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The thermal performance of helical-coil heat exchangers can be significantly enhanced when operated with ice slurry as a phase-change refrigerant. It is essential to also consider the hydrodynamics of ice slurry flow to determine the overall performance of the heat exchanger. This study presents a detailed numerical investigation of the thermo-hydrodynamic performance of a helical coil heat exchanger operated with a laminar and non-Newtonian flow of ethyl-alcohol ice slurry subject to phase change. The Bingham plastic model is used to reflect the non-Newtonian behavior of ice slurry. The phase change of ice slurry is modelled using the enthalpy-porosity method. The pressure drop and heat transfer of ice slurry in a double-turn helical coil are determined in terms of ice mass fraction and Dean number. The results show that an increase in the ice mass fraction and Dean number results in an increase of the heat transfer rate. This is, however, associated with an increase in pressure drop. The entropy generation analysis is introduced to evaluate the overall performance of the heat exchanger, taking into account the opposing effects of heat transfer and pressure drop. It is evident that, at certain ice mass fractions, there exists an optimal value of the Dean number that leads to minimum irreversibility and maximum overall performance.

The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Mardare, who studied the asymptotics of the Stokes flow in a cylindrical domain that becomes unbounded in one direction, and prove the convergence of the solution to the Bingham problem in a finite periodic domain, to the solution of the Bingham problem in the infinite periodic domain, as the length of the finite domain goes to infinity. As a consequence of this convergence, the existence of a solution to a Bingham problem in the infinite periodic domain is obtained, and the uniqueness of the velocity field for this problem is also shown. Finally, they show that the error in approximating the velocity field in the infinite domain with the velocity in a periodic domain of length 2l has a polynomial decay in l, unlike in the Stokes case (see [Chipot, M. and Mardare, S., Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, Journal de Mathematiques Pures et Appliquees, 90(2), 2008, 133–159]) where it has an exponential decay. This is in itself an important result for the numerical simulations of non-Newtonian flows in long tubes.

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

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

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

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

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

We report the synthesis of single crystalline octahedron-shaped magnetite microcrystals, the preparation of magnetorheological fluids (MRFs) and their magnetorheological properties under steady-state shear conditions. The magnetite microcrystals were synthesized via the template-free hydrothermal route. MRFs with three different particle concentrations (10, 20 and 40 weight%) were prepared and were subjected to steady shear conditions at various externally applied magnetic fields of strength up to 1.2 T. The shear rates were chosen up to high enough values to observe the yield behaviour of the MRFs. The dynamic yield strengths of MRFs, estimated using the Bingham plastic model fit to the steady-state shear response curves, showed that they scale-up with the applied magnetic field strength and amount of magnetic particles in the fluid. The origin of the mechanical strength in the MRFs due to the inter-particle interaction is explained using a simple dipolar model. The observed high yield strengths of the MRFs were explained on the basis of the particle shape (octahedrons) and magnetic nature (saturation magnetization). By comparing the values of the yield strength with the on-state to off-state viscosity ratio for the MRFs (for each particle concentration), an optimum content of particles in the carrier fluid to obtain high efficiency is suggested. Because the particles are single crystalline, the off-state viscosity of the MRFs even at the highest studied (40 wt%) particle concentration was very low, which is ideal for their application as quickly responding MRFs.

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

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

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

In order to study the different mix proportions on rheological properties of cemented coal gangue backfill (CGB). Firstly, by single-factor test, the appropriate dosage ranges of mass concentration, fly ash content and fine gangue ratio were determined. Then on this basis, by response surface methodology, the quadratic polynomial regression models of yield stress and plastic viscosity were constructed respectively. The results show that the rheological model of fresh CGB accorded with rheological behavior of the Bingham fluid. With the increase of mass concentration, the yield stress of fresh CGB increases significantly. With the increase of fly ash content, the plastic viscosity of fresh CGB increase significantly. With the increase of the fine gangue ratio, the yield stress of fresh CGB decreases first and then increases, and the plastic viscosity increases slowly. This study will provide theoretical support for practitioners to predict the rheological properties of fresh CGB with different material compositions, and optimize the pumping performance in order to guide the engineering application more accurately.

