Bingham Fluid Model Research Articles

Analytical spatiotemporal distribution equations of viscous slurry grouting pressure during the grouting process in rock fissures

To give a simpler theoretical solving approach for modeling the grouting process of viscous slurry in porous/broken rocks, this work derives two theoretical spatiotemporal distribution equations of viscous slurry penetration in rock fissures based on the Darcy seepage model (DM) and the Bingham fluid model (BM) through a hypothetical micro-element model. Through a two-dimensional (2D) conceptual grouting hole model with porous media, the applicability of the two proposed theoretical spatiotemporal distribution equations of viscous slurry pressure is validated by comparing the analytical results with the numerical results obtained from the two-phase flow simulation. The results indicate that the analysis results obtained from two proposed theoretical spatiotemporal distribution equations are well consistent with the simulation results at different times and under different grouting velocities. That means the time-consuming numerical simulation of the porous/broken rocks grouting process can be replaced by two proposed theoretical spatiotemporal distribution equations, which will greatly reduce the difficulty of real-time evaluation of the grouting effects in engineering practice and shorten the assessment time.

Implementation of a New Smart-Lubricant Model Using Generalized Newtonian Approach in Soft Elastohydrodynamic Lubrication

Abstract This is an inceptive attempt to replace the classical Bingham fluid model with a continuous double Newtonian power-law-based constitutive equation for smart lubricants like magneto-rheological, electro-rheological, and ferro-fluids. The implementation of Bingham model in hydrodynamic (HD) and elastohydrodynamic (EHD) lubrication analyses is highly challenging and inconvenient due to its inherent discontinuity. Therefore, the present work demonstrates the use of an already existing rheological model with an appropriate set of parameters to describe the flow behavior of smart lubricants in a soft-EHD lubrication algorithm based on the generalized Newtonian approach. The formation of both floating and adherent cores validates the proposed model. An extensive parametric study is also performed to explore the effects of operating speed, load, and slide-to-roll ratio on the soft-EHL characteristics. The results are very promising, showing that it's possible to customize smart lubricants to match specific operating conditions. This is achieved by adjusting the yield stress value accordingly, allowing for the desired variation in lubrication characteristics.

Unsteady double-diffusive Brinkman–Bénard convection in cylindrical enclosure saturated with hybrid bi-viscous Bingham nanoliquid

This paper aims to present an analytical as well as a comparative study to investigate the effect of the Brinkman porous medium on the onset of regular and chaotic motion in cylindrical enclosures of different heights. The hybrid bi-viscous Bingham nanoliquid is considered as the working fluid. Modified Brinkman–Buongiorno and bi-viscous Bingham fluid models are incorporated to obtain the flow governing dynamics. The thermophysical properties of the hybrid nanoliquid are calculated using phenomenological laws and the mixture theory. The study is carried out for the axisymmetric mode, and the Bessel functions are taken as the eigenfunctions of the problem. Double Fourier–Bessel series expansions are used for weakly non-linear stability analysis. The limiting cases of the study are obtained, and the results on the onset of convection, heat, and mass transport are discussed graphically. The behavior of the dynamical system is analyzed using the maximum Lyapunov exponent plot, the bifurcation diagram, and phase plots. Outcomes suggest that convection sets in earlier in the water-based hybrid nanoliquid than in the bi-viscous Bingham hybrid nanoliquid. The use of Single-walled carbon nanotubes enhances the heat transfer rate by approximately 17%. Further, it is concluded that a tall cylindrical enclosure is the most favorable geometry for achieving a higher heat transfer rate among the others.

