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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.

A crucial part in a two-dimensional discrete fracture network (DFN) model of two-phase flow in a naturally fractured rock is the updating algorithm for the fluid interface positions inside the fractures. In this study, a single fracture situated in an impermeable rock matrix is considered. Displacements of a Newtonian fluid by another Newtonian fluid, by a power-law fluid, or by a Bingham fluid are analysed. It is shown that a significant improvement in accuracy and computational efficiency in all three types of displacement can be achieved by updating the interface position with predictor–corrector scheme instead of forward Euler scheme currently used in such simulators. In order to achieve the same accuracy in the breakthrough time as with the forward Euler method, predictor–corrector can be run with a timestep that is 3 to 50 times larger. The gain in accuracy (or, equivalently, increase of the adjustable timestep) achieved with predictor–corrector is shown to outweigh the extra computational cost of this scheme. It is also shown that further increase in accuracy, e.g. by using the Runge–Kutta 4 scheme, does not pay off. In order to have control over the error in the interface positions, a viable strategy is to choose the timestep equal to a given fraction of the shortest single-fracture breakthrough time in the network. The value of this fraction can be chosen based on the required accuracy in the breakthrough time. In the case of Newtonian/Newtonian displacement, the optimal ratio of timestep to the single-fracture breakthrough time is found to depend only on the mobility ratio and the prescribed accuracy in the numerically computed breakthrough time. In case of a single interface in the fracture, numerical experimentation yields simple equations for recommended timestep in Newtonian/Newtonian displacement based on the fluid mobility ratio and the maximum allowed error in the breakthrough time.

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).

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

In this 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.

Avalanche is a natural disaster in the snow-covered mountainous area in winter, which may cause great disasters to human life and property. It is also a danger for skiers and climbers. This paper presents a new physically based algorithm to simulate the dynamic avalanches under position-based dynamics framework. To realistically simulate avalanches’ dynamic characteristics, we introduce the Bingham plastic model from geodynamics to model snow flow motion in avalanches. The interaction between snow flow in the avalanche and the surrounding objects is simulated by a level set-based two-way fluid–solid coupling model. We also propose static and kinetic friction mixed model to determine the accumulated transition of the avalanche. To create an avalanche scene with more realistic details, we employ an aerodynamics-based snow drag force model to generate snow fog effect. Finally, by choosing different criterion shear rate and friction parameters, different kinds of wet and dry avalanche scenes are realistically rendered. Compared with the real photographs of avalanches, our simulated results are quite satisfactory.

In nature, many fluid-like materials exhibit a yield stress below which they behave like a solid. The Bingham model aims to describe such materials. This paper draws some mathematical considerations on the flow of a Bingham fluid in a vertical channel. The situation due to the presence of an external magnetic field and natural convection is analyzed: the external magnetic field, which is orthogonal to the walls of the channel, generates the Lorentz forces that influence the motion through the Hartmann number. The behavior of the velocity, the induced magnetic field and the thickness of the plug regions are discussed and presented graphically. We find that the velocity is a decreasing function of the Bingham and Hartmann numbers. In particular, the presence of the external magnetic field increases the thickness of the plug region. The modulus of the induced magnetic field is not monotone when the Hartmann number changes, but it is a decreasing function of the Bingham number.

The paper examined a theoretical investigation of the stimulus of mass and heat transfer on the channel's peristaltic utilization of the MHD Bingham liquid. The research study is motivated to explore blood circulation in the little vessels by taking the slip, variable thermal conductivity, and thickness of the wall features into account. The leading constitutive equations are established based on low Reynolds number and approximations for long wavelengths. The solution for the resulting nonlinear energy and momentum equations is obtained using a semi-analytic method, while the exact solution for the concentration field is obtained. Using the MATLAB software, the influences of different constraints on the interest of physiological quantities are represented graphically. One of the considerable outcomes of the current model exposes that the existence of variable fluid properties boosts the rate as well as temperature level areas. The rheological and flow properties of various biological fluids can be derived from this model as a particular case. Moreover, the formation of stuck bolus diminishes for larger values of the magnetic and velocity slip constraints.

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.

Accurate pressure drop estimation is important for drill string and bit nozzles design and optimized fluid circulations as well as identifying the drilling problems such as bit nozzle(s) washout or plugging. In this study, the Bingham Plastic model has been modified by applying a coefficient to its turbulent pressure loss calculations. This coefficient encompasses the effects of the drill pipe tool joints and other effects in estimation of pressure losses. The range of the coefficient was determined in field applications for different hole sizes and mud types. The results showed that applying a correction coefficient of 1.08–1.12 to turbulent pressure loss equations (depending on borehole size and mud type) improves the pressure loss estimation. By applying this coefficient, the estimated pressure losses are increased to compensate the under-estimation of the Bingham Plastic model. This is considered a significant contribution to accurate calculation of borehole hydraulics and in-time detection and identification of borehole problems and reduction of invisible lost time. The findings also showed that this enhanced effect is independent of the mud type. The use of this coefficient removes the necessity of using rather complex mud rheological models such as the Herschel–Bulkley model.

