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The exploration addresses the effect of variable viscosity and thermal conductivity on the peristaltic mechanism of Bingham fluid. A two-dimensional non-uniform porous channel is considered for the fluid flow, which is assumed to be inclined. The impact of heat, slip conditions, wall properties, homogeneous and heterogeneous reactions are examined. The resulting nonlinear differential equations are solved by employing the perturbation method. The solutions acquired are analyzed and sketched through graphs that show that the variable viscosity renders a critical role in regulating the velocity of the fluid in the channel's central part. The stream function has been analyzed to observe the trapping phenomenon. Further, the obtained results find its application in understanding the flow of blood in micro arteries.

The rheological behaviors of highly concentrated fine particle suspensions (clay-silt-water mixtures) and coarse particle suspensions (coarse particles within a fine particle suspension) were investigated in this study. Experimental results demonstrated that the Bingham Fluid Model with two rheological parameters, Bingham yield stress and viscosity, well characterized the rheological behavior of fine particle suspensions at shear rates between 4 and 20 s−1. The inclusion of coarse particles within a fine particle suspension induced an enhancement to the rheological parameters. The rheological parameters of a coarse particle suspension not only depend on its total particle fraction but also on its relative fine/coarse particle fractions. Empirical equations of these two parameters were proposed, quantitatively related to both fine and coarse particle fractions. Results indicated that the Bingham yield stress and viscosity are much more (an order larger) sensitive to changes in fine particle fraction than to changes in coarse particle fraction.

An artery narrowing referred to as atherosclerosis or stenosis causes a reduction in the diameter of the artery. When blood flow through an artery consists of stenosis, the issue of solute dispersion is more challenging to solve. A mathematical model is developed to examine the unsteady solute dispersion in an overlapping stenosed artery portraying blood as Bingham fluid model. The governing of the momentum equation and the constitutive equation is solved analytically. The generalized dispersion model is imposed to solve the convective-diffusion equation and to describe the entire dispersion process. The dispersion function at steady-state decreases at the center of an artery as the stenosis height increase. A reverse behavior is shown at an unsteady-state. As the plug core radius, time and stenosis height increase, the dispersion function decreases at the center of an artery. There is a high amount of red blood cells at the center of the artery but no influences near the wall. Hence, this model is useful in transporting the drug or nutrients to the targeted stenosed region in the treatment of diseases and in understanding many physiological processes.

In this paper aims, we found the fluid concentration after calculating the velocity and temperature of the fluid with a variable viscosity that depends on the fluid moving through an inclined porous channel. We examined the influences of certain parameters that are active on fluid velocity by analyzing the graphs obtained 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 this study, we performed direct simulations of particle suspensions in a simple shear flow with a viscoplastic model (Bingham fluid) using a finite-element/fictitious-domain method, as a model system for cuttings transport with a drilling mud in the oil and gas exploration. Bulk rheology and particle interaction were investigated via several example problems including single-particle, two-interacting particle, and many-particle problems for various solid fractions in both Bingham and Newtonian fluids. We report that, at low shear rate, huge reductions occur in both the relative bulk viscosity and angular velocity of particle suspension in a Bingham fluid compared to that in a Newtonian fluid. This indicates that, although particle incorporation increases bulk viscosity in a Bingham fluid, the amount of increase appears much smaller than that with the Newtonian medium, and particle motions were restricted to some extend at a low shear rate with a yield stress fluid. Moreover, the suppression in viscosity increase with particles disappears at a high shear rate, just like Newtonian particle suspension. This phenomenon has been interpreted by the suppressed particle angular rotation in a Bingham fluid. In addition, flow fields with low shear regions, where the viscosity of a Bingham fluid is high and the fluid mobility decreased significantly, on the left and right sides of a particle also confirm this interpretation. The two-interacting particle problem reveals delayed particle interaction with increased time period in particle trajectories (drafting, kissing, tumbling and separation) in a Bingham fluid. Similar behaviors with the suppression in viscosity increase can be also observed in the many-particle problem.

