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In the present paper, the non-iterative PISO algorithm and finite volume method are employed to solve the exact Bingham fluid flow. The OpenFOAM solver, i.e., icoFoam, is modified to achieve this goal. The accuracy of numerical procedures is obtained by reproducing the results of Chupin and Dubois (Comput Math Appl 72:1263–1286, 2016. doi:10.1016/j.camwa.2016.06.026). Then, the Bingham fluid flow in a cylindrical enclosure with the rotating top wall is numerically studied by the modified solver for the following ranges of conditions: Reynolds number, $$ 1 \le \text{Re} \le 1000 $$, Bingham number, $$ 0 \le {\text{Bn}} \le 1000 $$ and aspect ratio (AR) of 1, 1/2, 1/4, 1/8 and 1/16. The variation of yielded regions percentage with Re and Bn is plotted for AR = 0.5 and 1. It is found that Reynolds number change in the range $$ 1 \le {\text{Re}} \le 10{\text{Bn}} $$ has no significant effect on the size and shape of the unyielded regions for constant Bn and AR = 1. The effect of Re, Bn and AR on the primary ($$ Q_{p}^{*} $$) and secondary ($$ Q_{s}^{*} $$) volumetric flow rate is also discussed. A correlation is proposed in terms of Re and Bn to approximate the torque coefficient ($$ C_{\text{T}} $$) for $$ 1\le {\text{Re}} \le 1 0 0,\,\, 0\le {\text{Bn}} \le 1000\, $$ and different aspect ratios.

By using dimension reduction and homogenization techniques, we study the steady flow of an incompresible viscoplastic Bingham fluid in a thin porous medium. A main feature of our study is the dependence of the yield stress of the Bingham fluid on the small parameters describing the geometry of the thin porous medium under consideration. Three different problems are obtained in the limit when the small parameter $\varepsilon$ tends to zero, following the ratio between the height $\varepsilon$ of the porous medium and the relative dimension $a_\varepsilon$ of its periodically distributed pores. We conclude with the interpretation of these limit problems, which all preserve the nonlinear character of the flow., Comment: 21 pages, 1 figure

Single-port laparoscopic surgery (SLS), which utilizes one major incision, can deliver favorable cosmetic outcomes with fewer patient hospitalization stays and less postoperative pain. However, current SLS instruments, which are rigid and slender, have been suffering from several drawbacks, including their inability to provide the optimum articulation required to complete certain SLS tasks. This paper reports on the development of a lightweight smart hydraulic actuation system that is proposed to be embedded at selected joints along current SLS instruments, in order to enhance their adaptability with a higher level of stiffness and degrees-of-freedom. The developed smart actuation system utilizes both conventional hydraulic and magnetorheological (MR) fluid actuation technologies. Electromagnetic finite element analyses were conducted to design the electromagnetic circuit of the smart actuator. A prototype of the developed actuation system was manufactured, and its performance was assessed using a dedicated experimental arrangement, which was found to agree well with the results obtained using a Bingham plastic theoretical model. Finally, the present design of the developed smart actuation system permits an angulation of about 90&deg, and a maximum force output in excess of 100 N, generated under a magnetic excitation of about 1.2 Tesla, which should be sufficient to resist torques of up to 500 mNm.

The stability of neutrally and non-neutrally buoyant particles immersed in a plane Poiseuille flow of a yield-stress fluid (Bingham fluid) is addressed numerically. Particles being carried by the yield-stress fluid can behave in different ways: they might (i) migrate inside the yielded regions or (ii) be transported without any relative motion inside the unyielded region if the yield stress is large enough compared to the buoyancy stress and the other stresses acting on the particles. Knowing the static stability of particles inside a bath of quiescent yield-stress fluid (Chaparian & Frigaard, J. Fluid Mech. , vol. 819, 2017, pp. 311–351), we analyse the latter behaviour when the yield-stress fluid Poiseuille flow is host to two-dimensional particles. Numerical experiments reveal that particles lose their stability (i.e. break the unyielded plug and sediment/migrate) with smaller buoyancy compared to the sedimentation inside a bath of quiescent yield-stress fluid, because of the inherent shear stress in the Poiseuille flow. The key parameter in interpreting the present results is the position of the particle relative to the position of the yield surface in the undisturbed flow (in the absence of any particle): the larger the portion of a particle located inside the undisturbed sheared regions, the more likely is the particle to be unstable. Yet, we find that the core unyielded plug can grow locally to some extent to contain the particles. This picture holds even for neutrally buoyant particles, although they are strictly stable when they are located wholly inside the undisturbed plug. We propose scalings for all cases.

