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A theoretical analysis of an asymmetric roller bearing system with cavitation that is hydro-dynamically lightly loaded and lubricated by a thin, incompressible fluid is presented. The lubricant adheres to the non-Newtonian Bingham plastic fluid concept, in which the viscosity of the fluid should change depending on the mean film temperature. The continuity and momentum equations, which regulate fluid flow, are first solved analytically and then numerically using MATLAB. Through graphs and tables, some key bearing features are addressed and further explained. This leads to the conclusion that there is a discernible difference between Newtonian and non-Newtonian fluids in terms of pressure, temperature, load, and traction. The findings are good in line with the body of literature.

AbstractUtilizing a non-Newtonian lubricant, such as Bingham plastic fluid, in a hydrodynamic journal bearing affords the opportunity to actively alter the operating performance of the bearing. In this work, the main purpose is to explore the behavior of the journal bearing lubricated by Bingham plastic using the computational fluid dynamics (CFD) method considering roughness and cavitation. Here, the concept of an engineered partial roughness pattern is proposed to create positive effects in improving tribological and acoustic performances under different roughness levels and eccentricity ratios. The cavitation phenomena is modeled using the mixture multiphase cavitation approach to get a more realistic result. The numerical results of this study indicate that the surface roughness level of the roughed journal bearing has a significant effect on the load-carrying capacity irrespective of the eccentricity ratio. Moreover, the larger the roughness level, the lower the load-carrying capacity. It is also found that compared to bearings without roughness, it is possible to achieve a 5% and 2% reduction in noise level and friction force, respectively, when the ”rough” level is employed on the roughed bearing. The findings of this research show that artificial partial roughness may be useful for enhancing journal bearing indices.

An attempt is made to analyse some lubrication characteristics of rigid cylindrical asymmetric rollers under adiabatic and isothermal boundaries with rolling and slidingmotion lubricated by a non-Newtonian incompressible Bingham plastic fluid under the behaviour of line contact. Here the lower surface is considered to move quicker than that of the upper surface; and the Roelands viscosity model is considered and assumed to depend upon the fluid pressure and the mean film temperature. The governing equations for fluid flow such as equations of motion with continuity and the momentum energy equation are solved using Runge-Kutta forth order and MATLAB is employed to solve these equations. Through graphs and tables for Newtonian and non-Newtonian fluids, the several crucial bearing characteristics including velocity, pressure, viscosity, mean temperature, load and traction are examined and a significant change is observed among them. The findings presented here are qualitatively consistent with the existing literature. [ABSTRACT FROM AUTHOR]

In order to study fluid film bearing systematically, the determination of optimal parameters is vital. A theoretical analysis of lubrication of asymmetric roller bearings with rolling and sliding motion lubricated by a non-Newtonian incompressible Bingham plastic fluid is presented with cavitation boundary conditions for heavily loaded rigid system. The Roeland lubricant viscosity is considered to vary with pressure and mean film temperature. The fluid flow governing equations such as equation of motion with continuity and momentum energy equations are first reduced to ordinary differential equations applying appropriate approximation and then solved numerically using MATLAB. This article discusses and elaborates on the various important characteristics of bearings including velocity, pressure, viscosity, mean temperature, load and traction. Graphs and table are introduced for Newtonian and non-Newtonian fluids to make clarity of this work. The results are found qualitatively in good agreement with those obtained by prior researchers. [ABSTRACT FROM AUTHOR]