Purpose The purpose of this study is to solve convective diffusion equation analytically by considering appropriate boundary conditions and using the Taylor-Aris method to determine the solute concentration, the effective and relative axial diffusivities. Design/methodology/approach >An analysis has been conducted on how body acceleration affects the dispersion of a solute in blood flow, which is known as a Bingham fluid, within an artery. To solve the system of differential equations analytically while validating the target boundary conditions, the blood velocity is obtained. Findings The blood velocity is impacted by the presence of body acceleration, as well as the yield stress associated with Casson fluid and as such, the process of dispersing the solute is distracted. It graphically illustrates how the blood velocity and the process of solute dispersion are affected by various factors, including the amplitude and lead angle of body acceleration, the yield stress, the gradient of pressure and the Peclet number. Originality/value It is witnessed that the blood velocity, the solute concentration and also the effective and relative axial diffusivities experience a drop when either of the amplitude, lead angle or the yield stress rises.

Present analysis is conducted for Bodewadt flow along a permeable plane surface immersed in a Bingham fluid, which represents a class of non-Newtonian fluids exhibiting yield stress. The resulting heat transfer phenomenon is analyzed in the existence of viscous dissipation. After implementing boundary layer approximations, von-Karman substitutions are employed resulting in a coupled non-linear system. For the numerical solution, a reliable numerical routine bvp4c based on collocation method, is adopted. Flow model contains a parameter Bn , measuring the relative importance of fluid yield stress. Boundary layer is markedly risen as a consequence of fluid yield stress. Viscous dissipation also remarkably influences the resulting heat transfer process. Subtle fluid dynamics quantities including normalized skin friction, disk cooling rate and volumetric flow rate are scrutinized under the influence of fluid yield stress. The results predict a deceleration in entrained flow whenever fluid exhibits yield stress.

Quick-setting grout has time-varying characteristics, and the space porosity of the injected medium changes after being grouted. The above two points need to be considered when loose and broken coal rock masses are grouted with rapid-setting grout. In other words, the coupling effect of the slurry-coal rock mass causes the slurry to exhibit the temporal and spatial characteristics of slurry viscosity (TSCSV). Based on the Bingham fluid constitutive model, a capillary group model with a linear increase in diameter was created, and a one-dimensional penetration grout diffusion model was established considering the TSCSV. The one-dimensional visualization splitting-permeation grout diffusion simulation test system was designed to obtain the space porosity of the broken coal rock mass under different final grouting pressures to obtain the law of the changes in grouting pressure and diffusion height with time under the condition of a fixed grouting rate. Furthermore, the mechanism of splitting-permeation grouting in loose and broken coal rock masses is analysed in depth considering the TSCSV. The results showed that the space porosity of coal rock masses increases linearly. In addition, the calculated value of the slurry diffusion distance was 0.93 – 1.1 times the experimental value considering the TSCSV. The calculated value was in good agreement with the experimental value. The calculated value of the final pressure of orifice grouting was approximately 1.5 times the test value without considering the unevenness of the space porosity distribution (USPD). The grouting pressure was overestimated without considering the USPD. Therefore, the TSCSV of the quick-setting slurry should be fully considered in the grouting design.

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

The superimposition of mechanical oscillations can lead to a remarkable modification in the friction factor (Cf) with a fixed flowrate for viscous non-Newtonian fluids in a pipe but cannot affect the flow of Newtonian types. Therefore, less driving pressure is required for fluids with a shear-thinning nature, while more for shear-thickening types. A validated computational fluid dynamics (CFD) model is employed to compare the efficacy of three modes of oscillation: longitudinal, transverse, and rotational within the laminar flow region. Rheologies considered here are power-law fluids and Bingham plastic types. At a given Reynolds number (Re), Cf is found to be a function of rheological parameters (i.e., flow behavior index, n and Bingham number, Bn) and the vibration intensity, λ. Longitudinal oscillation is the most effective, with transverse oscillation also producing comparable results. Rotational oscillation causes the least effect on the viscosity and therefore, the friction factor is even nearly unchanged while λ ≤ 20 for power-law fluids, and λ ≤ 5 for Bingham plastic rheologies. Expressions for Cf are proposed, giving a quantitative estimation on the effect of mechanical vibration on the driving pressure.

