynolds number range of 1 ≤ Re ≤ 100, Bingham number range of 0 ≤ Bn ≤ 100, and cone angle range of 20° ≤ α ≤ 150°. Governing equations (of continuity and momentum) are solved numerically using the finite element method to obtain velocity and pressure fields that are postprocessed to obtain values of the drag coefficient. Furthermore, the effect of cone orientation on the flow field is visualized and explored in terms of streamline contours and the morphology of yielded/unyielded regions. Finally, the obtained values of drag are correlated via a simple predictive expression in terms of the modified Reynolds number. The effect of the cone angle on drag is found to be moderate because the drag force acting on the lateral surface is a small fraction of the overall drag.

This paper presents the results of a study that used the constant shear strain test to characterize the strain rate dependence of asphalt mastic’ shear stress. A set of shear strain-stress tests was conducted using the dynamic shear rheometer of the Peak Hold program, which can apply constant shear strain to a specimen at a fixed rate throughout testing. The laboratory specimens consisted of two asphalt binders with four different filler volume fractions, respectively. The stress and corresponding strain were measured under various shear strain rates at 40 °C. The relation between the peak stress and strain rate was analyzed to identify the fluid type of asphalt mastic, and a regression model between the peak stress of asphalt bitumen and mastics was derived to predict the peak stress of mastics from bitumen. Then, by combining the regression model with a simple expression of the stress-strain curve, a prediction model was established to predict the shear strain-stress properties under different strain rates and filler volume fractions. Tests on mastics fabricated from a third asphalt binder and another mineral filler were carried out to obtain the shear stress-strain under different strain rate, and these tested results were compared with the results predicted from the equation to show the validity of the prediction model. Finally, the derivation of the prediction model with respect to the strain at different strain rates was used to characterize the damage of mastics during deformation. The results showed that peak stress increased linearly with strain rate, and asphalt mastic could be assumed to be Bingham fluid at 40 °C. The reliability analysis of the prediction model showed that the average error in peak shear stress between the value calculated and measured was 9.8%. The peak shear stress prediction equation, together with the simple expression of the stress-strain curve, provided a reasonably good prediction of asphalt mastic shear stress-strain behavior. Asphalt mastic at higher strain rates had a greater value of d σ / d e , but its decrease was aggravated by increased strain rate.

International audience; We study the steady incompressible flow of a Bingham fluid in a thin T-like shaped domain, under the action of given external forces and with no-slip boundary condition on the whole boundary of the domain. This phenomenon is described by non linear variational inequalities. By letting the parameter describing the thickness of the thin domain tend to zero, we derive two uncoupled problems corresponding to the two branches of the T-like shaped structure. We then analyze and give a physical justification of the limit problem; Dans ce travail nous étudions l'écoulement stationnaire d'un fluide incompressible de Bingham, dans un domaine mince en forme de T, sous l'action d'une force extérieure et avec des conditions de non glissement aux parois. Ce phénomène est décrit par des inéquations variationnelles non linéaires. En faisant tendre vers zéro le petit paramètre qui caractérise l'épaisseur du domaine mince, on obtient à la limite deux problèmes découplés, correspondant chacun à l'une des branches du T-domaine. Ensuite on analyse le problème limite et on en donne une interprétation physique.

The aim of this paper is to perform a model to understand and to predict the dynamic behaviour of steel fibres immersed in fresh cementitious materials when exposed to Homogeneous Magnetic fields. Fibres behaviour is of especial interest to improve and develop a method to achieve the alignment of fibres in reinforced composites by means of magnetic fields. The torques and forces that a magnetic field summit a ferromagnetic fibre during its alignment find an opposition, in a fresh cementitious composite considered as a Bingham fluid: shear rate () and yield stress () and plastic viscosity (). The torque necessary to rotate a single fibre is determined through a rotational rheometer and the relation between its geometry and the fresh cement rheology is determined. In this work, the alignment of fibres under magnetic fields within the range of 20 mT to 80 mT immersed in fresh mortars and fresh cements is studied. The orientation factor of the fibres after the magnetic field has been obtained. The probabilities of success depending on the initial angle of the fibres are also showed. The model to predict the alignment of fibres in cement-based materials presented here can be used also for different magnetic and rheological ranges. Sin financiación 4.419 JCR (2019) Q1, 10/63 Construction & Building Technology, 11/132 Engineering, Civil; Q2, 86/314 Materials Science, Multidisciplinary 1.491 SJR (2019) Q1, 15/248 Building and Construction No data IDR 2019 UEC

© 2018 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Supplementary Raw Research Data, is open data under the CC BY license http://creativecommons.org/licenses/by/4.0/ This author accepted manuscript is made available following 24 month embargo from date of publication (October 2018) in accordance with the publisher’s archiving policy, The start-up flow of a Bingham plastic in a channel is considered and Safronchik’s solution [1] for the initial evolution of the yield surface and the core velocity is revisited. Stricter time bounds for the validity of the above solution are derived and the solution is extended to include the velocity profile in the evolving yielded zone. Comparisons are made with another approximate solution derived under the assumption that the velocity in the yielded zone is parabolic adjusting with the evolving yield surface. This approximation performs well for small values of the yield stress, or, equivalently, for large values of the imposed pressure gradient.

