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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.

The present study investigates the effects of slip and heat transfer on peristaltic mechanism of Bingham fluid in an inclined tube. The sinusoidal, multi-sinusoidal, triangular, square and trapezoidal wave forms are considered. The analysis has been carried out under the assumptions of long wavelength and small Reynold's number approximations. The closed-form solutions are obtained for velocity, plug flow velocity, pressure gradient, streamlines, and temperature. The numerical integration is employed to investigate the effects of pressure rise and frictional force. The influence of relevant parameters on physiological quantities of interest is analyzed and discussed through graphs. The study reveals that velocity and thermal slip have a decreasing effect on velocity and temperature. Further, it is noticed that the volume of trapped bolus increases for increasing values of velocity slip parameter.

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

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.

A frequently used technological solution for reducing oscillations of rotors excited by imbalance, time-varying forces or ground vibrations consists in inserting damping devices in the rotor supports. To achieve their optimum performance in a wide range of operating speeds their damping effect must be controllable to be possible to adapt it to the current working conditions. This is enabled by application of magnetorheological squeeze film dampers. In mathematical models the magnetorheological oils are represented mostly by Bingham or Herschel–Bulkley theoretical materials. Recent experimental measurements carried out at several working places show that with respect to the shape of the flow curves obtained for different magnitudes of magnetic induction the real magnetorheological fluids behave like a bilinear material. This enables a more accurate implementation of magnetorheological fluids in mathematical models of squeeze film dampers. In addition, unlike the Bingham fluid the flow curve of a bilinear material is continuous which reduces the nonlinear character of the procedures for calculation of the hydraulic forces by which the oil film acts on the shaft journal and the rotor casing. A new developed mathematical model of a short magnetorheological squeeze film damper based on representing the lubricating oil by bilinear material was implemented in the computational procedures for analysis of the steady state response of a Jeffcott rotor loaded by a stationary force and by the weight and imbalance of the disc. The performed computational simulations proved that these procedures were numerically stable and arrived at the solution also in cases when the methods based on representing the magnetorheological oil by Bingham material failed.

This study aims to analyze mixed convection in a square cavity with two moving vertical walls by finite volume method. The cavity filled with Non-Newtonian fluid of Bingham model is heated from below and cooled by the other walls. This study has been conducted for certain parameters of Reynolds number (Re=1- 100), Richardson number (Ri=1-20), Prandtl number (Pr=1-500), and Bingham number has been studied from 0 to 10. The results indicate that the increase in yield stress drops the heat transfer and the flow become flatter, while increasing Reynolds number augments it. The convective transport is dominant when increasing Richardson number which leads to enhanced heat transfer in the cavity for both Newtonian and Non-Newtonian fluid. A correlation of Nusselt number is given in function of different parameters.

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

In this paper, we describe our study of the mixed convection of a Boussinesquian Bingham fluid in a vertical channel in the absence and presence of an external uniform magnetic field normal to the walls. The velocity, the induced magnetic field, and the temperature are analytically obtained. A detailed analysis is conducted to determine the plug regions in relation to the values of the Bingham number, the buoyancy parameter, and the Hartmann number. In particular, the velocity decreases as the Bingham number increases. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of diagrams illustrating the influence of various parameters involved in the problem is presented and discussed.

This work aims to study a flow of viscoplastic fluid in a two-dimensional (2D) 90 degree elbow at Re = 100 and Re = 1000 using a numerical approach. The fluid investigated is of sediment/clay suspension exhibiting yield stress characteristics. Bentonite-water suspension 7.5-15wt% and laponite-water suspension 3.5-5wt%, which correspond Bn = 19.76-1470.94 at Re = 100 and Bn = 1.976-147.09 at Re = 1000, are used for simulations. To model the viscoplastic effect, Herschel-Bulkley’s bi-viscosity model for Bingham type is employed. Various flow aspects, i.e., viscosity distribution, streamline pattern, formation of unyielded zones, and pressure distribution, are presented and analyzed in detail. Results show that at Re = 100, neither circulation wake nor static rigid zone is formed in the flow field pattern meanwhile at Re = 1000, the static rigid zone exists at Bn = 6.83 (bentonite 7.5wt%) and Bn = 20.88 (bentonite 10wt%). Moreover, the moving rigid zones generally become larger with the increasing Bn. Furthermore, results for pressure loss per length and friction factor are reported. Approximation functions for pressure loss estimation are also proposed.