The rheological behavior of many lubricants used in hydrodynamic bearings can reasonably be modeled using the Bingham plastic material model. This behavior is characterized by a strong discontinuity, from a pure solid state to a viscous fluid state depending on the local shear stress. In literature three methods have been presented to model a Bingham plastic lubricated film. A full CFD and thus expensive, numerical simulation has been used. A general Reynolds equation based simulation has been used, however with a less accurate numerical regularization of the material discontinuity. Or a general Reynolds equation based simulation has been used, but with a severe reduction of the geometric complexity. In this paper, an ’exact’ thin film lubrication simulation for a Bingham plastic fluid is presented. The model is said to be exact in the sense that it requires no additional approximations to those used in the derivation of the general Reynolds equation, and requires no numerical regularization of the Bingham plastic fluid model and can still be used on any lubricating film geometry. Simulations on both infinite and finite journal bearings shows that the results of this new method are in good accordance with literature, demonstrating the validity of the method.

We study the stability of laminar Bingham&ndash, Poiseuille flows in a sheet of fluid (open channel) down an incline with constant slope angle &beta, &isin, (0,&pi, /2). This problem has geophysical applications to the evolution of landslides. In this article, we apply to this problem recent results of Falsaperla et al. for laminar Couette and Poiseuille flows of Newtonian fluids in inclined channels. The stability of the basic motion of the generalised Navier&ndash, Stokes system for a Bingham fluid in a horizontal channel against linear perturbations has been studied. In this article, we study the flows of a Bingham fluid when the channel is oblique and we prove a stabilizing effect of the Bingham parameter B. We also study the stability of the linear system with an energy method (Lyapunov functions) and prove that the streamwise perturbations are always stable, while the spanwise perturbations are energy-stable if the Reynolds number Re is less than the critical Reynolds number Rc obtained solving a generalised Orr equation of a maximum variational problem.

This paper presents the numerical simulation results of a computational fluid dynamics (CFD) model that describes the layer shape in extrusion-based 3D Concrete Printing (3DCP). The simulation outcome is validated through an experimental program in which we investigated the influence of 3DCP processing parameters on the geometry of a single layer. Specifically, a set of single layers were printed using a O25 mm nozzle mounted on an 6-axis industrial robotic arm travelling at different speeds and with different layer heights. A fresh concrete – comprising CEM I 52,5 R - SR 5 (EA), limestone filler, fine sand, water, and admixtures (i.e. viscosity modifying agent, high-range water-reducing admixtures and a hydration retarder) – was pumped and extruded at a fixed volumetric rate. Once hardened, the extruded layers were sliced to examine the resulting cross-sections. Specifically, the cross-sections’ geometry were obtained by a custom image processing algorithm. Next, the extrusion flow was modelled with a CFD simulation using the software FLOW-3D®. The constitutive behavior of fresh concrete was modelled as a Bingham fluid, while the volume-of-fluid method was used to predict the free surface of the concrete and, thus, the layer geometry. The numerical results agree qualitatively with the experimental observations, enabling us to identify two non-dimensional 3DCP processing parameters that influence the overall cross-sectional shapes: 1) the geometric ratio between layer height and nozzle diameter, and 2) the ratio between the nozzle velocity and the extrusion volumetric flux. These findings – when complemented with a model describing the overall deformation of stacked layers – serve as the basis for correlating material rheological properties to 3DCP process parameters, promoting a better link between design and fabrication in a 3DCP context.