The linear instability characteristics of a core-annular pipe flow of a Newtonian fluid and a Bingham fluid separated by a mixed region is investigated. The main objective of this study is to investigate the effect of the yield stress of the annular fluid on the stability behaviour. The present linear stability analysis reveals that the corkscrew mode is the most dangerous mode for the parameters considered. The Bingham number seems to destabilise the flow via modifying the velocity profile. The mechanism of instability is found to be inviscid in nature. An energy budget analysis shows that the energy due to the gradient of viscosity perturbation in the radial direction, and the transfer of energy from the basic flow to the perturbation via the “Reynolds stress” term are responsible for the instability observed. The positive contributions of these terms towards instability increases with increasing the yield stress. The critical Reynolds number also decreases with increasing the Bingham number for the corkscrew mode, which indicates the destabilising influence of the yield stress.

Nowadays, development of heavy oil usually demands massive hot water injection and meanwhile produces considerable carbon footprint. Radiofrequency (RF) heating, as a “Non-aqueous” method, has potentials to be a cleaner and efficient way for heavy oil development in near future. In this paper, we presented a novel numerical model for simulating non-Newtonian Bingham fluid flow in heavy oil reservoirs based on RF heating. Compared to previous studies, this paper focuses on issues including: (1) Application of RF heating in heavy oil reservoir; (2) Non-Darcy flow induced by threshold pressure gradient (TPG) of Bingham fluid; (3) Temperature dependent TPG and viscosity; (4) Two-way coupling between non-Darcy flow, transient heat transfer and electromagnetic (EM) field. To incorporate TPG in numerical analyses, an effective method was utilized by modifying the gravitational acceleration vector in Darcy's law. This method was verified with analytical solution. By doing this, the induced moving boundary by TPG can be simulated, and pressure-disturbed area can be determined. Results show that RF heating significantly mitigates the impediment induced by TPG and high viscosity near well. The moving boundary stops motion at around 1000th day of production and the extreme disturbed distance is 63 m. Besides, it is found that no matter whether TPG is considered or not, RF heating has a positive impact on the reservoir development. However, for the production time less than 1000 days, RF heating is more effective when TPG is considered. Finally, we also found it very necessary to incorporate TPG in the simulations to determine optimal well spacing. If TPG is neglected in kinematic equation, the optimal well spacing would be overestimated by over 50%. At the same time, the change of TPG value with temperature cannot be ignored. Otherwise, the optimal well spacing would be underestimated by 15%. This paper reveals the potentials of RF heating method for non-Newtonian Bingham fluid production and provides an alternative way for clean, environmental, and highly efficient development of heavy oil reservoir.

Dense granular materials are universal in nature and some common examples of this kind of materials in our daily lives are sand, rice, sugar etc. Research in this area is motivated by numerous applications encountered in industrial processes, such as hopper discharge, chute flow, moving beds, sandpipe flow, etc. and also in geophysics for the description and prediction of natural hazards like landslide and rock avalanches. Here, a continuum description of these granular flows is appropriate. Granular materials in liquid-like state show strong non-Newtonian behavior, which is typically described by phenomenological constitutive laws with local rheology. Very often, fluidization and flows of granular materials are localized in thin shear bands, whereas the granular material remains in solid-like state outside these bands. In this paper we establish a benchmark problem for granular materials, namely as Couette flow which is a very common example for granular materials in industrial application. We formulate the rheology for the continuum approach in the framework of the regularized version of a Bingham fluid and use advanced numerical methods regarding discretization as well as solution aspects, so that we can provide mesh independent results with two different software packages, Featflow and Openfoam, which can be used for validation and evaluation of the different methods and approaches. The authors thank the German Research Foundation DFG for funding under the grants TU 102/44-1 and SCHW 1168/6-1 within the pilot for transnational cooperation of the Dutch Technology Foundation STW and the DFG. This work was also supported by DAAD.