The formulation of an oil-based mud was made possible with the oil extracted from rubber seeds using the famous soxhlet extraction method. The mud was formulated using the API standard of 25 g of bentonite to 350 mL base fluid. The choice of Rubber oil comes as a result of its flash point and aniline point which lies in the range of base oils used for mud formulation. The rheological properties of the rubber OBM were beyond the scope of the viscometer and hence thinner was added to reduce its viscosity and its suitability to compete favorably with diesel OBM was checked. The 10-sec and 10-min gel strength of the Rubber OBM was recorded as 68 lb/100 ft2 and 69 lb/100 ft2 respectively while that of Diesel was 65 lb/100 ft2 and 67 LB/100 ft2 . The plastic viscosity of Rubber OBM was 12 cp while that of Diesel was 17 cp. They both exhibited Bingham Plastic behavior and a similar yield point of 146 lb/100 ft2 . The formulated mud samples were subjected to temperatures of 60 oC and 75 oC and it was discovered that Rubber OBM was likely to retain its rheological property than diesel OBM. Comparison with other rheological properties of diesel OBM showed that the formulated mud could be used alternatively for diesel in drilling operations.

A mathematical model is constructed for MHD flow of Bingham fluid and Jeffrey fluid in a horizontal porous space with heat transfer effect. The dimensionless governing equations for this problem are solved analytically and expressions for velocity and temperature field are presented. Further, impacts of physical parameters on flow and heat transfer charcteristics has been studied and discussed graphically. It is found that increasing viscosity ratio enhances velocity and temperature field whereas thermal conductivity ratio gives the reverse effect. Increasing magnetic field parameter tends to suppress fluid velocity significantly whilst mixed behavior shown in temperature distribution. Velocity of the fluid increased considerably with increasing material parameter whereas the reverse trend can be noticed in temperature distribution. Further, it is observed that pressure gradient influenced significantly on velocity and temperature field. Increasing magnetic parameter reduces mass flow rate whereas it shows opposite trend in shearstress distribution.

This work aims to explore the T-channel momentum and heat transfer characteristics with the combined effect of Bingham plastic fluids (0.01 ≤ Bn ≤ 20) behavior and geometrical variation in terms of branching angle (30 deg ≤ α ≤ 90 deg). The problem has been solved over a wide range of Reynolds number (50 ≤ Re ≤ 300) and Prandtl number (10 ≤ Pr ≤ 50). For the momentum flow, qualitative and quantitative features are analyzed in terms of streamlines, structure of yielded/unyielded regions, shear rate contours, plug width and length variation, and local pressure coefficient. These features have been represented in terms of isotherm patterns, temperature profile, Nusselt number, and its asymptotic value for heat transfer characteristics. The recirculating flows have been presented here in the vicinity of T-junction, which promote mixing and heat transfer. Broadly, the size of this zone bears a positive dependence on Re and α. However, fluid yield stress tends to suppress it. The critical Reynolds and Bingham numbers were found to be strong functions of the pertinent parameters like α. The inclination angle exerts only a weak effect on the yielded/unyielded regions and on the recirculation length of main branch. Results show a strong relationship of the plug width and length with key parameters and branches. The Nusselt number exhibits a positive relationship with α, Bn, and Re but for lower Pr in the T-junction vicinity for both branches. Such length indicates the required optimum channel length for thermal mixing.