We have developed and tested a numerical model for turbulence resolving simulations of dense mud–water mixtures in oscillatory bottom boundary layers, based on a low Stokes number formulation of the two-phase equations. The resulting non-Boussinesq equation for the fluid momentum is coupled to a transport equation for the mud volumetric concentration, giving rise to a volume-averaged fluid velocity that is non-solenoidal, and the model was implemented as a new compressible flow solver. An oscillating pressure gradient force was implemented in the correction step of the standard semi-implicit method for pressure linked equations (SIMPLE), for consistency with the treatment of other volume forces (e.g., gravity). The flow solver was further coupled to a new library for Bingham plastic materials, in order to model the rheological properties of dense mud mixtures using empirically determined concentration-dependent yield stress and viscosity. We present three direct numerical simulation tests to validate the new MudMixtureFoam solver against previous numerical solutions and experimental data. The first considered steady flow of Bingham plastic fluid with uniform concentration around a sphere, with Bingham numbers ranging from 1 to 100 and Reynolds numbers ranging from 0.1 to 100. The second considered the development of turbulence in oscillatory bottom boundary layer flow, and showed the formation of an intermittently turbulent layer with peak velocity perturbations exceeding 10 percent of the freestream flow velocity and occurring at a distance from the bottom comparable to the Stokes boundary layer thickness. The third considered the effects of density stratification due to resuspended sediment on turbulence in oscillatory bottom boundary layer flow with a bulk Richardson number of 1 × 10 − 4 and a Stokes–Reynolds number of 1000, and showed the formation of a lutocline between 20 and 40 Stokes boundary layer depths. In all cases, the new solver produced excellent agreement with the previous results. [ABSTRACT FROM AUTHOR]

A theoretical analysis of an asymmetric roller bearing system with cavitation that is hydro-dynamically lightly loaded and lubricated by a thin, incompressible fluid is presented. The lubricant adheres to the non-Newtonian Bingham plastic fluid concept, in which the viscosity of the fluid should change depending on the mean film temperature. The continuity and momentum equations, which regulate fluid flow, are first solved analytically and then numerically using MATLAB. Through graphs and tables, some key bearing features are addressed and further explained. This leads to the conclusion that there is a discernible difference between Newtonian and non-Newtonian fluids in terms of pressure, temperature, load, and traction. The findings are good in line with the body of literature. [ABSTRACT FROM AUTHOR]

Utilizing a non-Newtonian lubricant, such as Bingham plastic fluid, in a hydrodynamic journal bearing affords the opportunity to actively alter the operating performance of the bearing. In this work, the main purpose is to explore the behavior of the journal bearing lubricated by Bingham plastic using the computational fluid dynamics (CFD) method considering roughness and cavitation. Here, the concept of an engineered partial roughness pattern is proposed to create positive effects in improving tribological and acoustic performances under different roughness levels and eccentricity ratios. The cavitation phenomena is modeled using the mixture multiphase cavitation approach to get a more realistic result. The numerical results of this study indicate that the surface roughness level of the roughed journal bearing has a significant effect on the load-carrying capacity irrespective of the eccentricity ratio. Moreover, the larger the roughness level, the lower the load-carrying capacity. It is also found that compared to bearings without roughness, it is possible to achieve a 5% and 2% reduction in noise level and friction force, respectively, when the "rough" level is employed on the roughed bearing. The findings of this research show that artificial partial roughness may be useful for enhancing journal bearing indices. [ABSTRACT FROM AUTHOR]

A journal bearing is a machine element that is used to keep the shaft rotating about its axis. The increasing demand for journal bearing applications in high-speed machines that are efficient and economical has resulted in the need for improvements to the acoustic and tribological performance of journal bearings. In order to improve the tribological and acoustic performance, this study aims to propose a novel journal bearing design by introducing a roughness condition in a specific zone of the stationary bearing surface. In addition, the impact of the application of engineered roughness on the performance of Bingham-plastic-lubricated bearings is investigated in more detail. Considering the effect of cavitation, the analysis was conducted using a 3D computational fluid dynamics (CFD) model of a journal bearing. In comparison with the Reynolds equation—which is inertialess—for lubrication analysis, the use of a 3D CFD model based on Navier–Stokes equations reflects more detailed flow characteristics. Moreover, in this work, variations in the area of surface roughness were employed, resulting in various roughness patterns on the surface of the journal bearing, so that the acoustic and tribological performances of the journal bearing were anticipated to be enhanced. The findings of this study show that under non-Newtonian lubrication of the bearing, the engineered roughness has a strong effect in altering the tribological performance. Furthermore, the well-chosen roughened surface was proven to be more pronounced in enhancing the load support and reducing the friction force. The simulation results also show that using an engineered surface has little effect on the noise of the bearing. [ABSTRACT FROM AUTHOR]