The effect of limestone powder (5%, 10% and 20%) on the rheological properties, drying shrinkage and mechanical properties of alkali-activated slag/fly ash grouting materials (AASFGM) are investigated. The results show that AASFGM with or without limestone powder conforms to the Bingham fluid model. The incorporation of fine limestone powder into AASFGM has a positive effect on rheology, strength and shrinkage properties. The yield stress, plastic viscosity and drying shrinkage properties activated by the solid waterglass are larger than those of the liquid type. However, the paste activated by the solid waterglass with 10% limestone powder exhibited satisfactory compressive strength and drying shrinkage after curing for 28 d. The shrinkage was decreased for finer limestone particle packing and filling to improve the compactness of AASFGM.

In order to investigate hydrodynamic characteristics of Bingham porous-flow mechanics in a heavy oil reservoir, this paper originally proposes a physical model of Bingham fluid flow for a horizontal well in a heavy oil reservoir. A corresponding mathematical model is established and solved. A series of typical pressure and pressure derivative curves are drawn by the use of the semi-analytical solution of the mathematical model. Hydrodynamic flow characteristics of Bingham fluid are thoroughly analyzed. Through the recognition of flow regimes from the typical curves, it is found that the flow process of Bingham fluid mainly includes the early radial flow regime, linear flow regime and late pseudo-radial flow regime. The curves controlled by different boundary conditions are especially studied, and it is found that the late curve shape, especially the shape of pressure derivative curve, differs completely for the various property of boundary. The curve sensitivity to different model parameters, such as dimensionless threshold pressure gradient and horizontal wellbore length, is deeply discussed. The findings are as follow: except the pure wellbore storage regime, the threshold pressure gradient influences the hydrodynamic flow behavior in all the regimes; the curve of Bingham fluid governed by the threshold pressure gradient upward deviates from that of Newtonian fluid; and the deviation of the curves increases with the increase of the threshold pressure gradient and the elapsed time. The research results of this paper sufficiently demonstrate the essential property of non-Newtonian porous-flow mechanics.

Substantially large pressure surges are generated while drilling a well due to tripping operations in which a central drillstring is being moved up or down through non-Newtonian fluid. The presence of these subsurface surge pressures must be considered and determined in almost every well drilled. Wells exhibiting high geothermal temperature gradient further complicate the determination of wellbore pressures since the classical viscometer does not characterize the non-Newtonian nature of fluids accurately at elevated temperatures. More importantly, rheological model selection also plays a key role for effectively proposing safe tripping speeds without violating the mud window constraints. Herschel-Bulkley rheological model has gained more reputation among others due to better predictions of wellbore hydraulic pressures as suggested by the American Petroleum Institute. 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. The proposed analytical method was applied on unweighted fresh water sepiolite mud as a non-Newtonian fluid since the sepiolite muds are among the few water based muds performing adequately at extreme temperatures as the synthetic and oil base muds. Already measured rheological constants of selected fluid system using both HTHP dynamic rheometer and classical viscometer were considered to obtain surge pressures at ambient to extreme temperature ranges. The results are compared with already developed Burkhardt method for Bingham Plastic fluid and Schuh method for Power Law fluid and other proposed numerical and analytical solutions. Substantial differences on the pressure surges between the conventional viscometer and the HTHP rheometer measurements were also presented. The precision of the developed model is shown to be acceptable for most practical applications. Being operationally easy and applicable with a convenient solution code make the proposed model straightforward to be used as a part of drilling software.

For this data article, the accuracy of different rheological models in estimation of rheological parameters of a bentonite-gel, water-based mud under ambient and elevated conditions were examined. The ambient conditions are pressure of 14.7 psia and 80 °F temperature while the elevated conditions are constant pressure of 5000 psi and different down hole temperatures of 120 °F, 160 °F and 200 °F. An OFITE, eight (8) speed rotational viscometer model 800 was used for ambient rheological properties measurement while a Chandler Model 7600 HTHP Viscometer was used to carry out rheological measurements at high temperature and pressure condition. The various rheological models under investigation are the Newtonian, Bingham Plastic, Power Law, American Petroleum Institute model (API 13D), Herschel–Bulkley, Unified and Casson Models. Keywords: Ambient condition, Rheological models, OFITE rotational viscometer, Chandler HTHP viscometer, Water based mud

The karst tunnel water inrush disaster causes not only casualties, but also serious damage to the groundwater system. At present, the grouting technology is mainly to adopted to control water inrush disaster. But the theory of dynamic water grouting is imperfect, and the grouting material is single. By the technical means of combining the theoretical analysis, the indoor test and the engineering projects, this paper deeply researches on the slurry diffusion and plugging mechanism of dynamic water grouting. In this paper, the dynamic water plugging criterion of the glass fiber cement slurry is formulated, and the flow pattern test is carried out for cement slurry and consolidation body with different glass fiber proportions. According to the analysis of experiment conclusion and engineering effect, this paper draws the following conclusions. Firstly, for the slurry mixed with a small amount of glass fiber (≤0.4%), when Power-law fluid changes to Bingham fluid, the water-cement ratio is 0.8 and when Bingham fluid changes to Newtonian fluid, the water-cement ratio is 1.2. In addition, when the water-cement ratio of the pure cement slurry is large, the flow pattern of the slurry is constant. Secondly, when glass fibers are added to the pure cement slurry, the fluidity of the pure cement slurry will be reduced. The larger the ratio of glass fiber is, the greater the influence is. Thirdly, by using glass fiber cement slurry for dynamic water grouting, the condition of water inrush is effectively improved.