International audience; During the past decade, researchers have used different Nano-Particles (NPs) due to their unique characteristics for improving formulation of Oil-Based Drilling Fluids (OBDFs). This study is the first research that investigates the effect of a Modified Nano Clay (MNC), namely CLOISITE 5 and non-functionalized Nano Graphene (NG) on rheology, electrical/emulsion stability, and filtration control ability, as the main properties of OBDFs. Initially, five concentrations of both NPs (0.25, 0.5, 1, 1.5, and 2 wt%) were added separately into an NP-free OBDF (the base fluid). Then, rheological properties and electrical stability of all prepared fluids were measured at three 90, 140, and 180 °F temperatures. Moreover, filtration test was carried out under 500 psi (3447 kPa) differential pressure and exposed to 300 °F temperature for all fluids. Since experimentally measured shear stresses followed well both Herschel Bulkley (shear-thinning) and Bingham Plastic models, effects of temperature and the NPs concentration on both model parameters are investigated more deeply in the paper. Activation energies calculated from Arrhenius model showed that MNC is more effective than NG on reducing the dependency of apparent and plastic viscosities of the base fluid on temperature. MNC, due to its amphiphilic structure, significantly stabilizes water-in-oil emulsion at all temperatures and concentrations, but NG with high electrical conductivity reduces the emulsion stability. The nanofluids containing 0.5 wt% MNC and 0.25 wt% NG which have respectively 32.6% and 43.5% fewer filtrate volumes than the base fluid, were considered as the optimal nanofluids from controlling filtration into formation aspect. Finally, MNC is applicable to enhance the formulation of the OBDF through supporting its commercial viscosifier, emulsifiers, and fluid loss control agent, but the negative effect of NG on emulsion stability limits its application.

According to the field test of urban subway tunnels, the internal force of the lining segment of the shield tunnel during the synchronous grouting stage is 1–1.5 times that in the steady stage. To study the distribution model of grouting pressure on the lining segment produced by synchronous grouting, we investigated Bingham fluid and a synchronous grouting slurry while they penetrate excavation soil and fill shield tail interspace. Then, we deduced the calculation formula for diffusion radius, the amount of grout during grouting behind a segment, the radial displacement of excavation caverns caused by the squeezing effect of penetration pressure, and the effective stress of soil in the diffusion zone. The amount of grout that can fill a shield tail interspace during synchronous grouting was identified. Considering the time-varying of slurry viscosity, the limit equilibrium equation and the fluid mechanics method were used for the deduction of the distribution model of grouting pressure on a lining segment produced by synchronous grouting. The calculated results indicated that the diffusion radius and the amount of grout that can fill a shield tail interspace increase as the grouting pressure increases and that grouting slurry diffusion reduces the grouting pressure on a lining segment. The actual measured grouting pressure value is consistent with the theoretical calculation results in this paper by combining the engineering example of the Changsha Metro Line 4. The theory proposed by this paper provides a theoretical basis for fine analysis of the distribution of grouting pressure during shield tunneling construction.

A simulation model of non-Newtonian fluid in vertical, concentric annular flow is used in this work. A prototype of a drilling device is manufactured to compare with the simulation results. Water-based mud rheology is described here with the Bingham plastic model. The simulation results reveal that Bingham plastic fluid has a good attitude during drill pipe rotation in terms of axial velocity, tangential velocity, and molecular viscosity. This influence of rotation on the axial velocity is mirrored in the behavior of the shear stresses inside annular space and hence on the friction factor. However, the rest situation of the drill pipe results in high fluid viscosity. Furthermore, it is found that 0.2 of eccentricity leads to increase the pressure drop inside annuli. Bingham plastic fluid has a great dependence on temperature, and the temperature decreases from top to bottom. This behavior occurs since Bingham fluid flows from up to down during drilling.

Magnetorheological fluid (MRF) models are important tools in the design of the material based-valve in a damper. Although Bingham Plastic and polynomial models are quite widely employed, these data-driven models have disadvantages in term of the accuracy and narrow applicable operating conditions, including magnetic field and shear rate. Therefore, this paper aims to utilize an extreme learning machine (ELM) based-shear stress model to design an magnetorheological (MR) valve. Firstly, an MRF model of MRF 132DG is built using rotational rheometer test results. Secondly, the model is employed to model a meandering MR valve drop pressure utilizing the known design parameters and a finite element magnetic method (FEMM) results. The comparison of the steady state pressure between the simulation and experimental results (in literature) has shown a good agreement in term of the pattern and accuracy with error of less than 3%. In summary, ELM has shown its potential to model MRF behavior while employing it to an MR device.