In this paper, simulation of non-Newtonian fluid flow in a two-dimension lid driven cavity is investigated. In this simulation Lattice Boltzmann method is used to solve computational fluid dynamics equations numerically. The particular approach of this research is to simulate non-Newtonian fluid flow by Sisko and Hershel Bulkley extended models for the first time beside other non-Newtonian models, by means of Lattice Boltzmann technique. The results of different models including x and y- velocity profiles and streamlines were presented. Then the simulation results of different non-Newtonian fluid flow by Sisko and Hershel Bulkley extended models have been compared with Power Law, Herschel Bulkley and Bingham plastic models. Also, the effect of the Reynolds Number and Power Law parameter (n) on the velocity profiles were studied. Increase of n parameter and Reynolds number leads to moving center of main vortex toward center of cavity. By increasing the parameter n, the maximum value of velocity increases and this indicates while n parameter is increased, vortex strength is excessed

We have developed and tested a numerical model for turbulence resolving simulations of dense mud–water mixtures in oscillatory bottom boundary layers, based on a low Stokes number formulation of the two-phase equations. The resulting non-Boussinesq equation for the fluid momentum is coupled to a transport equation for the mud volumetric concentration, giving rise to a volume-averaged fluid velocity that is non-solenoidal, and the model was implemented as a new compressible flow solver. An oscillating pressure gradient force was implemented in the correction step of the standard semi-implicit method for pressure linked equations (SIMPLE), for consistency with the treatment of other volume forces (e.g., gravity). The flow solver was further coupled to a new library for Bingham plastic materials, in order to model the rheological properties of dense mud mixtures using empirically determined concentration-dependent yield stress and viscosity. We present three direct numerical simulation tests to validate the new MudMixtureFoam solver against previous numerical solutions and experimental data. The first considered steady flow of Bingham plastic fluid with uniform concentration around a sphere, with Bingham numbers ranging from 1 to 100 and Reynolds numbers ranging from 0.1 to 100. The second considered the development of turbulence in oscillatory bottom boundary layer flow, and showed the formation of an intermittently turbulent layer with peak velocity perturbations exceeding 10 percent of the freestream flow velocity and occurring at a distance from the bottom comparable to the Stokes boundary layer thickness. The third considered the effects of density stratification due to resuspended sediment on turbulence in oscillatory bottom boundary layer flow with a bulk Richardson number of 1×10−4 and a Stokes–Reynolds number of 1000, and showed the formation of a lutocline between 20 and 40 Stokes boundary layer depths. In all cases, the new solver produced excellent agreement with the previous results.

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.

A journal bearing is a machine element that is used to keep the shaft rotating about its axis. The increasing demand for journal bearing applications in high-speed machines that are efficient and economical has resulted in the need for improvements to the acoustic and tribological performance of journal bearings. In order to improve the tribological and acoustic performance, this study aims to propose a novel journal bearing design by introducing a roughness condition in a specific zone of the stationary bearing surface. In addition, the impact of the application of engineered roughness on the performance of Bingham-plastic-lubricated bearings is investigated in more detail. Considering the effect of cavitation, the analysis was conducted using a 3D computational fluid dynamics (CFD) model of a journal bearing. In comparison with the Reynolds equation—which is inertialess—for lubrication analysis, the use of a 3D CFD model based on Navier–Stokes equations reflects more detailed flow characteristics. Moreover, in this work, variations in the area of surface roughness were employed, resulting in various roughness patterns on the surface of the journal bearing, so that the acoustic and tribological performances of the journal bearing were anticipated to be enhanced. The findings of this study show that under non-Newtonian lubrication of the bearing, the engineered roughness has a strong effect in altering the tribological performance. Furthermore, the well-chosen roughened surface was proven to be more pronounced in enhancing the load support and reducing the friction force. The simulation results also show that using an engineered surface has little effect on the noise of the bearing.