We study material flow in the vicinity of single shear bands in high strain-rate (10(4) -10(5) per second) deformation of metals. Shear band plastic flow, in three different materials, is shown to resemble unsteady planar Couette flow (Stokes first problem) of a Bingham fluid. Equivalent shear band viscosities and yield stresses are obtained, with the former similar to liquid metal viscosities and the latter being similar to 0.5 times the band nucleation stress. Reynolds and Bingham numbers, computed based on the shear band displacement measurements, are suggestive of boundary layer formation, consistent with the severe localization of deformation within shear bands. (C) 2018 Elsevier Ltd. All rights reserved.

At mid to high concentrations, fine mine tailings are non-Newtonian, and their rheology is commonly expressed as Bingham plastic. Discharges of such fine materials in tailing storage facilities form shallow channels. In this short communication, exact analytic expressions to relate the volume flow per unit width and the flow depth are derived for a Bingham plastic in terms of a newly-defined dimensionless parameter. Simplified approximations, valid for the near-plug and quasi-Newtonian fluid limits are proposed.

Buoyant miscible displacement flow of a Bingham fluid by a Newtonian fluid along a vertical plane-channel is studied, in the high Peclet number regime. The displacing fluid is lighter than the displaced fluid and the flow direction is upwards, hence density-unstable. The flow is effectively governed by 4 dimensionless parameters: the Newtonian Bingham number (BN), the viscosity ratio (m), the Reynolds number (Re), and modified Froude number (Fr). This is a simple model for micro-annulus formation in the primary cementing of oil and gas wells. The micro-annulus layers correspond to residual drilling mud that remains on the walls after displacement. Here we show that in density unstable situations static residual wall layers can exist for yield stresses below the minimum for density stable regimes. The layers are partially static and may also be thicker than the fully static layers encountered in density stable flows. Adverse buoyancy gradients (represented here by large χ = 2 R e F r 2 ), also seems to promote instability of the flow. These instabilities are various, ranging from Rayleigh–Taylor type frontal instabilities, through to Kelvin–Helmholz type inertial waves, and more viscous-controlled inverse bamboo and mushroom morphologies. We present an overview of flow regimes within our parameter space and approximate onset criteria. It is unclear whether or not the instabilities observed result in improved fluid displacement efficiency.

We consider the steady axisymmetric Poiseuille flow of a Bingham plastic under the assumption that both the plastic viscosity and the yield stress vary linearly with pressure. An analytical solution is derived for the case where the growth coefficients of both rheological parameters are equal, which is indeed a reasonable assumption for certain oil-drilling fluids allowing the existence of a separable solution with a cylindrical unyielded core. The conditions for the occurrence of flow and the effects of the growth coefficient on the radius of the unyielded plug, the velocity profiles and the pressure distributions are discussed.

To better understand the factors that influence seafloor serpentinite mudflows, such as those recently documented on the Marianas seamounts, we have conducted rheological measurements on composite serpentine-brucite suspensions at 7 °C and a salt concentration of 0.6 M. The resulting flow curves were fitted by the Bingham fluid model, from which the Bingham yield stress and plastic viscosity of each suspension was determined. Both the yield stress and plastic viscosity increase as the water content of the suspension decreases. Increasing the brucite fraction in the solid mixture results in an increase in yield stress and a decrease in viscosity of the suspension for the same water/solid ratio. Physicochemical parameters such as pH, temperature and electrolyte concentration also moderately affect the rheology of the suspension, but the influence is not as significant as has been previously observed for suspensions containing smectite. The results suggest that mineral composition of the serpentinite mud, especially the abundance of brucite, has as much of an impact as water content on variable mudflow behaviors such as those observed at the Mariana seamounts.

In construction of slurry engineering, especially in sand stratum of high permeability, small size fine particles in slurry are likely to flow through the stratum and washed away. In this study, nine groups of slurry fluid property tests were performed using a NXS-11A rotary viscometer in order to investigate infiltration of slurry in sand stratum. Additionally, a series of penetration tests were also conducted by a self-designed infiltration device. Experimental results show the test slurry meet characteristics of Bingham fluid at a medium to high shear rate, while it conforms to the Herschel-Bulkley model at a low shear rate. Darcy's law is no longer applicable to infiltration of slurry in sand stratum, because of the initial hydraulic gradient. The infiltration rate (vs) is not strictly linearly related to the hydraulic gradient at small hydraulic gradient (i). It is also indicated that the yield stress of slurry is the fundamental cause of initial hydraulic gradient during the infiltration process of slurry in sand stratum. The yield stress has a positive correlation with the initial hydraulic gradient. Ideally, initial hydraulic gradient is proportional to the dynamic shear force of slurry.