Hydration mechanism of red mud-fly ash based geopolymer

Geopolymer is considered the most promising alternative to Portland cement due to its excellent performance and low cost. In this study, the hydration mechanism of red mud-fly ash based geopolymer (RFG) was analyzed using low-field nuclear magnetic resonance (LNMR), rheological tests, Fourier transform infrared spectrometry (FT-IR), isothermal calorimetry, and scanning electron microscopy coupled with energy dispersive X-ray spectrometry (SEM-EDS). The compressive strength of RFG falls with increasing dosages of red mud, and initially increased and subsequently decreased with the increment of SiO2/Na2O ratio. According to the results of LNMR and rheological tests, the geopolymerical hydration process of RFG is divided into three phases: an induction phase, an acceleration phase, and a stabilization phase. When the SiO2/Na2O ratio of the activator is lower than 2.4, it has an activation effect on the cementitious material, and the optimal value is 2.1. The hydration rate of the cementitious material decreases as the dosage of red mud is increased. The slurry transitions from the Herschel-Barkley model to the Bingham fluid model as the hydration reaction advances. The hydration products is verified with different red mud dosage and SiO2/Na2O ratio by SEM-EDS. The findings of this study enrich our understanding of RFG, promote its engineering applications, and improve the utilization efficiency of red mud.

Motion of Air Bubbles in a Cement Slurry.

The dynamics of air (gas) bubbles in a column of cement slurry is examined numerically. The air injected at the bottom of a laboratory-scale column through a porous distributor plate spatially distributes and migrates as a swarm of bubbles throughout the slurry toward the freeboard. The two-phase system of the cement slurry and the air bubbles is modeled using the conservation equations of mass and linear momentum in the framework of the volume-of-fluid (VOF) approach. The cement slurry is modeled using the Herschel-Bulkley and Bingham fluid models. Results show that the mean Sauter diameter and the mean rise velocity of the bubbles decrease with the gas flow rate. Meanwhile, it is found that the rising of the bubbles is controlled by breakup events, along with relatively weak path instabilities of the bubbles resulting in relatively straight trajectories, independent of the gas flow rate. The extent of the yielded region appears larger for the Herschel-Bulkley model compared to the Bingham fluid model (by approximately 10%).

Dynamic patterns of electroosmosis peristaltic flow of a Bingham fluid model in a complex wavy microchannel

The purpose of this paper is to present a rigorous analysis of streamline patterns and their bifurcation to a viscoplastic Bingham fluid model that involves heat and mass transfer in an electroosmotic flow through a complex wavy microchannel. The Bingham fluid act as a solid medium in the core layer, which divides the channel into three distinct sections utilized to model the problem as a switched dynamical system between these zones. To track multiple steady states (stagnation points) and related trapping phenomena, we perform both analytical and numerical bifurcation analysis of each subsystem with respect to different physical effects such as electrical double layer thickness and Helmholtz-Smoluchowski velocity. The key feature of the technique presented here is its ability to reveal the peristaltic transport characteristics of the Bingham fluid model in the presence or absence of symmetric flow properties. The primary novelty here is the ability to regulate the location and stability of the equilibrium points in the domain of interest. This leads to the detection of global bifurcations that reflect important dynamic elements of the model. Our results highlighted a new category of complex behavior that controls transitions between qualitatively different transport mechanisms, as well as a class of non-classical trapping phenomena.

Unsteady solute dispersion in pulsatile Luo and Kuang blood flow (K - L Model) in a tube with wall reactive absorption

Unsteady solute dispersion in pulsatile non-Newtonian flow in a circular tube has been investigated considering higher order moments using the Aris’s method of moments. The Luo and Kuang(1992) (K - L Model) constitutive relation is used for the non-Newtonian fluid. The axial mean concentration of solute is estimated by considering exchange, convective, dispersion coefficients. In addition, considering the 3rd and 4th central moments, the skewness, and kurtosis in the mean concentration is examined. Variations of these five moments against the absorption parameter, K-L fluid parameters, and Womersley frequency parameter are thoroughly investigated. The increase in the Womersley frequency parameter led to the occurrence of a double frequency period for the dispersion coefficient, which influenced the skewness and kurtosis coefficients that led to the deviation from usual normal distribution of the mean concentration distribution at the starting of the dispersion process. The concentration distribution is skewed towards the central region of the tube. The concentration contours also reveal that the solute convection is more in the central region of the tube. The results for Newtonian, Bingham, and Casson fluid models are retrieved as special cases. The mean concentration has the highest peak for the K-L model and the lowest for the Newtonian fluid model. It is scattered axially more for the Bingham fluid than the Casson fluid. This investigation emphasizes that higher moments provide precise information about the solute dispersion in the flow field and its deviation from the normal distribution at small time scales. • This investigation examining the unsteady axial dispersion of a solute in the non-Newtonian pulsatile flow in a cylindrical tube, considering the impact of an irreversible first-order boundary reaction. Solute dispersion in K-L model has been introduced, which gives the shear thinning and thickening behaviour of blood flow even if yield stress is zero. • The present study initiated skewness and kurtosis analysis for steady/ unsteady, non-pulsatile/ pulsatile and Newtonian/ non-Newtonian fluid flow by using method of moments. Here analytical results for all transport coefficient with skewness and kurtosis has been discussed. • The perturbation and numerical solution of coupled and non-linear equation of shear stress and momentum equation has been obtained to get the velocity profile. A new class of computationally explicit Runge–Kutta (CERK) numerical method (Yadav et. al. (2022)) has been used to solve this stiff problem. A detailed comparison of perturbation and numerical solutions is also given in this manuscript. • The solution of the concentration equation is obtained analytically adopting the Aris0 s method of moments, with fourth-order precision. In the presence of boundary reaction, the transport coefficients are affected not only by time but also by the Womersley frequency parameter, other chemical variables, the wall absorption parameter, the yield stress, the amplitude of the fluctuating pressure component, and plasma viscosity. The non-Gaussian distribution of solute is visible for small time after injection. • The mean concentration as well as the two-dimensional concentration distribution are accurately described. The results for the Bingham model, the Casson model, and the Newtonian model are derived directly from this analysis.