The present analysis emphasizes the effects of variable properties on Bingham fluid under MHD peristaltic transport. Due to the impact of mechanical forces on the applied magnetic field on the conducting fluid, the fluid stream gets altered. These principle targets drug transport and control of blood flow during surgeries; hence the impact of MHD flow with convective and porous boundary conditions is considered. Further, the implications of homogeneous and heterogeneous reactions are analyzed by considering wall properties. The governing equations are turned dimensionless by appropriate similarity transformations. The series solution is obtained for temperature, velocity, and concentration by perturbation method with lubrication approach. The graphical representation of the pertinent parameters on the physiological flow quantities is depicted by applying for MATLAB 2019b program. The obtained results reveal that the rise in the magnetic parameter diminishes the velocity and temperature profiles. Further, the impact of variable viscosity slightly improves the magnitude of the trapped bolus. The homogenous and heterogeneous reaction parameters have a converse effect on the concentration distribution. Moreover, the present investigation finds its applications to perceive the complex rheological functioning of blood flow through narrow arteries.

This study presents the numerical solution of velocity and temperature fields based on mass conservation, momentum and energy balances for the time-dependent Couette-Poiseuille flow of Bingham materials through channels. The channel flow of Bingham fluid concerns the flow of cement paste in the building industry and the mudflow in the drilling industry. The specific aim is to introduce the magnetohydrodynamic (MHD) phenomena specified by both Ion-slip and Hall currents into the non-isothermal channel flow in a theoretical approach. The Bingham constitutive equation is formulated by the generalized Newtonian fluid technique and solved by employing the explicit Finite Difference Method (FDM) using the MATLAB R2015a and Compaq Visual FORTRAN 6.6a both. For the exactness of numerical performance estimations, the criteria for stabilization and the convergence factor are analyzed. The velocity and temperature profiles are discussed individually at the moving and stationary walls of the channel. It is observed that magnetohydrodynamic phenomena accelerate the flow, and the temperature distributions reach the steady-state situation earlier than velocity distributions. Furthermore, the dominance of MHD parameters on the velocity distributions, shear stress, temperature distributions, and Nusselt number are discussed.

This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the k−ε turbulence model. The rheology for calculating the laminar viscosity coefficient under consideration in this work is the one of a non-Newtonian Herschel–Bulkley (power-law) fluid with yield stress, which includes the Bingham fluid and classical Newtonian fluids as special cases. For the spatial discretization, we use edge-based staggered unstructured simplex meshes, as well as staggered non-uniform Cartesian grids. In order to get a simple and computationally efficient algorithm, we apply an operator splitting technique, where the hyperbolic convective terms of the RANS equations are discretized explicitly at the aid of a Godunov-type finite volume scheme, while the viscous parabolic terms, the elliptic pressure terms and the stiff algebraic source terms of the k−ε model are discretized implicitly. For the discretization of the elliptic pressure Poisson equation, we use classical conforming P1 and Q1 finite elements on triangles and rectangles, respectively. The implicit discretization of the viscous terms is mandatory for non-Newtonian fluids, since the apparent viscosity can tend to infinity for fluids with yield stress and certain power-law fluids. It is carried out with P1 finite elements on triangular simplex meshes and with finite volumes on rectangles. For Cartesian grids and more general orthogonal unstructured meshes, we can prove that our new scheme can preserve the positivity of k and ε. This is achieved via a special implicit discretization of the stiff algebraic relaxation source terms, using a suitable combination of the discrete evolution equations for the logarithms of k and ε. The method is applied to some classical academic benchmark problems for non-Newtonian and turbulent flows in two space dimensions, comparing the obtained numerical results with available exact or numerical reference solutions. In all cases, an excellent agreement is observed.

Soil conditioning is an available auxiliary measure to improve the efficiency and safety of earth pressure balance (EPB) shield tunneling. In order to optimize soil conditioning strategy during tunneling in gravelly sand stratum, it is essential to understand rheological and compressive behavior of conditioned muck and its flow characteristics inside chamber. This paper establishes a constitutive model of compressible modified Bingham fluid for characterizing macroscopically rheological and compressive behavior of foam-conditioned gravelly sand and determines the model parameters by vane shear tests with variable shear rate and lateral confining compression tests. Based on the above theory and computational fluid dynamics (CFD), crucial spatial distribution characteristics of conditioned muck static pressure and flow speed inside chamber are captured by numerical simulations, which is verified the reliability in simulating muck movement during tunnelling. Overall, investigation of macro-hydrodynamics behavior of foam-conditioned gravelly sand and numerical simulation of muck movement in excavation chamber and screw conveyor will inspire soil conditioning assessment while EPB shield tunneling in gravelly sand stratum.