The linear stability of thermocapillary liquid layer of a Bingham-plastic fluid is studied. Due to the yield stress of Bingham fluid, there is a plug region in the flow, which divides the yielded flow into two regions. When the flow is subjected to a small perturbation, the velocity perturbation below the upper surface of plug region is negligible, while the temperature perturbation can be found in all flow regions at moderate and small Prandtl numbers (Pr). The perturbation amplitude of the upper surface of plug region decreases rapidly with the increase of Pr. The preferred modes are the upstream oblique wave and the downstream streamwise wave at small and large Pr, respectively. The effects of the yield stress, gravity and the interfacial heat transfer on the flow stability are discussed. The perturbation amplitude only appears above the plug region, which differs from the cases in the plane Bingham–Poiseuille flow and the thermocapillary liquid layer of a Carreau fluid.

The Bingham fluid model represents viscoplastic materials that display yielding, that is, behave as a solid body at low stresses, but flow as a Newtonian fluid at high stresses. In any Bingham flow, there may be regions of solid material separated from regions of Newtonian flow by so-called yield boundaries. Such materials arise in a range of industrial applications. Here, we consider the helical flow of a Bingham fluid between infinitely long coaxial cylinders, where the flow arises from the imposition of a steady rotation of the inner cylinder (annular Coutte flow) on a steady axial pressure driven flow (Poiseuille flow), where the ratio of the rotational flow compared to the axial flow is small. We apply a perturbation procedure to obtain approximate analytic expressions for the fluid velocity field and such related quantities as the stress and viscosity profiles in the flow. In particular, we examine the location of yield boundaries in the flow and how these vary with the rotation speed of the inner cylinder and other flow parameters. These analytic results are shown to agree very well with the results of numerical computations.

Modeling of cement grout flow in rock fractures is important for the design, monitoring and execution of rock grouting that is widely used in a variety of rock engineering applications. This study presents a mathematical model based on the Reynolds flow equation for cement grout flow in a homogeneous water-saturated rock fracture. The model is based on two-phase flow, i.e. grout as a Bingham fluid and groundwater as a Newtonian fluid, and is used for investigating the importance of the water phase in rock grouting. The modeling results for the two-phase flow generally show the importance of the water phase that can significantly affect the pressure distribution and grout penetration in the fracture, especially under the condition of grout hardening. Such effects depend on the viscosity ratio between the grout and groundwater, which becomes increasingly important for cases with smaller values of the viscosity ratio. The grout density also affects the grout penetration length. Applying an analytical solution based on single-phase flow, i.e. neglecting the impact of groundwater flow, for modeling grout injection, will generally overestimate the penetration length.

Hydro-instability of hyper-concentrated flow in the Yellow River is one of the focuses of Chinese sediment research. In this research, the constitutive relations and the equations of the hydro-instability are first explores. Based on the experimental results and field data, Bingham fluid model is simple and appropriate for the hyper-concentrated flow. Next, the hydro-instability characteristics of hyper-concentrated flow in the Yellow River are discussed, which is judged with the neutral curve by using perturbation method and the summarized Bingham fluid model; then, the variation of the neutral curve is analyzed with sediment parameters, which are size distribution and its median, representing as critical concentration and concentration. Additionally, the variations of ratio of such characteristic parameters as Reynolds number of turbid water to clear water are obtained to represent the relation between Bingham fluid and ordinary Newtonian fluid, which can be applied to judge the flow pattern in the Yellow River.

We study a generalization of the Navier–Stokes–Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is continuously parametrized by the temperature. As such, the considered fluid may go through transitions between three of the following regimes: it can flow as a Bingham fluid for a specific value of the temperature, while it can behave as the Navier–Stokes fluid for another value of the temperature or, for yet another temperature, it can respond as the Euler fluid until a certain activation initiates the response of the Navier–Stokes fluid. At the same time, we regard a generalized threshold slip on the boundary that also may go through various regimes continuously with the temperature. All material coefficients like the kinematic viscosity, friction or activation coefficients are assumed to be temperature-dependent. We establish the large-data and long-time existence of weak solutions, applying the L ∞ L ∞ -truncation technique to approximate the velocity field.