Investigation of Newtonian and non-Newtonian Bingham fluid models for lateral flow simulation of liquefied soil

This study applies a Newtonian model and non-Newtonian Bingham model to simulate the lateral flow of liquefied soil and investigates the models’ parameters. First, the study derives analytical solutions for the lateral flow velocity under free-field conditions in both the transient and steady states for both models. The study determines that the solution derived for the Newtonian model can be applied to derive that for the Bingham model through a simple transformation considering the contribution of undrained residual shear strength of liquefied soil. Second, three-dimensional numerical analyses are executed using COMSOL to investigate the boundary conditions of experimental models, which significantly affect the fluid behavior of liquefied soil. The results reveal that the model length and sidewall effects can be ignored at a length-to-thickness ratio of >30 and width-to-thickness ratio of >6, respectively. The Bingham model can describe the behavior of liquefied soil under different boundary conditions using a single set of parameters. Through normalization, the Bingham and Newtonian models can share the same normalized velocity–time curve. Additionally, the Bingham model with boundary conditions can have a similar curve to that under the free-field condition through the replacement of the original viscosity coefficient with an apparent viscosity coefficient.

Flow loop study of a cold and cohesive slurry. Pressure drop and formation of plugs

Slurries of cohesive particles constitute a significant risk during subsea petroleum production due to their potential to plug the flow. This article describes a flow loop study of a slurry consistent with 0.23-mm ice particles in decane. The experiments were conducted for the concentration of particles up to 20.3% vol. and Re < 25000. The cohesion of ice was suggested by controlling the temperature of the slurry. The relative viscosity of the slurry was computed as a function of particle concentration using pressure drop measurements. The relative viscosity was 3.1 for the concentration of 20.3%. The Bingham-fluid model agreed with the empirical calculations within the discrepancy of 15.5%. Increased viscosity of slurry led to a higher pressure drop in the flow loop compared to the single-phase case. Pressure drops for 20.3% slurry flow were 5.2% and 44.4% higher than for pure decane at Reynolds numbers of 24778 and 4956, respectively. The test section of the loop was equipped with an orifice to induce the formation of plugs. The plugs were observed at particle concentrations below 7.0%. The article presents detailed experimental logs depicting the process of plug formation. The observed blocking cases partially agreed with flow maps from the literature. In addition, we note the applicability of the blockage risk evaluation technique from the Colorado School of Mines.

Mathematical Modeling of Unsteady Solute Dispersion in Bingham Fluid Model of Blood Flow Through an Overlapping Stenosed Artery

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.