This paper investigates the remarkable effects for introducing the Ion-slip characteristics in the magnetohydrodynamic phenomena on the drift of Bingham fluid when flowing through the inner territory of two porous parallel plates in correspondence with the suction case. The lower plate (L-plate) is as steady while the upper one (U-plate) is oscillatory, which oscillates in its own plane at time t>0. A magnetic field, which is uniform, is affixed perpendicular to the plates. The U-plate temperature oscillates while the L-plate temperature is constant. Numerical performance is presented by the MATLAB R2015a simulation tool with the explicit Finite difference Method (FDM) algorithm. To ensure the preciseness and convergence of the solutions, careful attention has been given on the criteria of stability and convergence of the FDM schemes. As an outcome, the converged solution is obtained for Pr ≥ 0.066, βi ≥ 2, Ha ≤ 20, h ≤ 8, S ≥ −10 and Re ≤ −0.017 with the arbitrary choice of βe = 0.10 and Ec = 0.01. The mesh sensibility test gives the competent mesh space at (m,n)=(60,60). The time sensibility test ensures that the solutions at dimensionless time, τ=2.0 will be steady-state. The exactitude of the current study is obtained by comparing with the published results. Finally, the physical influences of several governing parameters, including Ionslip on the fluid property like velocity, local shear stress, temperature and Nusselt number are discussed and decorated graphically.

The numerical modeling and simulation for the stationary Bingham fluid flow around two confined circular cylinders with various gap ratios are studied. The singularity in the model’s apparent viscosity is dealt by Papanastasiou’s regularization. The model equations are discretized by adopting the methodology based on finite element method (FEM) by choosing a mixed higher order LBB-stable P 2 − P 1 finite element pair. The direct solver PARADISO has been utilized to solve the linearized system of equations. Hydrodynamic forces represented by drag and lift coefficients are computed, and a correlation coefficient is calculated for the gap ratios 0.1 ≤ G p ≤ 0.3 and for several values of the Bingham number 0 ≤ B n ≤ 50 . Line graphs for horizontal and vertical velocities are drawn. Moreover, velocity and pressure profiles are plotted for pertinent values of the parameters. Plug and shear zones are revealed via velocity snapshots in the domain. Pressure is nonlinear in the vicinity of the obstacles and becomes linear downstream in the cylinders as expected in channel flows.

A numerical study of Bingham fluid flow in a two-dimensional (2D) pipe with a baffle is reported in this paper. Bingham fluid is a material characterized by a yield stress; it flows with a constant plastic viscosity when an applied shear stress exceeds the yield stress, and does not flow otherwise. Such a flow has many practical applications such as transport of sewage, underground drainage, oil and fresh concrete/cement in pipes or pumping systems. The studied flow is in both stationary (Reynolds − number of Re=100) and non-stationary (Re=1000) regimes with the Bingham number in the range of Bn=0-5. Various flow characteristics such as flow morphology, streamline pattern, velocity field, and vortex structure are analyzed. It is observed that at Re=100, the circulation structure behind the baffle becomes smaller as Bn increases. Unyielded (solid) zones, which are supposed to diminish the flowability and material mixing, are formed at the pipe's center and/or around the baffle; they however become larger as Bn is greater. However, at Re=1000, the solid zones are substantially reduced, hence enhancing the material mixing. In addition, effect of the baffle's length on the flow is analyzed. Major head loss due to viscous effect along the pipe and minor head loss at the baffle are also examined.