Modern concretes such as ultra-high performance concrete (UHPC) show excellent strength properties combined with favorable flow properties. However, the flow properties depend strongly on process parameters during production (temperature, humidity etc.), but also change sensitively even with slight variations in the mixture. In order to ensure desired processing of the fluidlike material and consistent process quality, the flow properties of the concrete must be evaluated quantitatively and objectively. The usual evaluation of measurements from concrete rheometers, for example of the ball probe system type, does not allow the direct determination of the objective material parameters yield stress and plastic viscosity of the sample. We developed a simulation-based method for the evaluation of rheometric measurements of fine grained high performance concretes like self-compacting concrete (SCC) and UHPC. The method is based on a dimensional analysis for ball measuring systems. Through numerical parameter studies we were able to describe the identified relationship between measuring quantities and material parameters quantitatively for two devices of this type. The evaluation method is based on the Bingham model. With this method it is possible to measure both the yield stress and the plastic viscosity of the fresh sample simultaneously. Device independence of the evaluation process is proven and an application to fiber-reinforced UHPC is presented.

Magnetorheological fluids can be used as a smart lubricant as a result of the fact that its properties can be changed with the use of a magnetic field. Local flow resistance and local pressure can be generated by applying a local magnetic field. This work presents a hydrostatic bearing in which the pressure profile of a conventional hydrostatic bearing is recreated with solely the use of a magnetic field and a magnetorheological fluid. The magnetic field is applied only locally at the outer edges of the bearing with the use of an electromagnet. The principle is demonstrated with the use of an experimental setup and a model from literature. [ABSTRACT FROM AUTHOR]

The pressure and temperature dependence of the yield stress is well established in oil drilling. In the present work, the steady, annular pressure-driven flow of a Bingham plastic is considered under the assumption that both the plastic viscosity and the yield stress vary linearly with pressure. A semi-analytical solution is derived for the case where the growth coefficients of both rheological parameters are equal, which, for certain oil drilling fluids, is indeed a reasonable assumption allowing the existence of a separable solution with an annular unyielded core. The inner and outer radii of the unyielded core are determined by solving numerically an algebraic system of equations. The pressure, which is two-dimensional in the yielded parts of the domain, and the velocity, which varies only with the radius, are calculated by means of explicit analytical expressions. The conditions for the occurrence of flow and the effects of the growth coefficient and the radii ratio on the width of the unyielded annular plug, the velocity profiles, and the pressure distributions are discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Highlights • The start-up plane Poiseuille flow of a Bingham fluid is considered. • The analytical expression for the velocity in the core is given. • The analytical solution is extended to include the velocity in the yielded zone. • Strict bounds on the validity of the analytical solution are provided. Abstract The start-up flow of a Bingham plastic in a channel is considered and Safronchik's solution [1] for the initial evolution of the yield surface and the core velocity is revisited. Stricter time bounds for the validity of the above solution are derived and the solution is extended to include the velocity profile in the evolving yielded zone. Comparisons are made with another approximate solution derived under the assumption that the velocity in the yielded zone is parabolic adjusting with the evolving yield surface. This approximation performs well for small values of the yield stress, or, equivalently, for large values of the imposed pressure gradient. [ABSTRACT FROM AUTHOR]

This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar–Gross–Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou’s modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re) and Bingham number (Bn). These results reveal the flow behavior of Bingham plastics.

The present article investigates the peristaltic transport of a Herschel–Bulkley fluid in an axisymmetric tube. The governing equations are solved using the long wavelength and small Reynolds number approximation. The closed-form solutions are obtained and analyzed for the effects of the fluid behavior index, amplitude ratio, and yield stress on pressure, pressure rise, frictional force, and streamlines. The present model reveals that the increase in flux against pressure rise for a Newtonian fluid is less when compared with Herschel–Bulkley fluid. Further, these changes are opposite to the behavior of frictional force against pressure rise. Also, it is noticed that pressure rise for a fixed value of amplitude ratio in Herschel–Bulkley model is more significant than that of a Newtonian, Power-law, and Bingham model. Furthermore, it is observed that, for small values of yield stress, there is not much difference between Herschel–Bulkley and Power-law fluids.