The flow of Bingham nanofluids at the ingress section functioning as non-Newtonian nanofluids in cylindrical concentric rollers have been studied. This analysis could be advantageous for chemical processing industries and thermal processing intensified systems. The silver(Ag), copper(Cu), Aluminum oxide(Al2O3) and Titanium dioxide(TiO2) nanofluids through water adjoining with Bingham fluid, which are refered as Bingham nanofluids with the yield value Bnf = 10. The investigative study had been carried out with the supposition that the cylindrical roller twain are revolving, with two different flow region space K = 0.3 and 0.8, in the selfsame along with the reverse directions including diverse angular velocity. Theoretically, this intensified system can be considered as an aircraft turbojet engine model. The continuity, momentum and energy equations were derived through the finite difference method. These equations were solved to find the pressure along the radial direction and to obtain velocity components such as axial, radial, tangential and thermal conductivity. Numerous non-Newtonian flow parameters, various concentrations with algebraic considerations were computed and results were obtained for the same. The major purpose of the present investigation is to identify the advancement of the velocities, pressure and thermal conductivity in the ingress section of considered processing intensified systems.

The assumption of cement grouts as ‘Bingham fluids’ has thus far facilitated the development of simplified analytical tools for rock grouting design. However, from a practical standpoint the use of the Bingham constitutive law throughout the design phase has several shortcomings that merit being more systematically addressed. For instance, the known key attributes of cementitious suspensions, e.g. wall-slip, thixotropy, shear rate and time dependency that influence the grout propagation especially at low shear rates are not considered when the Bingham model is used. As such, the consequences of overlooking such crucial phenomena whilst aiming for simplicity in design remain relatively unknown. In this work, we show how considering the shear rate aspects and stop criteria with the Bingham model can be better used for grouting design. Our design suggestions are based on fundamental analysis and theory of Bingham fluid radial flow and current knowledge on cement grout rheological behaviour, as reported from rheological experiments. Moreover, we contribute to the existing design procedure by presenting a nomogram that can readily be used for practical rock grouting design. The nomogram approach allows rapid computation of all key parameters, which in essence shows that unless wall slip is taken into account up to ~50% overestimation of grout travel results.

This study is primarily motivated to explore the onset of fluid yield stress on the Bodewadt flow involving Bingham fluid whose viscosity coefficient admits an inversely linear temperature dependency. Accompanying heat transfer process is studied by assuming isothermal surface temperature. A similarity solution is presumed which results into a system of coupled non-linear equations with three unknowns. Numerical solutions reveal that ignoring viscosity variation with temperature can lead to inaccurate calculations of skin friction coefficient and Nusselt number, which are important quantities from engineering viewpoint. For pure Bodewadt flow, axial flow accelerates and radial flow reduces when case of constant fluid properties is approached. In addition, a considerable growth in cooling rate of the surface is detected whenever suction velocity becomes higher. Both two-and three-dimensional streamlines are computed which reveal that Bingham fluid assumption combined with variable viscosity markedly affects the flow situation.

In this study, a numerical manifold method (NMM) based simulator, which is able to simulate the whole process of grouting reinforcement, including the migration and coagulation process of injected slurries in rock fractures networks, is developed for evaluating the effectiveness of grouting reinforcement in deep rock tunnels. To implement the migration process, the grouting hole generation algorithm, the Bingham fluid model, the migration network searching algorithm as well as the framework for fluid–solid (FS) coupling process are introduced into the zero-thickness cohesive element (ZE) based NMM (Co-NMM). To reflect the reinforcement effect of the slurry coagulation after the migration process, a bonding reinforcement algorithm based on the ZE model is proposed. To improve the computational efficiency, an explicit integration scheme is introduced. To validate and illustrate the capability of the developed method, an uncoupled and a coupled numerical examples are conducted and the simulation results are in good accordance with the analytical solutions or laboratory observations. In addition, a series numerical direct tensile test and uniaxial compressive test are conducted to verify the capability of the proposed bonding reinforcement algorithm. Finally, to demonstrate the capability of the developed simulator in simulating problems with large scale, grouting reinforcement in a deep rock tunnel model is conducted and the predicted results show that the convergence deformation and fragmentation-bulking phenomenon induced by excavation in the deep rock tunnel are effectively controlled through the grouting reinforcement.

This paper aims to study a mathematical model explaining the impacts influence of heat transfer on magnetohydrodynamics oscillatory flow for Bingham Fluid with variable viscosity through a porous channel. The governing equations are solved numerically by developing a suitable finite difference scheme. As an application of the theory in the field of magneto. We used the perturbation method to obtain a clear formula for fluid motion. The results obtained are illustrated by graphs after we reached the momentum equation solution, and used the MATHEMATICA program for plot the velocity and temperature of the fluid for two types of flow (Poiseuille and Couette).