Additive construction by extrusion (ACE), also known as construction-scale 3-D printing, is becoming a new paradigm for concrete construction. While significant cost and manpower savings are projected, many issues remain to be solved before ACE can be viewed as a mainstream technology. Among these is the formulation of a robust and sustainable binder that meets the demanding rheological and mechanical performance requirements of an ACE application. This paper investigates the development of such a binder by exploring pastes prepared from binary blends of cement with limestone powder at various proportions, supplemented with the incorporation of a retarder/accelerator admixture combination. Performance is chiefly characterized by applying a Bingham fluid model to characterize the rheological parameters of yield stress and plastic viscosity and by assessing hydration via isothermal calorimetry measurements. Matching the surface area of the limestone powder to that of the cement that it is replacing affords the opportunity to regulate rheology via water content adjustments, while engineering the cement:limestone powder ratio to provide the desired mechanical properties. The utilization of the retarder/accelerator combination produces a paste with a long pot life (stable rheology) that can be quickly stiffened via the injection of the accelerator (and retarded paste) into a static mixer just prior to the printer’s exit nozzle. Thus, these pastes demonstrate the potential to provide a robust and sustainable binder for ACE applications.

In this paper, double-diffusive natural convection, studying Soret and Dufour effects and viscous dissipation in an open cavity filled with Bingham fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM). In addition, entropy generations through fluid friction, heat transfer, and mass transfer has been studied. The problem has been solved by applying the regularized Papanastasiou model. However, the Bingham model without regularizations for some cases have been studied to demonstrate the accuracy of the applied regularization. This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 103, 104 and 105), Bingham number (Bn), Lewis number (Le=2.5, 5 and 10), Dufour parameter (Df=0, 1, and 5), Soret parameter (Sr=0, 1, and 5), Eckert number (Ec=0, 0.001, and 0.01), and the Buoyancy ratio (N=-1, 0.1, 1). Results indicate that the increase in Rayleigh number enhances heat and mass transfer for various Bingham numbers. The rise of Bingham number reduces heat and mass transfer. In addition, the increase in Bingham number enlarges the unyielded zones. The increase in the Lewis number augments mass transfer in different Rayleigh and Bingham numbers, although the enhancement of Lewis number causes heat transfer to drop marginally. The rise of Dufour parameter increases heat transfer gradually. The increase in Soret parameter enhances mass transfer for different Bingham and Rayleigh numbers. The addition of Soret parameter, Dufour parameter and Lewis number do not affect the unyielded zone considerably. The augmentation of the buoyancy ratio number enhances heat and mass transfer at Ra = 104 and 105. The rise of buoyancy ratio number alters the unyielded section significantly. The increase in Eckert number influences heat and mass transfer marginally. The augmentation of Rayleigh number enhances different entropy generations and reduces the average Bejan number. The increase in the Bingham number provokes various irreversibilities to drop significantly. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The rise of Eckert number alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters.

Forced convection heat transfer from an isothermal heated cone (apex up and down) in Bingham plastic fluids has been studied numerically. Extensive results are presented here in terms of isotherm and Nusselt number over ranges of conditions as: Reynolds number, 1 ≤ Re ≤ 100, Prandtl number, 10 ≤ Pr ≤ 100, Bingham number, 0 ≤ Bn ≤ 100 and cone angle, 20° ≤ α ≤ 150°. The rate of heat transfer is influenced mainly by the values of Re, Pr and Bn and to a lesser extent by the cone angle and orientation. The present results are consolidated in terms of the modified Reynolds (Re⁎) and Prandtl numbers (Pr⁎) incorporating the role of Bingham number.

During the past two decades of research and development in the field of grouting in hard jointed rock, the design process has taken a number of significant leaps forward. A grouting design in hard rock can now be based on the penetration length of grout in individual rock fractures. For cementitious grouts, the most common rheological model used is the one for a Bingham fluid. The model is a conceptualisation of grout spread where two rheological properties of the grout – viscosity and yield stress – govern the penetration length along with the fracture aperture and applied grouting overpressure. This paper focuses on verification of radial Bingham flow of cementitious grout using a fracture model constructed from acrylic glass. Each test conducted using the fracture model was filmed, allowing the grout spread to be analysed as penetration length over time. The measured penetration lengths were then compared with analytical solutions derived for Bingham grout in a plane parallel fracture. The results indicate that the penetration of cementitious grout in fracture apertures of 125 μm and 200 μm is verified for up to 40% of the maximum possible penetration length. This can be compared to normal grouting, where the penetration lengths achieved are around 20% of the maximum penetration length.