Highlights • Tailing discharges are often laminar and are modelled as Bingham plastic flows. • Analytical expressions for the uniform and steady flow of a Binghan plastic have been identified. • Results compare favorably with experimental measurements. Abstract At mid to high concentrations, fine mine tailings are non-Newtonian, and their rheology is commonly expressed as Bingham plastic. Discharges of such fine materials in tailing storage facilities form shallow channels. In this short communication, exact analytic expressions to relate the volume flow per unit width and the flow depth are derived for a Bingham plastic in terms of a newly-defined dimensionless parameter. Simplified approximations, valid for the near-plug and quasi-Newtonian fluid limits are proposed. [ABSTRACT FROM AUTHOR]

Highlights • The axisymmetric Poiseuille flow of a Bingham plastic is considered. • The rheological parameters are assumed to vary linearly with pressure. • A lubrication solution is derived. • The critical pressure difference for flow to occur is calculated. • The unyielded core expands if the yield stress grows faster than the plastic viscosity and vice versa. Abstract The lubrication flow of a Bingham plastic in long tubes is modeled using the approach proposed by Fusi and Farina (Appl. Math. Comp. 320, 1–15 (2018)). Both the plastic viscosity and the yield stress are assumed to vary linearly with the total pressure. The resulting nonlinear system of an ordinary differential equation and an algebraic one with unknowns the total pressure and the radius of the unyielded core are solved by using two different techniques. A pseudospectral numerical method utilizing Chebyshev orthogonal polynomials and an analytical perturbation method with the small parameter being the difference of the two dimensionless parameters which are introduced due to the pressure-dependence of the yield stress and the plastic viscosity of the material. The effects of the pressure-dependence of the material parameters on the critical pressure difference required for flow to occur and on the shape of the unyielded core are investigated and discussed. [ABSTRACT FROM AUTHOR]

Composition B-3 (Comp B-3) is a high explosive formulation composed of 60/40wt% RDX (1,3,5-trinitroperhydro-1,3,5-triazine) /TNT (2,4,6 trinitrotoluene). Above approximately 78°C this formulation partially melts to form a multiphase system with solid RDX particles in a molten TNT matrix. This multiphase system presents a number of phenomena that influence its apparent viscosity. In an earlier study explosive Composition B-3 (Comp B-3, 60/40wt% RDX/TNT) was examined for evidence of yield stress using a non-isothermal falling ball viscometer and a yield stress model was proposed. An integrated viscosity model suitable for use in computational fluid dynamics (CFD) simulations is developed to capture the transition from a heterogeneous solid to a Bingham viscoplastic fluid. This viscosity model is used to simulate the motion of imbedded spheres falling through molten Comp B-3. Comparison of the simulations to physical tests show agreement between the positions predicted by the model and the measured locations of the spheres as a function of temperature between 90C and 165C. [ABSTRACT FROM AUTHOR]

We consider the steady axisymmetric Poiseuille flow of a Bingham plastic under the assumption that both the plastic viscosity and the yield stress vary linearly with pressure. An analytical solution is derived for the case where the growth coefficients of both rheological parameters are equal, which is indeed a reasonable assumption for certain oil-drilling fluids allowing the existence of a separable solution with a cylindrical unyielded core. The conditions for the occurrence of flow and the effects of the growth coefficient on the radius of the unyielded plug, the velocity profiles and the pressure distributions are discussed. [ABSTRACT FROM AUTHOR]

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

The flow development of a Herschel–Bulkley fluid in a horizontal channel is considered assuming that slip occurs only on the upper wall due to slip heterogeneities. Hence, the velocity profile is allowed to be asymmetric as was the case in recent experiments on softy glassy suspensions [13]. A power-law slip equation is employed, which generalizes the Navier-slip law. The one-dimensional fully-developed solutions are derived and the different flow regimes are identified. The two-dimensional development flow is solved numerically using finite elements along with the Papanastasiou regularization for the constitutive equation. Due to the asymmetry and the viscoplastic character of the flow, the classical definition of the development length is not applicable. The global and upper-wall development lengths are thus considered and the combined effects of slip and the Bingham number are investigated. Numerical results are presented for two values of the power-law exponent, i.e. n  = 1 (Bingham plastic) and n  = 1/2 (Herchel–Bulkley fluid). It is demonstrated that the global development length increases with the Bingham number and that flow development is slower near the no-slip wall. The global development length increases with slip exhibiting two plateaus and an intermediate rapid increase zone and doubles in the limit of infinite slip. [ABSTRACT FROM AUTHOR]