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

This framework presents heat transfer analysis for swirling flow of viscoplastic fluid bounded by a permeable rotating disk. Problem formulation is made through constitutive relations of Bingham fluid model. Viscous dissipation effects are pre-served in the mathematical model. Entropy production analysis is made which is yet to be explored for the von-Karman flow of non-Newtonian fluids. Having found the similarity equations, these have been dealt numerically for broad parameter values. The solutions are remarkably influenced by wall suction parameter and Bingham number which measures the fluid yield stress. Akin to earlier numerical results, thermal boundary-layer suppresses upon increasing wall suction velocity. Thermal penetration depth is much enhanced when fluid yield stress becomes large. Higher heat transfer rate can be accomplished by employing higher suction velocity at the disk. However, deterioration in heat transfer is anticipated as fluid yield stress enlarges. Current numerical results are in perfect line with those of an existing article in limiting sense.

We study the onset of convection within a rectangular porous cavity which is saturated with a Bingham fluid and subjected to a uniform internal heat generation. When such a cavity is saturated by a Newtonian fluid, convection takes place at all nonzero values of the Darcy–Rayleigh number, Ra. In such cases convection takes the form of two contrarotating cells with flow down the cold sidewalls when Ra first increases from zero. However, when the enclosure is saturated by a Bingham fluid, then we find that the cavity remains stagnant until the Darcy–Rayleigh number is sufficiently large that buoyancy overcomes the yield threshold. Numerical solutions are obtained using a second-order accurate finite-difference methodology where convergence is accelerated using line relaxation. The presence of the yield surfaces, which mark the boundaries of stagnant regions, is modelled by means of a regularization of the yield threshold. It is found that the critical value of Ra above which convection arises depends roughly linearly on the value of Rb, which may be described as a convective porous Bingham number. When the cavity has a sufficiently large aspect ratio, the fluid admits more than one stable steady-state solution.

We present rheological and mechanical behaviors of a partially cured photopolymer. When an ultraviolet (UV)-curable resin is exposed to UV light in atmospheric conditions, a partially cured layer is formed on the top of the resin owing to inhibitory effects of oxygen. Interestingly, such a partially cured resin behaves like a Bingham plastic with a yield stress, being a rigid solid at low shear stress and a viscous liquid at high stress. Unlike typical Bingham plastic materials, however, deformation rate saturation is observed with an increase in applied stress, which is attributed to the gradient in the degree of photopolymerization of the resin (termed “gradient Bingham plastic”). This gradient Bingham plastic can be utilized for the robust fabrication of diverse 3D, multiscale structures.

A mathematical study is developed for the electro-osmotic flow of a non-Newtonian fluid in a wavy microchannel in which a Bingham viscoplastic fluid model is considered. For electric potential distributions, a Poisson-Boltzmann equation is employed in the presence of an electrical double layer (EDL). The analytical solutions of dimensionless boundary value problems are obtained with the Debye-Huckel theory, the lubrication theory, and the long wavelength approximations. The effects of the Debyelength parameter, the plug flow width, the Helmholtz-Smoluchowski velocity, and the Joule heating on the normalized temperature, the velocity, the pressure gradient, the volumetric flow rate, and the Nusselt number for heat transfer are evaluated in detail using graphs. The analysis provides important findings regarding heat transfer in electroosmotic flows through a wavy microchannel.

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

In an effort to further extend bearing life, the authors have attempted to acquire greater knowledge regarding lubricating grease behavior in a bearing. While conducting experiments, some kinds of difficulties commonly arise when attempting to observe grease behavior directly from the bearing exterior without removing seals and shields. Making a breakthrough such a troubling aspect, X-ray computed tomography (CT), which is one of the non-destructive inspection techniques, was employed and resulted in visualizing remarkable details of grease distribution in a resin ball bearing. Hydrodynamic grease transition from churning to channeling state was well revealed by the mixture distribution of urea and barium-based greases which have different properties of X-ray absorption capability. Furthermore, the three dimensional unsteady liquid-gas multi-phase flows analysis was performed. Hydrodynamic feature of grease was regarded as a non-Newtonian fluid, which shows a highly non-linear flow curve, and the constitutive equation of modified Bingham plastic model proposed by Papanastasiou was applied to rheological property. Through these novel experimental and calculation approaches, several new insights about grease behavior inside a ball bearing were brought out.

