Search

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.

Understanding flow of non-Newtonian fluids in porous media is critical to successful operation of several important processes, including polymer flooding, filtration, and food processing. In some cases, such as when a non-Newtonian fluid can be represented by the power-law model, simulation of its flow in a porous medium is a straightforward extension of that of Newtonian fluids. In other cases, such as flow of Bingham fluids, there is a minimum external threshold pressure below which there would be no macroscopic flow in the porous medium. Computing the threshold pressure is a difficult problem, however. We present a new algorithm for determining the threshold pressure for flow of a Bingham fluid through a porous medium, modeled by a pore-network (PN) model. The algorithm, the ant colony optimization (ACO), is described in detail and together with the PN model is used to determine the minimum pressure for flow of Bingham fluids in a heterogeneous porous medium, the Mt. Simon sandstone, whose PN and morphological properties were extracted from the sandstone’s image. To assess the accuracy and computational efficiency of the ACO algorithm, we also carry out the same computations with two previous methods, namely invasion percolation with memory (IPM) and the path of minimum pressure (PMP) algorithms. The IPM does not guarantee identification of the optimal flow path with the minimum threshold pressure, while the PMP algorithm provides an approximate, albeit accurate, solution of the problem. We also compare the computational complexity of the three methods. For large PNs, both the IPM and PMP are much less efficient than the ACO algorithm. Finally, we study the effect of the morphology of the pore space on the minimum threshold pressure.

Solutions for radial flow of a Bingham fluid are analyzed in this paper. It aims to eliminate confusions in the literature concerning the plug flow region in different solutions for analysis and design of grouting in rock fractures. The analyses based on the force balance equation reveal that the plug flow region in Bingham radial flow is independent of the fracture radius, and is not a growth function adapted from the solution of one-dimensional (1D) slit flow according to ‘similarity’. Based on the shear stress distribution, we analytically proposed that a non-uniform plug flow region cannot exist. The Bingham fluid (grout) penetration and flowrate evolution as functions of grouting time are given using the correct expression for the plug flow region. The radius-independent plug flow region and the presented flowrate evolution equation are also verified numerically. For radial flow, the relative penetration length is equal to the relative width of plug flow region, which is the same as that for 1D channel flow. Discrepancies in analytical solutions for grout penetration and flowrate evolution were also illustrated. The clarification of the plug flow region and evaluation of discrepancies in analytical solutions presented in this work could simplify modeling and design of grouting in rock engineering applications.

The current paper is focused on analyzing the flow of viscoplastic fluid in a cavity that is driven by the two walls. The Lattice Boltzmann method (LBM) is used to solve the discrete Boltzmann equation. To represent the stress-strain rate relationship of viscoplastic fluids, the Bingham Papanastasiou constitutive model is considered. Cavity flow filled with Bingham fluids is considered for validating the present LBM code. After successful validation of the code, the analysis is extended for three dissimilar wall motions-simultaneous and opposed movement of the parallel facing walls, and the simultaneous motion of non-facing walls. The flow dynamics of Bingham fluid is influenced by Reynolds and Bingham numbers which can be studied using velocity and streamline plots. Subsequently, the yielded and un-yielded zones in a cavity have been effectively tracked using the limiting condition of yield stress. Further, the effect of wall motion on the variation of those zones inside a cavity has been studied. Finally, the drag coefficient for considered wall motions is presented.

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 the present work, the sloshing phenomenon in a rectangular tank with non-Newtonian Bingham fluid is modeled. The numerical method used is the Incompressible Smoothed particle Hydrodynamics (ISPH...

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.

The linear stability of channel flows driven by pressure drops is carried out for fluids that exhibit a yield stress, the mechanical response of which is prescribed by the Bingham constitutive relation or two of its regularizations: the model due to Allouche and co-workers that is usually referred to as the “simple model”, and Papanastasiou model. Despite the fact that these two regularized models provide a good approximation of the steady Poiseuille flow of a Bingham fluid, they fail to predict the stability characteristics of the exact Bingham model. The critical thresholds for the onset of turbulence predicted by using the simple and Papanastasiou models are essentially the same, but they differ significantly from that of the exact Bingham model. This discrepancy is shown to be due to the absence of energy dissipation in the rigid core of a Bingham fluid.