Cementitious materials for 3D printing have special requirements for rheological properties, which are significantly affected by many factors, including sand gradation and packing fraction. Fuller Thompson theory and Marson-Percy model are classic approaches for sand gradation and packing fraction optimiza- tion, respectively. This paper attempts to apply Fuller Thompson theory and Marson-Percy model in designing cementitious materials for 3D Cementitious Materials Printing (3DCMP). Various gradation methods adopted in this study were Fuller Thompson gradation (mixture A), uniform-gradations (mix- ture B and C), gap-gradations (mixture D and E). Besides these mixtures with special gradation approaches, one mixture using natural river sand (mixture F) was prepared as well. Rheological proper- ties were characterized by static/dynamic yield stress and plastic viscosity in Bingham Plastic model. Buildability was examined by printing a column with 10 cm inner diameter via a gantry printer. Rheological test results indicate that mixture A designed by continuous gradation possesses the highest static/dynamic yield stress and lowest plastic viscosity. During printing test for buildability, mixture A can easily reach up to 40 layers without notable deformation, while all other mixtures deformed notice- ably and fell down before the 35th layer. Finally, a large-scale printing was carried out with mixture A and a structure with the height of 80 cm was printed successfully without notable deformation. Density, compressive strength and flexural strength of printed filaments were also characterized. Mechanical performance test results illustrate mixture A has the highest density and appropriate com- pressive strength, and a relative high flexural strength at different curing ages. These results indicate that Fuller Thompson theory and Marson-Percy model can serve as a reasonable guide for material rheology design for 3DCMP. NRF (Natl Research Foundation, S’pore) Accepted version

In this study, applicability of peristaltic waves as an efficient means for bio-particle manipulation is numerically investigated using the lattice Boltzmann method (LBM). The analysis is carried out in a flow configuration which comprises a two-dimensional, closed-ended, vertical cavity filled with a Bingham fluid and equipped with two flexible side walls and two rigid upper and lower plates. It is shown that by judicially adjusting the working parameters of the peristaltic waves (e.g., wavelength, amplitude, speed, and/or phase lag) it is possible to control the dynamics/trajectory of a large, circular bio-particle immersed in the fluid. It is also shown that a suspending circular particle moves faster if the surrounding fluid possess a yield-stress. Based on our obtained numerical results, for a given cross-sectional area, circular particles move faster than elliptical particles when excited peristaltically.

In this work, the effects of tilt angle and fluid yield stress on the laminar natural convection from an isothermal square bar cylinder in a Bingham plastic fluid confined in a square duct has been investigated over the following ranges of conditions: Rayleigh number, 102 ≤ Ra ≤ 105; Prandtl number, 10 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 100; aspect ratio, 0.125 ≤ B ≤ 0.5 and angle of inclination, 0° ≤ λ ≤ 45°. Extensive results on the detailed flow and temperature fields are discussed in terms of the streamline and isotherm contours, yield surfaces, local and average Nusselt numbers as functions of the aforementioned parameters. All else being equal, the Rayleigh number promotes yielding of fluid (enhances convection) whereas the Bingham number counters this tendency. For given values of Ra, Pr, λ and B, there exists a limiting Bingham number (Bnmax ) at which the entire body of fluid is frozen so to say and heat transfer occurs solely by conduction and this limiting value of the average Nusselt number is only a function of the geometry of the system, i.e., the values of B and λ. Also, the rate of heat transfer increases with the increasing angle of inclination while a negligible effect is observed for high Bingham number values due to the strong influence of conduction. However, for the intermediate values of Bingham number (0

In this paper, double-diffusive natural convection, studying Soret and Dufour effects and viscous dissipation in a square cavity filled with Bingham fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM). In addition, entropy generations through fluid friction, heat transfer, and mass transfer has been studied. The problem has been solved by applying the regularised Papanastasiou model. This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 103,104 and 105), Bingham number (Bn), Lewis number (Le = 2.5, 5 and 10), Dufour parameter (Df) = 0, 1, and 5), Soret parameter (Sr) = 0, 1, and 5), Eckert number (Ec = 0, 0.001, and 0.01), inclined angle (Θ = 0, 40, 80, and 120) and the Buoyancy ratio (N = −1, 0.1, 1). Results indicate that the increase in Rayleigh number enhances heat and mass transfer for various Bingham numbers and inclined angles. The alteration of the inclined angle changes heat and mass transfer. In addition, the rise of the inclined angle alter the unyielded zones. The increase in the Lewis number augments mass transfer in different inclined angles while it causes heat transfer to drop marginally at Θ = 0, 40, and 120. The heat transfer increases with the rise of the Dufour parameter and the mass transfer enhances as the Soret parameter increases for different Bingham numbers and Rayleigh numbers. In some cases, the augmentation of Soret and Dufour parameters alter the behavior of heat and mass transfer against the alteration of the inclined angle. The addition of Soret and Dufour parameters and Lewis numbers do not affect the unyielded zone considerably. The augmentation of the buoyancy ratio number enhances heat and mass transfer. The rise of buoyancy ratio number alters the unyielded section significantly. The increase in Eckert number declines heat transfer, but it has a marginal effect on mass transfer. The augmentation of Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the Bingham number provokes various irreversibilities to drop significantly. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The rise of Eckert number alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters.