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

On the basis of the laws of conservation and the principles of thermodynamics, a mathematical model of the flow of a two-phase granular fluid is proposed. One of the phases is the viscoplastic granular Bingham fluid; the other phase is a viscous Newtonian fluid. The equations for flows in the Hele–Shaw cell are analyzed asymptotically, i.e., when the flat-channel width is much less than its length. The correlations between the phase flow rates and the pressure gradient leading to equations of filtration for a two-phase granular viscoplastic fluid are constructed. The criterion is found for the initiation of motion of a granular phase in a porous medium. It is established that, depending on the shear-yield stress, such a phase does not flow if either the pressure gradient or the channel thickness is small. The phase flow rates are analyzed numerically at various input parameters such as the phase viscosities, phase resistivities, ultimate shear stress, etc. The factors slowing down the penetrating motion of the solid phase into the porous medium are revealed.

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

A thin fluid film formed by withdrawing a vertical plate is being studied theoretically. It is the case of a viscoplastic fluid described by the Bingham model. The boundary-value problem is formulated by the lubrication theory. The analysis presented herein required to solve numerically a system of ordinary differential equations at appropriate boundary conditions. For the viscoplastic fluid, we have predicted a film thickness over a wide range of a capillary number (10−4 to 10), with a particular emphasis on finding the free surface location at various conditions: (a) the unyielded region is much larger than the yielded one; (b) without the yielded region; and (c) the unyielded region is smaller but is compared with the yielded one. For the case of Bingham fluid and the limiting case of Newtonian fluid, the agreement was found between our theory and the experiment for the considered capillary number range.A thin fluid film formed by withdrawing a vertical plate is being studied theoretically. It is the case of a viscoplastic fluid described by the Bingham model. The boundary-value problem is formulated by the lubrication theory. The analysis presented herein required to solve numerically a system of ordinary differential equations at appropriate boundary conditions. For the viscoplastic fluid, we have predicted a film thickness over a wide range of a capillary number (10−4 to 10), with a particular emphasis on finding the free surface location at various conditions: (a) the unyielded region is much larger than the yielded one; (b) without the yielded region; and (c) the unyielded region is smaller but is compared with the yielded one. For the case of Bingham fluid and the limiting case of Newtonian fluid, the agreement was found between our theory and the experiment for the considered capillary number range.

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

This work analyses the entrance region flow of Bingham nanofluids in cylindrical concentric annuli. In this discussion, water is used as the base fluid which is embedded with the silver(Ag) and copper(Cu) nanoparticles coalescing with Bingham fluid. The investigation has been carried out by rotating the inner cylinder, while the outer cylinder is assumed to be at rest. A finite-difference analysis is used to obtain the axial, radial, tangential velocity components and the pressure along the radial direction. With the Prandtl's boundary layer assumptions, the continuity and momentum equations are solved iteratively using a finite difference method. Computational results are obtained for various non-Newtonian flow parameters, different volume fraction parameters and geometrical considerations. This work’s main interest is to study the development of velocity profiles and pressure drop in the entrance region of the annuli. The present results are compared with the results available in the literature for various particular cases and it is found to be in good agreement.

We are concerned with a system of partial differential equations (PDEs) describing internal flows of homogeneous incompressible fluids of Bingham type in which the value of activation (the so-called yield) stress depends on the internal pore pressure governed by an advection–diffusion equation. After providing the physical background of the considered model, paying attention to the assumptions involved in its derivation, we focus on the PDE analysis of the initial and boundary value problems. We give several equivalent descriptions for the considered class of fluids of Bingham type. In particular, we exploit the possibility to write such a response as an implicit tensorial constitutive equation, involving the pore pressure, the deviatoric part of the Cauchy stress and the velocity gradient. Interestingly, this tensorial response can be characterized by two scalar constraints. We employ a similar approach to treat stick-slip boundary conditions. Within such a setting we prove long-time and large-data existence of weak solutions to the evolutionary problem in three dimensions.