Liquid gel temporary plugging agents were widely applied in many oilfield operations, such as temporary plugging for well workover, diverting re-fracturing for old wells, separate layer fracturing for horizontal well. In this work, an intelligent liquid gel based on magnetorheological fluid (MRF) was developed with hydrophilic magnetic Fe3O4 nanoparticles, dispersant polyvinylpyrrolidone (PVP), and stabilizer SiO2 nanoparticles. The hydrophilic magnetic Fe3O4 nanoparticles were prepared by virtue of chemical co-precipitation and double-layer surfactant coating methods, and characterized by scanning electron microscope (SEM), infrared spectrometer (IR). And then, the performances of the MRF liquid gel were investigated, such as magneto-rheological properties, bearing capacity, and core permeability damage. The results showed that MRF liquid gel under magnetic field is consistent with Bingham fluid. When the magnetic field intensity is 0.73T, the yield strength reaches at 74.453 kPa. With an increase of magnetic field intensity, the core plugging property of MRF liquid gel becomes better. The breakthrough pressure of MRF liquid gel can reach 15.81 MPa at magnetic field intensity of 0.6T and the plugging rate is higher than 97%, while the core permeability damage rate is less than 5.5%. Theoretically, the low-damage MRF temporary plugging agent can be controlled in real time by applying an external magnetic field, providing a new method for oilfield temporary plugging operations.

Rheology is a very critical property of slurries in deciding the optimum solid concentration in slurry transportation system. Using advanced computerized rheometer, the rheological experimental investigations were performed and found that the slurry with lean solid concentration (10–40% by weight) consumes a huge amount of water and requires high energy power pumps. The rheological properties are strongly dependent on shear frequency, solid density, and distribution of particle size. With solid concentration, the plastic viscosity and yield stress increased. At higher solids concentrations, the experimental data fitted well with the Bingham plastic model. The results show that plastic viscosity and yield stress of the slurry samples get increased for the flow of finer solid particles. The viscosity of Bingham plastic depends primarily on the distribution of solid concentration and particle size.

It is of great significance for the improvement of grouting technology and engineering practice to master the flow law of grout between parallel plates. However, the traditional calculation model ignores the influence of the inertia term and only considers the stable flow of slurry, so there is a big error in some cases. It is difficult to solve the motion equation of a Bingham fluid considering the inertial force term directly. Combined with the relationship between the steady-state flow equation of a Bingham fluid and a Newtonian fluid, the approximate unsteady-state flow equation of a Bingham fluid suitable for describing slurry flow is constructed. In addition, according to the unsteady flow equation, the relationship between the time and distance of slurry flow in parallel plate fractures can be obtained, and the simplified conditions of the Bingham fluid unsteady flow model are given. Finally, the accuracy of the flow equations and the simplified conditions are verified by experiments and numerical calculations.

Recently, Hoang et al. (2021) discussed our paper Zou et al. (2020). In our paper, we made a statement that Dai and Bird (1981)'s solution for two-dimensional (2D) radial Bingham fluid flow between parallel plates violates mass balance. Hoang et al. pointed out that Dai and Bird (1981)'s solution does not violate the mass balance because Dai and Bird (1981)'s solution and our analysis are based on different assumptions, i.e. with consideration of the vertical velocity component in the continuity equation or not, which leads to two different approximation models. In this sense, the mass balance of Dai and Bird (1981)'s solution should not be checked using our solution as a reference. In this reply, we add remarks on the two approximation models and their implication for rock grouting analysis. The discussion by Hoang et al. and this reply are helpful to thoroughly eliminate the existing confusion regarding the two solutions in the rock grouting research community.

This paper presents the results of injection analysis to understand the injection process of cement grout into the rock voids. The injection process into the rock voids is classified into three large processes. There are a transportation process of cement particles, a clogging process in the rock voids and a hardening process. In the analysis, the clogging process and the transportation process were analyzed. As to the analysis of the clogging process, the material transport equation considering the filtration theory was introduced and used. As to the analysis of the transportation process, the equation of the plug flow that was related to Bingham fluid instead of Darcy’s law was expanded and used. From the results of these analyses, the existence of grout concentration corresponding to the purpose was suggested.