In the practice of drilling horizontal, directional, and unstable well profiles, the friction produced by bit balling, wellbore instability, cavings, and dog-legs resulted in excessive torque and drag. The friction along with high torque and drag, which results from the drill string, casing, and wellbore contact, leads to pipe stucks, overpulls during tripping-outs, and even closure of the oil and gas well. Heat generated from metal contact between casing and drill string is the cause of wear of drill string and casing. Oil-based drilling fluids are identified to produce minimum friction and torque than that of water-based drilling fluid/mud (WBM). However, the use of oil-based drilling fluids is becoming obsolete due to stringent environmental regulations. Therefore, it is critical to identify and design a water-based drilling mud with lubricant additives that are environmentally friendly, cost-effective, and give better lubrication similar to oil-based and synthetic-based drilling fluid. The objective of this study is to investigate the effect of two additives PC60 (the product of the reaction of glycerol ​+ ​tall oil fatty acid) and graphene nanoparticles on the rheological and lubrication properties of water-based drilling fluid. All together total 14 drilling fluid samples have been prepared for the detailed analysis. Extensive experimental work has been done to study the effect of lubricant additives (PC60 and graphene nanoparticles) on the rheology and lubrication of various WBMs with different additive concentrations (1, 2, and 3% by volume) at 30, 60, and 90 ​°C. All samples were investigated for their rheology, viscoelastic behavior, and lubrication properties before and after hot rolling. The experimental data generated in this work have been successfully utilized to find various fitting parameter for the Bingham plastic rheological model, followed by a discussion on foaming tendency of the samples and effect of pH on the rheological stability of drilling fluid. Subsequently, a relationship between the coefficient of friction (in the presence of different lubricant additives in the mud) and rheological properties (plastic viscosity and yield point) of different drilling fluid samples have been proposed.

Polymer flooding (PF) in heterogeneous heavy oil reservoirs is not only closely related to polymer degradation, but also to non-Newtonian flow. In this paper, both experimental and simulation methods are combined to investigate this type of flooding. Through experiments, the degradation of polymer, rheological properties of fluids, and flow of fluids in porous media were determined. Based on the experimental results, a novel mathematical model was established, and a new PF simulator was designed, validated, and further applied to study the effects of polymer degradation, polymer solution shear thinning, and non-Newtonian flow on PF in heterogeneous heavy oil reservoirs. These experimental results demonstrated that the polymer first-order static degradation rate constant was lower than the polymer first-order dynamic degradation rate constant, the polymer solution and heavy oil were non-Newtonian fluids, with shear thinning and Bingham fluid properties, respectively, and the heavy oil threshold pressure gradient (TPG) in low-permeability porous media was higher than that in high-permeability porous media. All comparison results showed that the designed simulator was highly accurate and reliable, and could well describe both polymer degradation and non-Newtonian flow, with special emphasis on the distinction between polymer static and dynamic degradation and heavy oil TPG. Furthermore, the simulation results verified that polymer degradation, polymer solution shear thinning, and heavy oil TPG all had negative effects on the efficiency of PF in heterogeneous heavy oil reservoirs.

This paper presents an experimental and theoretical study of Newtonian and non-Newtonian (Bingham plastic) emulsion drop impact on a solid non-heated surface. The utilization of different emulsifiers at a constant concentration of continuous and dispersed phases in emulsions allows the considerable variation of the surface tension at the liquid–liquid interface. Our data for the maximum spreading diameter of water, n-decane, and emulsion drops impacting on a surface are compared with that predicted from the existing models for single-phase liquid drops. All selected models underpredict the experimental data. As a result, the importance of considering the capillary effects at the internal interfaces of the emulsion drops and the careful examination of all rheological properties in the case of Bingham plastic fluids is confirmed experimentally and is taken into account theoretically. The models of Pasandideh-Fard et al. [“Capillary effects during droplet impact on a solid surface,” Phys. Fluids 8, 650 (1996)] and Ukiwe and Kwok [“On the maximum spreading diameter of impacting droplets on well-prepared solid surfaces,” Langmuir 21, 666–673 (2005)] are modified and adapted to the emulsion drop by means of including the additional surface energy term at the liquid–liquid interface of the emulsion drop in the energy conservation equation and the non-Newtonian Reynolds number. The predictions of the maximum spreading diameter give good agreement with the measured one. Several constraints and future lines of research that relate to a specific behavior of the compound liquid drops at the impact on a solid surface are highlighted.