Using a smart fluid, for example, magnetorheological or electrorheological, in a hydrostatic bearing gives the possibility to actively change the bearing properties during operation. This work presents an analytical model to predict the load and stiffness of a planar hydrostatic bearing lubricated with a Bingham plastic fluid. The model is validated with the use of a numerical model that uses the Bingham–Papanastasiou regularization to achieve convergence. The model gives insight into the size of the operational range of the bearing and the load characteristic.

In underground project, water inrush disaster often occurs, resulting in a large number of casualties and economic losses. To solve these problems, grouting is one of the main techniques for controlling water inrush. At present, the research results on the treatment of water inrush by grouting are based on anhydrous or hydrostatic grouting. However, the study of dynamic water grouting is relatively few and the grouting materials are a little bit. In this paper, water-soluble polyurethane was selected as grouting material, modified by adding hydroxypropyl methyl cellulose, and the bond strength and microstructure change before and after modification are studied via bond strength experiment and microscopic observation. In addition, the WPU (water-soluble polyurethane) diffusion regularity of dynamic water grouting is studied by indoor flat grouting test. The research also adopts the Bingham fluid model according to the slurry characteristics to derive the grouting diffusion radius. The results show that the compactness of HPMC (hydroxypropyl methyl cellulose)-WPU is improved, the heterogeneity is reduced by 50.4%, and the bonding strength is increased by 153%. Therefore, the anti-scour ability of the HPMC-WPU is enhanced. The deviation of the WPU in the X-axis diffusion radius is 7.7 cm, and the HPMC-WPU is 4.39 cm. What’s more, the formula of grouting diffusion radius is derived. By comparing the formula with experiment results, the deviation is less than 15%, therefore, the formula has the significance of guiding engineering practice.

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

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

Modal and non-modal stability analyses are performed for Poiseuille flow of a Bingham fluid overlying an anisotropic and inhomogeneous porous layer saturated with the same fluid. In the case of modal analysis, the resultant Orr–Sommerfeld type eigenvalue problem is formulated and solved via the Chebyshev collocation method, using QZ decomposition. It is found that no unstable eigenvalues are present for the problem, indicating that the flow is linearly stable. Therefore, non-modal analysis is attempted in order to observe the short-time response. For non-modal analysis, the initial value problem is solved, and the response of the system to initial conditions is assessed. The aim is to evaluate the effects on the flow stability of porous layer parameters in terms of depth ratio (ratio of the fluid layer thickness $d$ to the porous layer thickness $d_{m}$), Bingham number, Darcy number and slip coefficient. The effects of anisotropy and inhomogeneity of the porous layer on flow transition are also investigated. In addition, the shapes of the optimal perturbations are constructed. The mechanism of transient growth is explored to comprehend the complex interplay of various factors that lead to intermediate amplifications. The present analysis is perhaps the first attempt at analysing flow stability of viscoplastic fluids over a porous medium, and would possibly lead to better and efficient designing of flow environments involving such flow.

The effect of temperature on the apparent rheological properties of concentrated synthetic fiber suspensions was investigated experimentally. Aqueous suspensions of viscose rayon, acrylic, and nylon 6,6 fibers of various fiber concentrations, sizes, and shapes were used. At a fixed shear rate, the apparent viscosity of all the suspensions decreased reversibly with increasing temperature. The steady-state flow behavior is well described by the Bingham fluid model where the yield stress is a decreasing function of temperature and follows an Arrhenius dependence with an activation energy in the range of 2–80 kJ/mol, which is the same order of magnitude as that reported for 20 wt. % fibrous biomass suspensions below 55 °C. The fiber suspensions exhibited a negative plastic viscosity at low temperatures, and as the temperature was increased, the plastic viscosity became less negative. This temperature-dependent rheological behavior is qualitatively similar to that observed for concentrated fibrous biomass suspensions. The fiber suspensions formed heterogeneous networks where the state of aggregation depended on the experimental conditions and thus affected the macroscopic rheology.

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

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

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

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.

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

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 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.

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.