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.

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

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.

This paper discusses the well posedness of an initial value problem describing the motion of a Bingham fluid in a basin with a degenerate bottom topography. A physical interpretation of such motion is discussed. The system governing such motion is obtained from the Shallow Water-Bingham models in the regime where the Froude number degenerates, i.e taking the limit of such equations as the Froude number tends to zero. Since we are considering equations with degenerate coefficients, then we shall work with weighted Sobolev spaces in order to establish the existence of a weak solution. In order to overcome the difficulty of the discontinuity in Bingham's constitutive law, we follow a similar approach to that introduced in [G. DUVAUT and J.-L. LIONS, Springer-Verlag, 1976]. We study also the behavior of this solution when the yield limit vanishes. Finally, a numerical scheme for the system in 1D is furnished.

Accurate determination of hydraulic parameters such as pressure losses, equivalent circulation density (ECD), etc. plays profound roles in drilling, cementing and other well operations. Hydraulics characterization requires that all factors are considered as the neglect of any could become potential sources of errors that would be detrimental to the overall well operation. Drilling Hydraulics has been extensively treated in the literature. However, these works almost entirely rely on the assumption that the drill string lies perfectly at the center of the annulus—the so-called “concentric annulus”. In reality, concentricity is almost never achieved even when centralizers are used. This is because of high well inclination angles and different string geometries. Thus, eccentricity exists in practical oil and gas wells especially horizontal and extended reach wells (ERWs) and must be accounted for. The prevalence of drillstring (DS) eccentricity in the annulus calls for a re-evaluation of existing hydraulic models. This study evaluates the effect of drilling fluid rheology types and DS eccentricity on the entire drilling hydraulics. Three non-Newtonian fluid models were analyzed, viz: Herschel Bulkley, power law and Bingham plastic models. From the results, it was observed that while power law and Bingham plastic models gave the upper and lower hydraulic values, Herschel Bulkley fluid model gave annular pressure loss (APL) and ECD values that fall between the upper and lower values and provide a better fit to the hydraulic data than power law and Bingham plastic fluids. Furthermore, analysis of annular eccentricity reveals that APLs and ECD decrease with an increase in DS eccentricity. Pressure loss reduction of more than 50% was predicted for the fully eccentric case for Herschel Bulkley fluids. Thus, DS eccentricity must be fully considered during well planning and hydraulics designs.

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.

The paper is devoted to the study of convective motions of viscoplastic fluids in closed two-dimensional rectangular domains with different aspect ratios under lateral heating. The problem was solved numerically using the ANSYS Fluent software. The Herschel-Bulkley model was chosen for describing the rheological behavior of the fluid. Under certain rheological parameters, this model was transformed into a Newtonian fluid model, whose behavior was also simulated as a limiting case. Based on the calculated results, the dependences of the maximum value of the stream function in the cavity on the Rayleigh number are plotted. It was found that at small Rayleigh numbers the intensity of motion is close to zero. At a certain threshold value of the Rayleigh number there is a sharp increase in the intensity of motion, and a further increase in the Rayleigh number causes an almost linear growth of the maximum value of the stream function. For each of the considered ratios of cavity sides, the "threshold" values of the Rayleigh number, at which a sharp increase in the intensity of motion of liquid is observed, were determined. The obtained values of Rayleigh numbers turned out to be close to the "threshold" values of the Rayleigh number for the Bingham fluid found in the works of other authors earlier. The fields of the stream function and the square root of the second invariant of the viscous stress tensor were obtained for different values of the Rayleigh number and different aspect ratios. The scenarios of rearrangement of quasisolid motion zones with increasing Rayleigh number were compared with the available results for the Bingham fluid.

Modeling of fluids with complex rheology in the lattice Boltzmann method (LBM) is typically realized through the introduction of an effective viscosity. For fluids with a yield stress behavior, such as so-called Bingham fluids, the effective viscosity has a singularity for low shear rates and may become negative. This is typically avoided by regularization such as Papanastasiou’s method. Here we argue that the effective viscosity model can be re-interpreted as a generalized equilibrium in which no violation of the stability constraint is observed. We implement a Bingham fluid model in a three-dimensional cumulant lattice Boltzmann framework and compare the direct analytic effective viscosity/generalized equilibrium method to the iterative approach first introduced by Vikhansky which avoids the singularity in viscosity that can arise in the analytic method. We find that both methods obtain similar results at coarse resolutions. However, at higher resolutions the accuracy of the regularized method levels off while the accuracy of the direct method continuously improves. We find that the accuracy of the proposed direct method is not limited by the singularity in viscosity indicating that a regularization is not strictly necessary.

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.