Experimental study of the rheology of water–kaolinite suspensions

Abstract How the added electrolyte condition and size of primary sediment particles, as well as the particle concentration, affect the rheological behaviours of water–sediment suspension remains to be of interest in the sediment field. In this work, rheological experiments of water–kaolinite suspensions with different electrolyte conditions, two particle sizes and 39 solid concentrations were performed. The Bingham fluid model has been adopted to fit the experimental data, and the viscosity and Bingham shear stress values were calculated for each suspension. It has been found that an increase in electrolyte concentration and/or valence leads to a larger viscosity value of the suspension, whereas an increase in electrolyte valence yields a smaller Bingham shear stress value. A simple interpretation based on DLVO theory was presented in this study. It has also been observed that a fine-grained kaolinite suspension corresponds to larger suspension viscosity and Bingham shear stress values. Additionally, some experimental information on the viscosity–solid concentration and Bingham shear stress–solid concentration relationships were also presented in this study. For the viscosity–solid concentration data, the Krieger and Dougherty formula provided the best fit, and a simple exponential relation showed a good fit for the measured shear stress–solid concentration data.

Numerical Investigation of Surge Waves Generated by Submarine Debris Flows

Submarine debris flows and their generated waves are common disasters in Nature that may destroy offshore infrastructure and cause fatalities. As the propagation of submarine debris flows is complex, involving granular material sliding and wave generation, it is difficult to simulate the process using conventional numerical models. In this study, a numerical model based on the smoothed particle hydrodynamics (SPH) algorithm is proposed to simulate the propagation of submarine debris flow and predict its generated waves. This model contains the Bingham fluid model for granular material, the Newtonian fluid model for the ambient water, and a multiphase granular flow algorithm. Moreover, a boundary treatment technique is applied to consider the repulsive force from the solid boundary. Underwater rigid block slide and underwater sand flow were simulated as numerical examples to verify the proposed SPH model. The computed wave profiles were compared with the observed results recorded in references. The good agreement between the numerical results and experimental data indicates the stability and accuracy of the proposed SPH model.

An extended numerical manifold method for simulation of grouting reinforcement in deep rock tunnels

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.

Development of smoothed particle hydrodynamics (SPH) method to model the interaction of sand and water during liquefaction with bingham fluid model adaptation

Smoothed Particle Hydrodynamics (SPH) is a mesh-free numerical method that models the movement of particles in the Langrangian method. SPH method treats the domain as discrete particles instead of continuous entities, making it more accurate to model phenomenons that have a big deformation. The purpose of this research is to analyze the interaction between soil and water particles, based on the particle movements, density, pressure, internal forces, and external forces. This research continues the previous research of interaction between fluid-fluid particles in SPH by applying the Bingham fluid model to one type of fluid to represent coarse-grained soil particles. In the future, we hope this research can be further developed into a liquefaction prediction model by quantifying the main factors of liquefaction, such as the amplitude of shear strain, effective stress reduction, and excess pore water pressure.

Second law analysis of heat transfer in swirling flow of Bingham fluid by a rotating disk subjected to suction effect

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.

A Direct Effective Viscosity Approach for Modeling and Simulating Bingham Fluids with the Cumulant Lattice Boltzmann Method

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.

Study of the velocity of artificial mudflow on a laboratory stand

In August 2020, an experiment was conducted to measure the velocity of an artificial coherent mudflow on a laboratory stand. The stand is a rectangular cross-section tray with a length of 3.0 m, a width of 0.25 m, a depth of 0.25 m, slope – 29°. 4 racks were installed in the tray to measure the hydrodynamic pressure of the mudflow. The movement of the mudflow was filmed by a high-speed video camera. Velocity of artificial mudflow were measured. Most of the mudflow mixture soil is made up of particles less than 0.25 mm in size (34%). The density of the prepared mudflow mixture was 1 880 kg/m3. Density of mudflow deposits 2 040 kg/m3. Despite the small values of the Reynolds number, the turbulent movement of the mudflow was observed. Comparison of the results of the measured mudflow velocities with the velocities calculated by different methods of calculating the mudflow velocity based on the structure of the Shezi formula (for Newtonian fluids) showed a strong variation of the calculated values. The methods either greatly overestimate or, on the contrary, greatly underestimate the measured values. This is probably due to the fact that the connected mudflow is not a Newtonian fluid, but a non-Newtonian fluid. The closest physical analogue of a connected mudflow is a pseudoplastic (non-Newtonian) fluid whose viscosity decreases with increasing shear stress. As a physical model of a connected mudflow, it is advisable to use the Bingham fluid model, the flow of which is similar to the flow of coherent debris-flows and mudflows