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.

We consider two unsteady free convection flows of a Bingham fluid when it saturates a porous medium contained within a vertical circular cylinder. The cylinder is initially at a uniform temperature, and such flows are then induced by suddenly applying either a new constant temperature or a nonzero heat flux to the exterior surface. As time progresses, heat conducts inwards and this may or may not overcome the yield threshold for flow. For the constant temperature case, flow begins immediately should the parameter, Rb, which is a nondimensional yield parameter, be sufficiently large. The ultimate fate, though, is full immobility as the cylinder eventually tends towards a new constant temperature. For the constant heat flux case, the fluid remains immobile but will begin to flow eventually should Rb be sufficiently large. The two cases have different critical values for Rb.

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.

This work reports results on the drag and heat transfer from an in-line array of three isothermal spheres falling in a cylindrical confinement filled with Bingham plastic fluids. The effects of dim...

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.

Based on the interface theory, taking the corresponding surface of the yielding depth of debris flows as the interface, the viscous debris flows can be divided into the ideal fluid and the Bingham ...

The theory of slow viscous flow around a slender body is generalized to the situation where the ambient fluid has a yield stress. The local flow around a cylinder that is moving along or perpendicular to its axis, and rotating, provides a first step in this theory. Unlike for a Newtonian fluid, the nonlinearity associated with the viscoplastic constitutive law precludes one from linearly superposing solutions corresponding to each independent component of motion, and instead demands a full numerical approach to the problem. This is accomplished for the case of a Bingham fluid, along with a consideration of some asymptotic limits in which analytical progress is possible. Since the yield stress of the fluid strongly localizes the flow around the body, the leading-order slender-body approximation is rendered significantly more accurate than the equivalent Newtonian problem. The theory is applied to the sedimentation of inclined cylinders, bent rods and helices, and compared with some experimental data. Finally, the theory is applied to the locomotion of a cylindrical filament driven by helical waves through a viscoplastic fluid.

The Folgar–Tucker fiber orientation model coupled with weakly compressible Smoothed Particle Hydrodynamics is used to simulate the process of casting of fiber reinforced concrete and to predict the spatial-temporal evolution of the probability density function of fiber orientation. The flowable concrete-fiber mix is modeled as a viscous Bingham-type fluid. Model predictions qualitatively agree with fiber orientations observed in an L-box test with fibers suspended in transparent gel. Important factors and assumptions regarding the fiber flow are reviewed and conclusions are drawn based on numerical experiments.

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.

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

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 main purpose of this study is to determine the mud rheological properties of the Chorfa dam (region of Mascara, Algeria) and to propose a rheological model that describes mud flow behavior. This study helps on one hand to give a better understanding of fine sediment transport dynamics in the dam, as well as contributing to reduce the dredging costs, and on other hand to valorize dredged sediments in road construction. Rheological measurements were conducted using an Engler viscometer and a Haake RS 600 rheometer. Mud samples were prepared with purified water at a range of solids concentration varying between 5.0 and 32.5%. Besides, the physical, chemical and mineralogical characteristics of the Chorfa dam’s mud and the rheological tests were presented and the effect of solids concentration on mud viscosity was studied. The results indicate that the Chorfa dam’s mud showed a non-Newtonian behavior for solids concentration higher than the critical solids concentration, and the apparent viscosity increases with increasing solid concentration at different shear rates. In addition, for a fixed concentration, the apparent viscosity decreases with increasing shear rates, which approves the shear thinning behavior of the Chorfa dam’s mud. Fitting results of four rheological models (Bingham Plastic Model, Ostwald–de Waele (power law), Herschel–Bulkley and Casson) to the experimental data were presented. Hence, the Ostwald–de Waele model was the best fitting model for mud samples.