The steady, pressure-driven flow of a Herschel-Bulkley fluid in a microchannel is considered, assuming that different power-law slip equations apply at the two walls due to slip heterogeneities, allowing the velocity profile to be asymmetric. Three different flow regimes are observed as the pressure gradient is increased. Below a first critical pressure gradient G , the fluid moves unyielded with a uniform velocity, and thus, the two slip velocities are equal. In an intermediate regime between G and a second critical pressure gradient G , the fluid yields in a zone near the weak-slip wall and flows with uniform velocity near the stronger-slip wall. Beyond this regime, the fluid yields near both walls and the velocity are uniform only in the central unyielded core. It is demonstrated that the central unyielded region tends towards the midplane only if the power-law exponent is less than unity; otherwise, this region rends towards the weak-slip wall and asymmetry is enhanced. The extension of the different flow regimes depends on the channel gap; in particular, the intermediate asymmetric flow regime dominates when the gap becomes smaller than a characteristic length which incorporates the wall slip coefficients and the fluid properties. The theoretical results compare well with available experimental data on soft glassy suspensions. These results open new routes in manipulating the flow of viscoplastic materials in applications where the flow behavior depends not only on the bulk rheology of the material but also on the wall properties. [ABSTRACT FROM AUTHOR]

Observations of capillary-driven flow of a liquid in a nanochannel can be used to study the liquid’s rheology. Capillary-driven flow of several pure liquids and bitumen diluted in Heptol (80:20) were studied using a nanofluidic chip. Filling speed of water was lower than the theoretical predictions, as expected. However, for methanol and ethanol, experimental values agreed well with theoretical predictions. 5 and 11 wt.% bitumen solutions in heptol (80:20) followed the theoretical predictions quite well at the initial times but demonstrated deviation for longer penetration times. However, for 20 and 40 wt.% diluted bitumen, experimental observations significantly deviated from the theoretical models. Those deviations were related to the continuous changes in the observed dynamic contact angle of the advancing meniscus. Nanochannel blockage has frequently occurred due to the presence of asphaltenes aggregates when 20 wt.% diluted bitumen was used. Theoretical model for capillary filling of Bingham Plastic fluid was developed to probe the possible non-Newtonian behavior of diluted bitumen above the onset of asphaltenes precipitation. Given very small yield stress, it was difficult to precisely distinguish between Newtonian and non-Newtonian Bingham Plastic behavior. Nevertheless, our results show that Bingham Plastic model can describe the rheology of 5 wt.% and 11 wt.% bitumen at nanoscale more accurately than the Newtonian model. Our study shows nanochannels provide an experimental platform to analyze the flow of petroleum in the nanoporous media. [ABSTRACT FROM AUTHOR]

The development of Bingham plastic flow in tubes and channels is investigated numerically using the Papanastasiou regularization and finite element simulations. It is assumed that slip occurs along the wall following Navier's law, according to which the slip velocity varies linearly with the wall shear stress. Alternative definitions of the development length are discussed and the combined effects of slip and yield stress at low and moderate Reynolds numbers are investigated. It is demonstrated that even for the Newtonian channel flow using the conventional centerline development length is not a good choice when slip is present. Similarly, the development length definition proposed by Ookawara et al. (2000) for viscoplastic flows results in misleading conclusions regarding the effect of yield stress on flow development. To avoid such inconsistencies a global development length is employed. In general, the global development length is monotonically increasing with the Reynolds and Bingham numbers. As slip is increased, the latter length initially increases exhibiting a global maximum before vanishing rapidly slightly above the critical point corresponding to sliding flow. [ABSTRACT FROM AUTHOR]