The Poiseuille flow of a Bingham fluid with the yield slip condition at the wall is examined. The governing equations are solved employing the accelerated augmented Lagrangian method for both the viscoplastic model and the yield slip equation. We solve numerically the flow in pipes with different cross sections: equilateral and isosceles triangles, L-shape, and hourglass-shape. The combined effects of viscoplasticity and slip on the flow have been investigated. The evolution of the unyielded regions has been studied. The computations cover the full range of the two main dimensionless numbers and exhibit complex flow patterns: all the different flow regimes are identified in ducts of various cross sections.

The laminar forced convection momentum and heat transfer aspects of a circular disk oriented normal to the flow and maintained at a constant flux or a constant temperature condition in a stream of ...

The plane Poiseuille flow of a Bingham plastic with pressure-dependent material parameters is analysed. Both the plastic viscosity and the yield stress are assumed to vary linearly with pressure and analytical solutions are derived for the two-dimensional pressure and the one-dimensional velocity. The effects of the plastic-viscosity and yield-stress growth parameters on the thickness of the unyielded plug and the conditions for the occurrence of flow are discussed.

We study the peristaltic transport of a Bingham fluid in a channel with small aspect ratio whose walls behave as a periodic traveling wave. The governing equations in the unyielded phase are obtained writing the integral formulation for the momentum balance. As shown in Fusi et al. (2015), this approach allows to overcome the so-called “lubrication paradox” which may arise in the thin film approximation. We consider the case in which the inlet flux is prescribed and the one in which the flow is driven by a given pressure drop. In both cases the solution of the problem is determined solving a nonlinear integral equation for the yield surface. We perform some numerical simulations to illustrate the behavior of the yield surface, assuming that the traveling wave describing the peristaltic motion has a sinusoidal shape.

In this study, we prepared calcium ferrite (CaFe2O4) nanocrystal clusters by a solvothermal method and evaluated their application potential in magnetorheological (MR) fluid. The morphology, composition, microstructure and magnetic properties of the CaFe2O4 nanocrystal clusters were investigated in detail. The as-prepared CaFe2O4-based MR fluid showed typical Bingham fluid behavior, changing from a liquid-like to a solid-like structure under an external magnetic field. Compared with carbonyl iron (CI) particles, the MR fluid based on CaFe2O4 nanocrystal clusters showed enhanced sedimentation stability, which can be mainly due to the reduced density mismatch between dispersed phase and carrier fluid. In conclusion, the as-prepared CaFe2O4 nanocrystal clusters are considered as a promising candidate for high-performance MR fluid.

In the heavily silt-laden river, density current belongs to an excellent method for flushing the input sediment without water level drawn down. Heavily silt-laden fluid mud in reservoir comes from heavily silt-laden density current. Density current comes into being in the reservoir and may reach the front of the dam with certain flood duration in addition. And the flood also needs to meet a certain sediment concentration and discharge. That makes water and sediment input need to provide density current with energy to overcome the energy loss during the forming process. For example, in a density current creeping process, the current energy shortage often can unsuccessfully reach the front of the Xiaolangdi dam, the stop makes a muddy pond before the dam. Another situation occurs during the density current flushing process. When the input flood ends without subsequent enough energy retention, the foremost density current creeps slowly and suspends before the dam. In these two cases, the muddy layer along the vertical section in front of the reservoir dam will be called fluid mud in this paper. On the basis of understanding the mixing characteristics of hyper-concentrated flow settlement characteristics, viscoelastic and Bingham fluid in the Yellow River, under the flume experiments combined with theoretical analysis method, the formula which concludes high sediment rheological properties of mud and sediment particle size, the volume ratio of sediment concentration, is established and fluid mud layer theoretical analysis had been carried out and flume experiments had been combined to carry out about the effect between density currents and fluid mud. It is found that the difference between the fluid mud with the Bingham shear stress and the flow shear stress due to different sediment concentration, which can divide the movement regime into 2 types, named invasive and interface. The heterogeneous density flow of different sediment does not only affect the muddy water thickness and blending extent, but also determine the movement regime of the head. The flow discharge mainly affects the muddy water thickness and the velocity of the density current. The density of fluid mud increased from fast to slow with the time lasting, which is formed due to settlement. Through the theoretical deduction, the critical judgment parameter of the fluid mud layer incipient motion is obtained. The calculation formula which concluded volumetric sediment concentration, slope and density current thickness is proposed based on the experiments. Obviously, timely opening the desilting tunnel or with the help of the subsequent flood, this will enable the fluid mud incipient motion and flushing out of the reservoir to achieve the purpose of efficient sediment transport. With the adhesion of the fine sediment mud layer in group settlement mechanism and process, conditions on follow-up density current occurrence, and fluid mud layer motion possibility, and its interaction are the basis and key technology of efficient way flushing sediment out of the reservoir in the heavily silt-laden river. The research results can enrich the contents of river sediment dynamics and provide technical reference for the operation and planning of sediment-laden river reservoir