The evolution equations for the particle distribution functions are written in a divergence form applicable in three dimensions. From this set, it is shown that the continuity equation and the equations of motion are satisfied in Cartesian, cylindrical and spherical coordinates for all fluids when additional source terms are added to the equations of evolution in the latter two coordinate systems. If the body forces are present, a new set of source functions is required in each coordinate system and these are described as well. Next, the energy equation is derived by using a separate set of particle distribution functions. Modifications of the relevant equations to be applicable to incompressible fluids is described. The incorporation of boundary conditions and the description of the numerical scheme for the simulation of the flows employing the new approach is given. Validation results obtained through the modelling of a mixed convection flow of a Bingham fluid in a lid-driven square cavity, and the steady flow of a Bingham fluid in a pipe of square cross-section are presented. Next, using the cylindrical coordinate version of the evolution equations, numerical modelling of the steady flow of a Bingham fluid and the Herschel–Bulkley fluid in a pipe of circular cross-section have been performed and compared with the simulation results using the augmented Lagrangian method as well as the analytical solutions for the velocity field and the flow rate. Finally, some comments on the theoretical differences between the present approach and the existing formulations regarding Lattice Boltzmann Equations are offered.

The unclassified tailings paste (UTP) is a typical non-Newtonian fluid with a mass fraction over 70%, and the UTP disposal technology is of great significance to solve the disaster of tailings ponds and underground voids. The widely used Buckingham equation for predicting the pressure gradient of UTP in pipe flow does not consider the effect of wall slip drag reduction and the prediction accuracy is relatively low. To this end, a theoretical derivation based on the apparent wall slip equations established by previous scholars, sedimentation tests, loop tests and rheological tests were carried out. When the UTP is a Bingham fluid, the proposed new pressure gradient model which considers the wall slip effect is composed of the Buckingham equation and a dimensionless wall slip correction coefficient. The correction coefficient decreases with increases in either slip layer thickness and plastic viscosity of UTP, and increases with increases in either pipe diameter and slip layer viscosity. In this study, the dimensionless correction coefficient is 0.83∼0.85. When using the new pressure gradient model, the ratio of solids volume fraction to the maximum packing volume fraction of UTP (the filling degree) is at least 0.76. Compared with the measured pressure gradient from the loop tests in this study and the literature, the average error of the new pressure gradient model is 11.3%, whereas the average error of the Buckingham equation is 29.8%. The advantages of the new pressure gradient model are that the required parameters are easy to obtain, the model is easy to solve, and the prediction accuracy is better than the Buckingham equation. When the UTP is a Herschel-Bulkley fluid, the reliability of the pipe pressure gradient model which considers the wall slip effect still needs to be verified.

This study presents an extensive numerical investigation on the flow phenomena of a blood analogous fluid through an axisymmetric stenosed artery under both steady and pulsatile flow conditions. Most of the previous investigations, carried out for this benchmark problem, used either a simple Newtonian fluid model or a generalized Newtonian (GNF) fluid model like the power-law or Bingham plastic fluid model to represent the rheological behaviour of blood. However, many prior rheological studies showed that the real and whole blood exhibits both the shear-thinning and viscoelastic properties. In this study, for the first time, a multi-mode sPTT (simplified Phan-Thein-Tanner) model is used to carry out the numerical computation, which accounts for both the shear-thinning and viscoelastic rheological properties of blood. Additionally, a realistic set of viscoelastic model parameters, obtained by fitting the response of real and whole blood in standard viscometric flows, is used in this study. An excellent agreement is seen between the experimentally determined apparent viscosity (in simple shear flows) of blood with that predicted by the present viscoelastic model and other prior models developed for blood. Therefore, we believe that this study presents more accurate and realistic numerical results for the flow of blood through a stenosed artery than that presented by the previous studies in the literature. A simple Newtonian fluid model is also used in the present analysis to compare and show how the flow behavior of blood can be influenced by its complex rheological properties under otherwise identical conditions. We find a significant difference in the flow characteristics (in terms of the streamline profiles, velocity magnitude, pressure drop, etc.) obtained with the Newtonian and viscoelastic fluid models. For instance, the velocity gradient is seen to be large near the artery wall for the viscoelastic fluid model than that seen for the Newtonian model; whereas, a reverse trend is seen for the pressure drop across the stenosis. Furthermore, we find that the flow dynamics is strongly modulated by the stenosis geometry, Reynolds number and flow types, i.e., whether it is steady or pulsatile.