In this research paper we have theoretically analyzed the effects of the angle of convergence and the non-Newtonian characteristics on the performance of an externally pressurized converging circular thrust bearing using Bingham fluid as the lubricant. Since Bingham lubricants are known to have a characterized yield value, there will be a formation of unyielding core in the region between the plates of the bearing. The solutions are obtained for the pressure and load carrying capacity of the bearing for various values of Bingham number and the angle of convergence. The effects of the Non-Newtonian characteristics of the lubricant and the angle of convergence on the performance of the bearing are discussed.

Proper selection of rheological models is very important in flow characterization. These models are often used to evaluate parameters that help in the characterization of food samples. Rheological models also provide flow predictions for extreme conditions where the flow nature of the fluid cannot be determined, Hence the need for appropriate selection of rheological models. The principal aim of this study is to suggest a rheological model that best characterize the rheological behavior of native cassava starch and to determine the effect of state variables like temperature and concentration on the accuracy of rheological models. Five rheological models (i.e. Herschel-Bulkley model, Robertson-Stiff model, Powerlaw model, Bingham plastic model and Prandtl-Eyring model) were selected for this study and these models were modified into statistical models by the inclusion of the error variance (e). The least-square method was used in evaluating the various model parameters for each model. From this study, it was seen that the Herschel-Bulkley model and the Robertson-Stiff model most accurately described the rheological patterns in cassava starch production. The sensitivity analysis of the different rheological models also shows that the accuracy of the Herschel-Bulkley model, Robertson-Stiff model and Powerlaw model is not significantly affected by variations in temperature and concentration of the cassava starch. However, it was observed that the Bingham plastic model and Prandtl-Eyring model gave less accurate predictions at higher concentration and lower temperature respectively. A lot of the industrially accepted models such as the Bingham plastic model may not necessarily be the best model for characterization cassava starch production as shown in this study, hence rheological model optimization is recommended for further study. Specifications Table Subject area Chemical.

The flow induced by a sphere rotating inside a non-Newtonian, Bingham fluid has been investigated numerically. The rotating sphere is enclosed in a concentric cubic box with solid boundaries. The Bingham number varied between 0.01 and 100,000 and the Reynolds number varied between 0.01 and 10,000. The torque increases with the Bingham number and reaches an asymptotic state at large Bn. The torque is independent of the Reynolds number at high Bn. The yielded region around the sphere has been determined and an empirical equation is found for its extent.

This study is conducted to investigate the Bingham—Papanastasiou fluid flow driven by a rotating infinite disk. The Bingham—Papanastasiou model is a modification of the Bingham plastic model, which is developed by introducing a continuation parameter to overcome its discontinuity. The von K´arman similarity solution is used to transform the flow equations from ordinary differential equations to a nonlinear system of partial differential equations, which is solved numerically. The effect of the Bingham flow parameters on the radial, tangential, and axial velocities, pressure, and radial and tangential skin friction coefficients is discussed.

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.

This paper presents fully discrete stabilized finite element methods for two-dimensional Bingham fluid flow based on the method of regularization. Motivated by the Brezzi-Pitkäranta stabilized finite element method, the equal-order piecewise linear finite element approximation is used for both the velocity and the pressure. Based on Euler semi-implicit scheme, a fully discrete scheme is introduced. It is shown that the proposed fully discrete stabilized finite element scheme results in the h1/2 error order for the velocity in the discrete norms corresponding to L2(0,T;H1(Ω)2)∩L∞(0,T;L2(Ω)2).

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.