Thermal and rheological effects in a classical Graetz problem using a nonlinear Robertson‐Stiff fluid model

AbstractThe present article elaborates the Graetz problem for the Robertson‐Stiff fluid model with imposed iso‐thermal conditions. The closed‐form expression of Robertson‐Stiff fluid velocity is obtained. Employing the classical separation of variables approach, the energy equation of the said problem is reduced into an eigenvalue problem. The solution of the eigenvalue problem is developed numerically via the MATLAB built‐in algorithm BVP4C. The constants appearing in series solutions are computed by Simpson's rule. The special case of this analysis with appropriate scaling is also applicable for the Bingham, power‐law, and Newtonian fluid models. The impact of the dissipation function on Nusselt numbers and mean temperature is also considered. The pictorial representation of average temp7erature and Nusselt number are discussed in the presence of the plug radius, power‐law index, and Brinkman number. It is observed that the presence of the plug radius and power‐law index delay the prevalence of fully developed conditions for the Nusselt number. Moreover, the local Nusselt number for channel confinement attains higher values as compared with tube confinement. The present investigation has numerous applications in the field of engineering, nanotechnology, biomedical sciences, and development of several thermal types of equipment or microfluidic devices.

Study of mechanical properties and early-stage deformation properties of graphene-modified cement-based materials

The subject of the study was the possibility of graphene improving the mechanical and crack resistance of cement-based materials. Graphene was dispersed and incorporated into cement-based materials. The flexural strength, compressive strength, splitting tensile strength, stress–strain relationship, vickers microhardness, and rheological properties of composites prepared were tested to study mechanical properties. Furthermore, the deformation properties were tested by measuring autogenous and drying shrinkages. The test results indicated that incorporating graphene increased the cement paste’s viscosity while the effect of graphene content on the viscosity of cement paste is not obvious. The shear stress of cement paste demonstrated a good linear relationship with the shear rate, indicating that the cement paste conformed to the Bingham fluid model. The incorporation of an appropriate amount of graphene enhanced the macro-mechanical properties of cement-based materials. For instance, when the graphene amount was 0.06 wt% of cement mass, the compressive and flexural strength increased by 10%. Graphene could enhance the micro-mechanical properties of cement-based materials. When the graphene amount was 0.06 wt%, it could increase the vickers microhardness by 8.6%. Furthermore, the elastic modulus of cement-based materials could be affected by incorporating graphene. When the incorporated amount of graphene reached 0.09 wt%, the elastic modulus could increase to more than 20%. Besides, incorporating an appropriate amount of graphene had a good inhibition effect on the autogenous shrinkage and drying shrinkage of cement-based materials. When the graphene amount was 0.06 wt%, the shrinkage performance of graphene-modified cement-based materials has an optimal increase rate close to 30%.

Rayleigh–Bénard convection of a viscoplastic liquid in a trapezoidal enclosure

The objective of this paper is to clarify the role of sloping walls on convective heat transport in Rayleigh–Bénard convection within a trapezoidal enclosure filled with viscoplastic fluid. The rheology of the viscoplastic fluid has been modeled with Bingham fluid model. The system of coupled nonlinear differential equations was solved numerically by Galerkin's weighted residuals scheme of finite element method. The numerical experiments are carried out for a range of parameter values, namely, Rayleigh number (5.103 ≤ Ra ≤ 105), yield number (0 ≤ Y ≤ Yc), and sidewall inclination angle (ϕ = 0, π/6, π/4, π/3) at a fixed Prandtl number (Pr = 500). Effects of the inclination angle on the flow and temperature fields are presented. The results reveal that inclination angle causes a multicellular flow and appears as the main parameter to govern heat transfer in the cavity. The heat transfer rate is found to increase with the increasing angle of the sloping wall for both Newtonian and yield stress fluids. On the other hand, the plug regions also found to increase with increasing φ, which is unusual but perhaps not unexpected behavior. In the yield stress fluids, the flow becomes motionless above a critical yield number Yc because the plug regions invade the whole cavity. The critical yield number Yc is also affected by the change of inclination angle and increases significantly with the increase of φ.