Shear-induced particle migration in monodisperse and bi-disperse suspension of spherical particles in a Bingham fluid is considered. Previous models of particle migration in Newtonian suspensions are extended to account for the existence of un-yielded regions in the visco-plastic domain when forced to flow in a tube and in a concentric Couette device. In suspension with a monodisperse particle phase, it is shown that particle concentration is continuously augmented in low shear rate regions. The yield boundary is monotonically shifting, affecting the velocity profiles, and the power to maintain the flow is monotonically reduced. When the suspension size distribution is bi-modal, the migration, eventually, results in a separation of the species. Larger particles migrate to the low shear rate zones and the smaller phase is pushed away from there. The velocity profiles, yield boundary and power do not change monotonically, and several stages in this dynamics can be identified. [ABSTRACT FROM AUTHOR]

We solve numerically the cessation of the pressure-driven Poiseuille flow of a Bingham plastic under the assumption that slip occurs along the wall following a generalized Navier-slip law involving a non-zero slip yield stress. In order to avoid the numerical difficulties caused by their inherent discontinuities, both the constitutive and the slip equations are regularized by means of exponential (Papanastasiou-type) regularizations. As with one-dimensional Poiseuille flows, in the case of Navier slip (zero slip yield stress), the fluid slips at all times, the velocity becomes and remains plug before complete cessation, and the theoretical stopping time is infinite. The cessation of the plug flow is calculated analytically. No stagnant regions appear at the corners when Navier slip is applied. In the case of slip with non-zero slip yield stress, the fluid may slip everywhere or partially at the wall only in the initial stages of cessation depending on the initial condition. Slip ceases at a critical time after which the flow decays exponentially and the stopping times are finite in agreement with theory. The combined effects of viscoplasticity and slip are investigated for wide ranges of the Bingham and slip numbers and results showing the evolution of the yielded and unyielded regions are presented. The numerical results also showed that the use of regularized equations may become problematic near complete cessation or when the velocity profile becomes almost plug. [ABSTRACT FROM AUTHOR]

This paper presents a three-dimensional (3D) parallel multiple-relaxation-time lattice Boltzmann model (MRT-LBM) for Bingham plastics which overcomes numerical instabilities in the simulation of non-Newtonian fluids for the Bhatnagar-Gross-Krook (BGK) model. The MRT-LBM and several related mathematical models are briefly described. Papanastasiou's modified model is incorporated for better numerical stability. The impact of the relaxation parameters of the model is studied in detail. The MRT-LBM is then validated through a benchmark problem: a 3D steady Poiseuille flow. The results from the numerical simulations are consistent with those derived analytically which indicates that the MRT-LBM effectively simulates Bingham fluids but with better stability. A parallel MRT-LBM framework is introduced, and the parallel efficiency is tested through a simple case. The MRT-LBM is shown to be appropriate for parallel implementation and to have high efficiency. Finally, a Bingham fluid flowing past a square-based prism with a fixed sphere is simulated. It is found the drag coefficient is a function of both Reynolds number (Re) and Bingham number (Bn). These results reveal the flow behavior of Bingham plastics. [ABSTRACT FROM AUTHOR]

In this paper, an exact analytical solution for creeping flow of Bingham plastic fluid passing through curved rectangular ducts is presented for the first time. The closed form of axial velocity distribution, flow resistance ratio, and wall shear stress are derived using bounded Fourier transformation. An extensive investigation on mutual effects of Hedstrom number, curvature ratio, and aspect ratio is conducted. The results indicate that a drag reduction is caused in the flow field by increasing the Hedstrom number. It is shown that unlike the Newtonian creeping Dean flow, the critical aspect ratio (an aspect ratio in which the flow resistance ratio is independent from curvature ratio) does not exist at large enough Hedstrom numbers. Analytical solution also indicated that as Hedstrom number is increased, the value of Poiseuille number is enhanced, and unlike the Newtonian flows, the value of Poiseuille number is not zero at edges of cross section. [ABSTRACT FROM AUTHOR]