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

Magnetorheological fluids (MRF) are suspensions of magnetic particles that solidify in the presence of a magnetic field. While non-magnetic additives could improve MRF performance, explorations into such additives have not coalesced into an understanding of their influence, and particularly the role of additive morphology. Here, we explore α-Ni(OH)2 2D sheets, with aspect ratios of ∼25,000, as highly anisotropic MRF additives. Experiments studying pressure-driven flow of an MRF with and without these sheets show that their addition can increase the saturation pressure by as much as 46 %. However, shear-mode rheology reveals that they can also weaken the MRF by inhibiting the chaining of the iron particles at low field strengths and have no effect at higher field strengths. In order to reconcile the strikingly different results, we propose that 2D materials introduce a non-Newtonian handle to modify smart fluids in a manner that depends on the curvature of the shearing strain rate profile. Specifically, we identify a modification to the Buckingham-Reiner model of pressure-driven flow for a Bingham plastic in which the sheets widen the solidified plug. This work highlights the subtle interaction between particles in smart fluids and flows while emphasizing the opportunity for using anisotropy to tune this interaction.

Laminar Bingham fluid flow in the entrance region of a circular pipe is investigated using a momentum integral model. The fully developed flow is uniform in the core region, while the velocity changes in the annular part of the cross section of the pipe. The inlet-filled region concept is adopted. In the inlet region, the boundary layer thickness increases until the size of the plug flow area reaches the fully developed flow size. The model converges to the fully developed solution in the filled region. The model provides the velocity, pressure drop, and skin friction coefficient profiles. The pressure drop results are in good agreement with published experimental data. The flow results asymptotically converge to the fully developed values. In addition, the results are consistent with published Newtonian fluid flow experimental data and theoretical results for the boundary layer thickness, pressure drop, and centerline velocity for small values of the Bingham number.

Grouting reinforcement is an important method used to solve problems encountered during tunnel construction, such as collapse and water gushing. The grouting diffusion process is greatly influenced by the structural characteristics of the fractures in a rock mass. First, an analytical grouting diffusion model of a single rough fracture under constant-pressure control is established based on the constitutive equation of a Bingham fluid. Second, the &ldquo, quasi-elliptical&rdquo, grouting diffusion pattern under the influence of roughness is revealed through a grouting diffusion experiment, which is conducted with an independently developed visualized testing apparatus. Furthermore, the analytical formula of roughness-corrected grouting diffusion characterized by the saw tooth density is established. Finally, an elaborate numerical simulation of the diffusion process of cement slurry (Bingham flow type) in a single rough fracture is carried out by introducing the Bingham&ndash, Papanastasiou rheological model. The temporal and spatial distribution characteristics of the velocity field and pressure field during the grouting diffusion process are analyzed as well. Moreover, the method and range of the roughness correction factor in the analytical grouting diffusion model are proposed based on the fracture roughness unit.

The study of the entrance region flow is, nowaday, assuming considerable technical importance due to its immediate applications in various designs of chemical and biomedical equipments in which the flows of non-Newtonian fluids are encountered. The flow characteristic of non-Newtonian fluid that is independent of time, and which obeys Bingham’s stress–strain relations, has been investigated at the entrance region of the annular space between two rotating coaxial cylinders. This analysis has been carried out for both the cases when each rotates with different speed in the same direction and as well as in the opposite direction with constant angular velocity. Discussions have been presented for a steady, laminar, isothermal flow condition of the Bingham fluid. The continuity and momentum equations are solved iteratively with finite difference method by using the Prandtl’s boundary layer assumptions. The velocity components and pressure distributions have been obtained numerically for various values of Bingham number and aspect ratio.

The effects of inertia on the squeeze flow of a Bingham fluid between two approaching parallel plates with a constant squeeze velocity is investigated using matched asymptotic expansions. This analysis is an extension to the prior study of Muravleva (2015), who has investigated the planar squeeze flow of a Bingham fluid in the absence of inertia. In the present study, the expressions for the shear stress field, velocity, pressure field and squeeze force are derived. The combined effects of the fluid inertia and yield stress on the pressure field and squeeze force are investigated. We found that the pressure and eventually squeeze force increases with increase in Reynolds number. The squeeze force decreases with an increase in the value of the gap aspect ratio.