Experimental data for the pressure-driven flow of concentrated lignocellulosic biomass (corn stover) in a circular pipe are presented. A positive curvature was observed in the pressure profile at steady state, both when the biomass was flowing, and for several minutes after the flow had stopped. After the flow into the pipe was stopped, biomass continued to be expelled for at least five minutes, suggesting that the material is compressible. Occasionally, the pressure and outlet flow rate exhibited rapid, transient fluctuations. The fluctuations would cease when dryer-than-average heterogeneities exited the pipe. A mathematical model is developed to treat the biomass as a compressible Bingham fluid with a density-dependent yield stress. This model quantitatively reproduces steady-state pressure profiles for both flowing and nonflowing states, and captures the transition between the two states after the inlet flow rate is set to zero. Our model cannot predict the rapid pressure fluctuations that appear to be associated with heterogeneities in composition.Experimental data for the pressure-driven flow of concentrated lignocellulosic biomass (corn stover) in a circular pipe are presented. A positive curvature was observed in the pressure profile at steady state, both when the biomass was flowing, and for several minutes after the flow had stopped. After the flow into the pipe was stopped, biomass continued to be expelled for at least five minutes, suggesting that the material is compressible. Occasionally, the pressure and outlet flow rate exhibited rapid, transient fluctuations. The fluctuations would cease when dryer-than-average heterogeneities exited the pipe. A mathematical model is developed to treat the biomass as a compressible Bingham fluid with a density-dependent yield stress. This model quantitatively reproduces steady-state pressure profiles for both flowing and nonflowing states, and captures the transition between the two states after the inlet flow rate is set to zero. Our model cannot predict the rapid pressure fluctuations that appear to b...

We have numerically studied the effect of a fluid’s yield stress on the performance of a peristaltic mixer reinforced by cylindrical pillars, typical of those used in microfluidic systems. A multiple-relaxation-time, Lattice Boltzmann code was used to investigate the effect of a fluid’s yield stress on mixing efficiency for a viscoplastic fluid obeying the bi-viscous model. A Lagrangian particle-tracking method called “boxcounting” has been utilized for evaluating the mixing performance of the channel through introducing a stirring index parameter. Numerical results indicate that for both Newtonian and Bingham fluids, wave amplitude is the most potent tool for controlling the mixing performance of the mixer. It is shown that while for Newtonian fluids the mixing index is dropped if the channel is equipped with circular pillars, for Bingham fluids pillars can play a slightly positive role in enhancing the mixing efficiency of the mixer, and this is particularly so when the confinement ratio is sufficiently large. A more dramatic increase in the mixing efficiency can be attained when only one of the membranes is vibrating (i.e., the asymmetric case).

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.

Composition B-3 (Comp B-3) is a high explosive formulation composed of 60/40wt% RDX (1,3,5-trinitroperhydro-1,3,5-triazine) /TNT (2,4,6 trinitrotoluene). Above approximately 78°C this formulation p...

This paper reports a two-dimensional numerical investigation of mixed convection inside a liddriven square enclosure, completely filled with a non-Newtonian fluid obeying the Bingham model, having two rectangular adiabatic partitions mounted in different dispositions. Due to the problem’ complexity, the latter is solved using finite volume method when the SIMPLER algorithm is adopted for the pressure-velocity coupling. In order to investigate the yield stress effects on flow field and heat transport, we maintain the Richardson number (Gr/Re2) as 0.01, 1 and 10, respectively, which generates a good simulation of forced, mixed and natural convection dominated flow. The Prandtl and Grashof numbers are fixed at 50 and 104, respectively, while the Bingham number covers the range from 0 to 30. The validity of the computing code was ascertained by comparing our results with the numerical ones already available in the literature and that for both cases: Newtonian and non-Newtonian fluid. The phenomenon is analyzed through the streamlines, the isotherms and the Nusselt numbers with special attention to the partitions’ arrangement and its size. It is found that all parameters related to the geometrical dimensions of the partitions play a crucial role on the temperature distribution, flow field and heat transfer enhancement. For all values of the Bingham number, the mean Nusselt number is found as an increasing function of the decrease Richardson number. Thus, the heat transfer improves.

In this study, we report the theoretical resistance force of a magneto-rheological (MR) shock absorber. We use the Bingham plastic model to theoretically represent the dynamic behavior of MR fluid flow in a circular pipe under the effect of a magnetic field. Because an MR fluid has yield stresses, the flow is divided into two regions: shear flow and plug flow. We reveal the relation between the resistance force of the MR shock absorber and the applied magnetic field. We conduct experiments and compare the experimental and analytical results to verify the theoretical approach.