We develop an asymptotic solution for the axisymmetric squeeze flow of a viscoplastic medium. The standard lubrication-style expansions of the problem predict a plug speed which varies slowly in the principal flow direction. This variation implies that the plug region cannot be truly unyielded. Our solution shows that this region is a pseudo-plug region in which the leading order equation predicts a plug, but really it is weakly yielded at a higher order. We follow the asymptotic technique suggested earlier by Balmforth and Craster (1999) and Frigaard and Ryan (2004). This method involves no relaxation of the exact Bingham model. The analytical expression for the squeeze force is in good agreement with previous numerical results. In the second part of the paper, the axisymmetric squeeze flow of a Bingham fluid with slip yield boundary condition at the wall is considered. We provide an asymptotic solution for this type of flow. Depending on the ratio of two dimensionless parameters partial slip (stick-slip) or full slip at the wall (slip) are possible.

The effect of modifying yield stress on turbulent pipe flow of generalised Newtonian fluids at a friction Reynolds number of 323 is investigated using direct numerical simulations. Simulations are carried out for Bingham and Herschel–Bulkley fluids with the yield stress varying from 0% to 20% of the mean wall shear stress. Results show that the effect of increasing yield stress is mostly similar to shear thinning in power-law fluids. The turbulent viscous stress which arises due to viscosity fluctuations is negative for a yield stress fluid and is higher in magnitude for higher yield stress. An analysis of the turbulent kinetic energy budget showed that the effect of yield stress is mainly significant near the wall for y + ≲ 60 which was also seen for shear-thinning power-law fluids at similar Re τ . Additional shear thinning enhances the yield stress effect. The main difference between shear thinning and yield stress is that the effect of yield stress is maximum outside the viscous sublayer whereas shear thinning has a more significant effect inside the viscous sublayer.

Accurate rheological measurements of barite-weighted ultrahigh density water-based drilling fluids with a rotational viscometer may be hindered by the wall slip effect. This paper describes a correction method that is based on the principle of flow curves gap dependence. A two-stage Tikhonov regularization numerical strategy was developed to obtain the true viscous behavior and wall slip of barite-weighted drilling fluids containing a high particle fraction. The proposed approach does not depend on the narrow gap assumption or the prescribed form of rheological models. The results show that barite-weighted ultrahigh density drilling fluids start to slip after reaching a small value of critical shear stress, and the wall slip velocity increases linearly as a function of shear. There are significant discrepancies between the slip-corrected rheological models and the apparent models. Curve fitting results show that the slip-corrected flow curves are linear as would be expected for Bingham plastic fluids, while the uncorrected apparent flow curves are nonlinear as one would expect for yield power law fluids. Failing to correct for the wall slip effect would result in seriously underestimating the bulk viscosity of barite-weighted ultrahigh density water-based drilling fluids.

We study numerically isoviscous displacement flows of a Bingham fluid by a Newtonian fluid in a horizontal plane channel. We consider a heavy-light displacement flow with a laminar imposed flow. We analyze the flow from various perspectives, using the three dimensionless parameters that largely describe the flow: the Bingham number (Bn), the densimetric Froude number (Fr) and the Reynolds number (Re). In particular, we are able to categorize three classes for the main flow regimes, viz., center-type and slump-type, no-back-flow and temporary-back-flow, and stable and unstable displacements, for which we also quantify their transition boundaries versus the aforementioned dimensionless numbers. We show that the appearance of unstable flows can eventually lead to a number of different flow patterns, such as sinusoidal shaped wave and periodic-detachment forms. In addition, we study in depth an interesting feature exclusively associated to viscoplastic fluid displacements, i.e., the formation of static residual layers on the upper/lower walls of the channel. We also study the evolution of the key displacement flow features, i.e., the trailing and leading fronts, and classify certain secondary flow features related to the leading front, such as plug-like, inertial tip, semi-detached and fully-detached fronts. Finally, we quantify the velocity of the leading front at long times.