In industrial practice greases are mainly used as lubricants in hydrodynamic plain bearings and roller bearings. The use in hydrostatic bearings is avoided due to the difficult controllability. One reason is the complex non-Newtonian flow behavior of greases. The motivation for this paper is the use of greases to increase the efficiency of hydrostatic bearings. The assumption is that the so-called yield stress of consistent greases can lead to self-sealing behavior in the bearing under stationary operation conditions. Assuming a volume-flow-free operation of the bearing, a concept for the active control of the sealing gap height and thus the bearing stiffness was developed. The concept idea is the use of a second medium with Newtonian characteristic for pressure transfer. The grease and the pressure control fluid are structurally separated. The grease is induced in the shortest possible way into the bearing pocket to keep the pressure losses as low as possible. The results of test bench investigations indicate the feasibility of a gap height control with very high bearing stiffness under use of highly consistent greases and initiate further investigation on non-stationary operation.

The accuracy of fitting the rheological model to the properties of actual drilling fluid minimises the errors of the calculated technological parameters applied while drilling oil wells. This article presents the methodology of selecting the optimum drilling fluid rheological model. Apart from classical rheological models, i.e., the Newtonian, Bingham Plastic, Casson, Ostwald de Waele and Herschel–Bulkley models, it has been proposed to consider the Vom Berg and Hahn-Eyring models, which have not been applied to describe drilling fluids so far. In the process of determining rheological parameters for the Bingham Plastic, Casson, Ostwald de Waele and Newtonian models, it is proposed to use a linear regression method. In the case of the Herschel–Bulkley, Vom Berg and Hahn-Eyring models, it is suggested to use a non-linear regression method. Based on theoretical considerations and mathematical relations developed in the Department of Drilling and Geoengineering, Drilling, Oil and Gas Faculty, at AGH University of Science and Technology, an original computer program called Rheosolution was developed, which enables automation of the process of determining the optimum drilling fluid rheological model. Some examples show the practical application of the method of selecting the optimum drilling fluid rheological model. Taking into account data from actual measurements of drilling fluid properties, it has been proven that the Vom Berg and Hahn-Eyring rheological models are best fitted to the description of drilling fluid rheological parameters.

20 pages, 12 ref., 9 fig.; A lubrication equation is obtained for a simplified shear-thinning fluid. The simplified rheology consists of a piecewise linear stress tensor, resulting in a two-viscosity model. This can be interpreted as a modified Bingham fluid, which can be recovered in a specific limit. The lubrication equation is obtained in two steps. First two scalings are performed on the incompressible Navier-Stokes equations, namely the long-wave scaling and the slow motion scaling. Second, the resulting equations are averaged along the vertical direction. Numerical illustations are provided, bringing to light the different possible behaviours.

The underground disposal of drill cuttings waste is a common practice for the gas/oil industry to achieve zero-discharge sustainable development. In this study, a numerical modeling approach was developed to simulate the slurry flow for underground disposal of drill cuttings waste. The modeling approach was coupled with and implemented in the well-known general purpose subsurface multiphase flow simulator, TOUGH2. The new modeling approach treats the slurry flow behavior in subsurface systems as Bingham plastic liquid, with a linear relationship representing the yield stress and the concentration of the gelatinizer in the slurry. In addition, the precipitation-dissolution process was taken into account for solid-aqueous phase changes of the water-slurry mixture under and over the threshold pressure. The model has been verified by the analytical solution of a transient flow of single-phase Bingham fluid, and has further been tested by modeling field-scale injection of drill cutting wastes into a multi-layered geological formation in Texas. A hypothetical model has also been used to conduct sensitivity analysis of the impact of slurry density, injection depth and injection pattern on the storage formation performance. The results revealed that the effect of injection volume is greater than the mass on pressure buildup. In addition, a short period of intermittent reinjection can lead to an earlier formation breakdown due to particle sedimentation and reduce the storage capacity. The developed model can be used to evaluate the prediction of slurry transport, storage capacity, pressure distribution, and the formation breakdown time in a drill cuttings waste disposal project.