Magnetorheological fluids (MRFs) exhibit rapidly adjustable viscosity in the presence of a magnetic field, and are increasingly used in adaptive shock absorbers for high speed impacts, corresponding to high fluid shear rates. However, the MRF properties are typically measured at very low ( γ ̇ <1000 s −1 ) shear rates due to limited commercial rheometer capabilities. A custom high shear rate ( γ ̇ >10,000 s −1 ) Searle cell magnetorheometer, along with a full scale rotary-vane magnetorheological energy absorber ( γ ̇ >25,000 s −1 ) are employed to analyze MRF property scaling across shear rates using a nondimensional Mason number to generate an MRF master curve. Incorporating a Reynolds temperature correction factor, data from both experiments is shown to collapse to a single master curve, supporting the use of Mason number to correlate low- and high-shear rate characterization data. [ABSTRACT FROM AUTHOR]

In the present paper a two fluid model for pulsatile blood flow through stenosed artery has been developed. The model consists of a core region of suspension of all the erythrocytes assumed to be a Bingham plastic fluid and a peripheral layer of plasma as Newtonian fluid. The analytic expressions for blood flow characteristics namely velocity, wall shear stress, flow rate, plug core radius and effective viscosity are obtained by using perturbation method. The effects of body acceleration and slip velocity have been discussed. We have shown the variation of flow variables with the different parameters and discussed with the help of graph. It is observed that the velocity and flow rate increases but effective viscosity decreases, due to a slip velocity. Body acceleration further enhances the velocity and flow rate. [ABSTRACT FROM AUTHOR]

We solve numerically the Poiseuille flow of a Herschel–Bulkley fluid in a duct of rectangular cross section under the assumption that slip occurs along the wall following a slip law involving a non-zero slip yield stress. The constitutive equation is regularized as proposed by Papanastasiou. In addition, we propose a new regularized slip equation which is valid uniformly at any wall shear stress level by means of another regularization parameter. Four different flow regimes are observed defined by three critical values of the pressure gradient. Initially no slip occurs, in the second regime slip occurs only in the middle of the wider wall, in the third regime slip occurs partially at both walls, and eventually variable slip occurs everywhere. The performance of the regularized slip equation in the two intermediate regimes in which wall slip is partial has been tested for both Newtonian and Bingham flows. The convergence of the results with the Papanastasiou regularization parameter has been also studied. The combined effects of viscoplasticity and slip are then investigated. Results are presented for wide ranges of the Bingham and slip numbers and for various values of the power-law exponent and the duct aspect ratio. These compare favorably with available theoretical results and with numerical results in the literature obtained with both regularization and augmented Lagrangian methods. [ABSTRACT FROM AUTHOR]

The injection of reactive mineral suspensions is a possible process to either reinforce or seal wells in geologic carbon sequestration sites. Among others, olivine slurries could be used as CO2-triggered cements, as they carbonate under the thermodynamic conditions of deep storage. However, injection of such slurries requires to control their initial fluidity and its evolution during the displacement. For this purpose, we have characterized the rheological evolution of olivine suspensions, of particle sizes 1−10 μm, sheared at 100 s−1, in the ranges of 10−40% for the volume fractions, 20−50 bars for the CO2 pressure, and 60-110°C for the temperature. The apparent viscosity, measured at 100 s−1, increases exponentially, with a characteristic time ranging from less than 1 h to more than 10 h, and decreasing with olivine concentration, CO2 pressure, and temperature. Moreover, a careful characterization of the slurry rheology carried out in the initial stages of slow evolution, shows that the slurry obeys a Bingham plastic law, with a yield stress ΣB, and a Bingham viscosity µB increasing from 1 to 20 Pa and from 4 to 110 mPa s, respectively, when the olivine volume fraction φ is increased from 10 to 30%. Such variations can be accounted by classical models (Wildemuth and Williams [1984]: Rheologica Acta, 23,627-635, Krieger [1972]: Advances in Colloid and Interface Science, 3, 111-136). © 2013 American Institute of Chemical Engineers Environ Prog, 33: 572-580, 2014 [ABSTRACT FROM AUTHOR]