When drilling an oil well, a viscous fluid is injected to aid drilling. This fluid is also responsible for removing the cuttings and maintaining structural stability of well. The rheology of this drilling fluid has a direct influence on the cleaning of the well, on the dynamics of the fluid in pipe and annular areas. Linear mathematical extrapolations for high pressure and high temperature environments can lead to rheology errors up to 75%. In this study, a finite volume model was developed to simulate the flow of a water-based mud in annular and jetting environments in the drilling environment. Annulars were made by steel pipes and permeable formations. The fluids evaluated were developed empirically with xanthan gum and bentonite clay. The numerical results are consistent with literature and represent characteristics of a Yield Power Law fluid and a Bingham plastic. A comparison was made with water, allowing a correlation between rheological effects and fluid dynamics in annular and high vorticity regions.

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.

In this paper, we study the peristaltic transport of incompressible Bingham plastic fluid in a curved channel. The formulation of the problem is presented through, the regular perturbation technique for small values of is used to find the final expression of stream function. The numerical solution of pressure rise per wave length is obtained through numerical integration because its analytical solution is impossible. Also the trapping phenomenon is analyzed. The effect of the variation of the physical parameters of the problem are discussed and illustrated graphically.

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.

During well drilling operations, unexpected gas influx may take place when the bottom hole pressure falls below the pore pressure. The conventional procedure to control the influx consists of shutting-in the well and waiting for pressure stabilization. The pressures measured at the surface after the well closure and the pit gain are used to estimate the pore pressure, the gas density, and the kick magnitude. However, the drilling fluid compressibility and rheology can undermine pore pressure transmission to the surface, which can affect the pit gain and the well closing pressure. The current work presents a transient compressible isothermal mathematical model to predict pit gain and pressure transmission along the well during gas kicks. The model is based on the balance equations of mass and momentum that are solved by the method of characteristics. Three types of drilling fluids are analyzed: Newtonian, Bingham Plastic and thixotropic. The Darcy's law is used to represent the gas influx through the rock formation. The results indicate that the usual pressure balance used to estimate the pore pressure may lead to mistaken values and also that the drilling fluid compressibility and rheology have considerable effect on the pit gain and on the gas volume that invades the well. In all cases investigated, the gas volume within the well is at least 50% higher than the pit gain. Therefore, drilling fluid compressibility cannot be neglected on the estimation of the formation fluid volume within the well.

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.

It is well known that the Non-Newtonian Bingham fluid flow in porous media does not obey the conventional linear Darcy’s law due to the yield stress for the Bingham fluid: There exists a threshold pressure gradient, which means that the seepage flow only happens when the threshold pressure gradient is overcome. The principle of non-Darcy seepage flow with the threshold pressure gradient is also applicable into the situation of the fluid flow in the low-permeable porous media. Here, a nonlinear moving-boundary mathematical model is built for the semispherical centripetal non-Darcy seepage flow with the threshold pressure gradient in a three-dimensional infinite heavy oil reservoir with the type of Bingham fluid; wherein the moving boundary conditions are incorporated for describing the effect of the threshold pressure gradient. In consideration of the strong nonlinearity of the model, the similarity transformation method is applied into obtaining the exact analytical solution of the model. In order to keep full self-similarity for the model, the inner boundary condition is set as variable flow rate that increases linearly with the time. As a result, an exact analytical solution for the nonlinear moving-boundary mathematical model of semispherical centripetal non-Darcy seepage flow with the threshold pressure gradient is obtained. The existence and the uniqueness of the exact analytical solution are also strictly proved. It is also theoretically proved that as the threshold pressure gradient tends to zero, the exact analytical solution can be reduced to that of a mathematical model of semispherical centripetal Darcy’s seepage flow. The presented exact analytical solution can be used for strictly verifying the validity of the numerical methods for solving the three-dimensional moving boundary models of non-Darcy seepage flow with the threshold pressure gradient in the actual engineering problems. From the exact analytical solution, it is also revealed that when the threshold pressure gradient exists, the spatial pressure distribution exhibits an instructive feature of compact support; as the threshold pressure gradient tends to zero, the sensitivity of its effect on the transient distance of the moving boundary and the transient pressure will grow, which reveals the difficulty in accurately determining the position of the moving boundary by the numerical methods and the serious uncertainty problem in the interpretation of the threshold pressure gradient by the pressure transient analysis method in engineering as the threshold pressure gradient is rather small. Through the comparison of the two different exact analytical solutions that corresponds to the two different models with and without incorporating the moving boundary conditions for describing the effect of the threshold pressure gradient, it is demonstrated that when the moving boundary conditions are not incorporated in the modeling, the effect of the threshold pressure gradient on the spatial pressure distribution, the transient pressure and the productivity index can be overestimated largely. Therefore, it is very necessary to incorporate the moving boundary conditions in the modeling of non-Darcy seepage flow with the threshold pressure gradient. The study in the paper definitely provides solid theoretical basis of fluid mechanics for the relevant engineering applications in the development of heavy oil reservoirs and low-permeable reservoirs in petroleum engineering and in the development of water resources in low-permeable formations in hydraulic engineering.