Fluid flow modeling is a major area of interest within the field of rock mechanics. The main objective of this study is to gain insight into the performance of grout injection inside jointed rock masses by numerical modeling of grout flow through a single rock joint. Grout flow has been widely simulated using non-Newtonian Bingham fluid characterized by two main parameters of dynamic viscosity and shear yield strength both of which are time dependent. The increasing value of these properties with injection time will apparently affect the parameters representing the grouting performance including grout penetration length and volumetric injection rate. In addition, through hydromechanical coupling a mutual influence between the injection pressure from the one side and the joint opening/closing behavior and the aperture profile variation on the other side is anticipated. This is capable of producing a considerable impact on grout spread within the rock joints. In this study based on the Bingham fluid model, a series of numerical analysis has been conducted using UDEC to simulate the flow of viscous grout in a single rock joint with smooth parallel surfaces. In these analyses, the time-dependent evolution of the grout fluid properties and the hydromechanical coupling have been considered to investigate their impact on grouting performance. In order to verify the validity of these simulations, the results of analyses including the grout penetration length and the injection flow rate were compared with a well-known analytical solution which is available for the simple case of constant grout properties and non-coupled hydraulic analysis. The comparison demonstrated that the grout penetration length can be overestimated when the time-dependent hardening of grout material is not considered. Moreover, due to the HM coupling, it was shown that the joint opening induced by injection pressure may have a considerable increasing impression on the values of penetration length and injected grout volume.

Understanding the rheological properties of clay suspensions is critical to assessing the behavior of sediment gravity flows such as debris flow or turbidity current. We conducted rheological measurements of composite smectite-quartz suspensions at a temperature of 7 degrees C and a salt concentration of 0.6M. This is representative of smectite-bearing sediments under conditions on the seafloor. The flow curves obtained were fitted by the Bingham fluid model, from which we determined the Bingham yield stress and dynamic viscosity of each suspension. At a constant smectite-quartz mixing ratio, the yield stress and the dynamic viscosity tend to increase as the solid/water ratio of the suspension is increased. In the case of a constant solid/water ratio, these values increase with increasing smectite content in the smectite-quartz mixture. Additional experiments exploring differing physicochemical conditions (pH1.0-9.0; temperature 2-30 degrees C; and electrolyte (NaCl) concentration 0.2-0.6M) revealed that the influence of temperature is negligible, while pH moderately affects the rheology of the suspension. More significantly, the electrolyte concentration greatly affects the flow behavior. These variations can be explained by direct and/or indirect (double-layer) interactions between smectite-smectite particles as well as between smectite-quartz particles in the suspension. Although smectite is known as a frictionally weak material, our experimental results suggest that its occurrence can reduce the likelihood that slope failure initiates. Furthermore, smectite can effectively suppress the spreading distance once the slope has failed.

In this paper we consider the non-isothermal flow of a Bingham fluid with rheological parameters depending on pressure and temperature. The governing equations are scaled in order to evaluate the relevance of the various kinematical and thermodynamical effects represented by some non-dimensional groups such as the Reynolds, second Froude, Brinkman, Peclet and Bingham numbers. We consider a perturbative approach in which the small parameter is the product of the reference temperature and the thermal expansion coefficient. In a recent paper (Fusi in Meccanica, 2017. doi: 10.1007/s11012-017-0655-8 ) this problem has been investigated under the hypothesis that the Reynolds number is of order one. Here we study the case in which the Reynolds number is small (creeping flow). The differences with Fusi (Meccanica, 2017. doi: 10.1007/s11012-017-0655-8 ) are far from trivial. In particular we show that in the situation studied here we can obtain a non-isothermal Stokes Oberbeck approximation in which the buoyancy and frictional effects are taken into account.

The Richtmyer–Meshkov and Rayleigh–Taylor instabilities in viscoplastic (Bingham) fluids are studied in two-dimensional setting. The evolution of the Richtmyer–Meshkov instability in a Bingham fluid is analyzed as compared with its evolution in a Newtonian fluid. The critical amplitude of the initial perturbation in the velocity field is estimated. Numerical results obtained for Richtmyer–Meshkov and Rayleigh–Taylor instabilities in a Bingham fluid are presented and compared with those obtained for a Newtonian fluid.