To describe the macroscopic rheological behavior of thixotropic elasto-visco-plastic (TEVP) materials, phenomena that take place in their microstructure must be accounted for. To this end, we couple the tensorial constitutive model by Saramito for EVP materials with thixotropy, extending the ideas of isotropic hardening, and with kinematic hardening (KH), to account for back stresses. We use a scalar variable that describes the level of structure at any instance and a modified Armstrong–Frederick KH equation, thus providing rules governing the dynamics of the apparent yield stress. The material viscosity, yield stress, and back stress modulus feature a nonlinear dependence on the structural parameter, enabling the model to make accurate predictions with a single structural parameter. To avoid unphysical stress evolution in both shear and extensional flows, we propose a modified back stress constitutive equation that keeps the components of the stress tensor bounded. The predictions of the new model are compared to experimental data and predictions of previously proposed TEVP models in simple rheometric flows, including steady and step-shear tests, flow reversal, intermittent step tests, small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear. In most cases, the proposed model reproduces more accurately these experimental data than the other models, highlighting its predictive capabilities. Moreover, SAOS illustrates that introducing viscoplasticity via the Saramito model necessarily reduces G″ to zero in the linear strain regime. This calls for model adjustments in the solid state. Finally, we examined the proposed model in uniaxial elongation and concluded that it is important to include this flow in the rheological characterization and modeling of such systems.To describe the macroscopic rheological behavior of thixotropic elasto-visco-plastic (TEVP) materials, phenomena that take place in their microstructure must be accounted for. To this end, we couple the tensorial constitutive model by Saramito for EVP materials with thixotropy, extending the ideas of isotropic hardening, and with kinematic hardening (KH), to account for back stresses. We use a scalar variable that describes the level of structure at any instance and a modified Armstrong–Frederick KH equation, thus providing rules governing the dynamics of the apparent yield stress. The material viscosity, yield stress, and back stress modulus feature a nonlinear dependence on the structural parameter, enabling the model to make accurate predictions with a single structural parameter. To avoid unphysical stress evolution in both shear and extensional flows, we propose a modified back stress constitutive equation that keeps the components of the stress tensor bounded. The predictions of the new model are co...

In this paper, laminar flow of non-Newtonian (Bingham) fluid is studied numerically in a two-dimensional lid-driven skewed cavity that incorporates Papanastasiou exponential regularization approach...

The influence of a sudden change in the external magnetic field on the flow of an electrically conducting Bingham fluid in a two-dimensional channel is considered. It is demonstrated that a method of independent descriptions of the flows in plastic and viscous regions can be used for studying magnetohydrodynamic flows of the Bingham fluid. An exact equation is derived for the position of the plastic flow region boundary as a function of time and magnetic field induction. It is shown that the corresponding Cauchy problem has a unique asymptotically stable solution. Results of numerical integration for some values of parameters are presented; these result confirm the qualitative conclusions.

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.

Considering a mathematical model for the bilateral, frictionless contact between two Bingham fluids, establish a variational formulation for the problem and prove estimates on the velocity and pressure which are independent of the small parameter. The passage to the limit on \(\varepsilon \) permits us to obtain the existence and uniqueness of the velocity. A specific Reynolds equation associated with variational inequalities is obtained.