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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]

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]

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]

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]

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]

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]

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]

Highlights: [•] A regularized slip equation with slip yield stress is proposed. [•] The cessation of the axisymmetric Poiseuille flow of Herschel-Bulkley fluids is solved numerically. [•] Different steady-state flow regimes are identified depending on relative values of the slip parameters. [•] In the case of zero slip yield stress, the velocity of viscoplastic fluids becomes and remains flat till complete cessation. [•] The stopping time of viscoplastic flow is finite only if the slip exponent is less than unity. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by Papanastasiou [J. Rheol. 31 (1987) 385–404]. It is shown that the convergence rate of the standard SIMPLE pressure-correction algorithm, which is used to solve the algebraic equation system that is produced by the finite volume discretisation, severely deteriorates as the Bingham number increases, with a corresponding increase in the non-linearity of the equations. It is shown that using the SIMPLE algorithm in a multigrid context dramatically improves convergence, although the multigrid convergence rates are much worse than for Newtonian flows. The numerical results obtained for Bingham numbers as high as 1000 compare favourably with reported results of other methods. [Copyright &y& Elsevier]

Abstract: A numerical framework capable of predicting the free surface flow of a suspension of rigid particles in a non-Newtonian fluid is described. The framework is a combination of the lattice Boltzmann method for fluid flow, the mass tracking algorithm for free surface representation, the immersed boundary method for two-way coupled interactions between fluid and rigid particles and an algorithm for the dynamics and mutual interactions of rigid particles. The framework is able to simulate the flow of suspensions at the level of the largest suspended particles and, at the same time, the model is very efficient, allowing simulations of tens of thousands of rigid particles within a reasonable computational time. Furthermore, the framework does not require any fitting constants or parameters devoid of a clear physical meaning and it is stable, robust and can be easily generalized to a variety of problems from many fields. [Copyright &y& Elsevier]

Abstract: In the present study, the flow of bulk materials is characterised as a non-Newtonian fluid and modelled using the lattice Boltzmann method. A power law and a Bingham model is implemented in the LBM, which is hydrodynamically coupled to the discrete element method (DEM) for structural interaction. The performance of both non-Newtonian models is assessed, both qualitatively and quantitatively, in benchmark problems. The validated, non-Newtonian LBM–DEM framework is then applied to the geometry of a cylindrical Couette rheometer to numerically determine the constitutive response of a sample of Leighton Buzzard sand. The numerical results, which employ the power law, are compared with experimental data, and a number of other synthetic soil samples are defined using the presented process of numerical rheometry. Finally, the numerical stress–strain rate response of the synthetic soil samples is interpreted within the context of a regularised Bingham model, and the similarities discussed. [Copyright &y& Elsevier]

Abstract: The augmented Lagrangian/Uzawa method has been used to study benchmark one-dimensional cessation flow problems of a Bingham fluid, such as the plane Couette flow, and the plane, round, and annular Poiseuille flows. The calculated stopping times agree well with available theoretical upper bounds for the whole range of Bingham numbers and with previous numerical results. The applied method allows for easy determination of the yielded and unyielded regions. The evolution of the rigid zones in these unsteady flows is presented. It is demonstrated that the appearance of an unyielded zone near the wall occurs for any non-zero Bingham number not only in the case of a round tube but also in the case of an annular tube of small radii ratio. The advantages of using the present method instead of regularizing the constitutive equation are also discussed. [Copyright &y& Elsevier]

Abstract: For steady state, stratified, laminar, fully developed two-phase flow which one of them is Newtonian and the other one is Bingham plastic, the motion equations in horizontal pipe with appropriate boundary conditions have been solved analytically. Pressure drop, velocity distribution and location of plug region related to Bingham plastic fluid have been reported. The results show that the non-Newtonian rheological properties have negligible effects on two-phase velocity profile and consequently on pressure gradient in small viscosity ratio of two fluids. With promotion of viscosity ratio, the influence of yield stress on two-phase velocity profile is more considerable. [Copyright &y& Elsevier]

Abstract: Network modeling is used to study the flow in porous media of Ellis and Herschel–Bulkley fluids, which model a large group of time-independent non-Newtonian fluids. Previous work is extended to include yield-stress and shear-thickening phenomena. We use two topologically-disordered networks representing a sand pack and Berea sandstone. Analytical expressions for the volumetric flow rate in a single tube are derived and implemented in each pore and throat to simulate single-phase flow in the pore space. An iterative technique is used to compute the relationship between flow rate and pressure gradient across the whole network. The single tube behavior is compared to that of the network. Experimental data in the literature are compared to the network simulation results to validate the model and investigate its predictive capabilities. Good agreement is obtained in many cases. The flow of yield-stress fluids in porous media is analyzed. Two algorithms to predict the network threshold yield pressure are implemented and compared to the numerically computed threshold yield pressure of the network. [Copyright &y& Elsevier]

Abstract: In the present paper the flow of a Bingham fluid between two parallel porous walls is studied. One of the walls moves with constant velocity parallel to the other, which is fixed, while a longitudinal pressure gradient exists, as well as a transverse flow field due the porosity of the walls. An exact analytical solution is given for the u-velocity field, which has four different forms depending on the values of the three dimensionless parameters, which are the Bingham, Couette and Reynolds numbers. [Copyright &y& Elsevier]

Abstract: We numerically solve the cessation of the annular Poiseuille flow of Bingham plastics for various values of the diameter ratio, using the regularized constitutive equation proposed by Papanastasiou and employing finite elements in space and a fully implicit scheme in time. When the yield stress is not zero, the calculated stopping times are finite and just below the theoretical upper bounds provided by Glowinski [R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, New York, 1984]. [Copyright &y& Elsevier]

Abstract: Remote sensing methods used to determine the rheology and SiO2 composition of lava flows on Mars were utilized to estimate the composition of lava deposits in the Philippines. Test cases were conducted on two lava domes and two lava flow deposits to determine whether remote sensing methods can be applied as a rapid and economical means to assess hazards associated with volcanoes in the humid tropics. Our study shows that dimensional parameters derived from digital elevation models (DEMs) generated from airborne sensors are effective in determining the SiO2 content of lava deposits. The SiO2 values computed from the rheological properties of lava are found to be comparable to geochemically analyzed field samples. These results suggest that remote sensing methods to estimate the composition of lava deposits is viable and can serve as a potentially useful tool for rapid and economic hazards assessment of volcanoes in tropical regions. With the growing number of high-resolution satellite sensors that routinely image the Earth''s surface, such a technique can be widely utilized. [Copyright &y& Elsevier]

Abstract: New results for the squeeze flow of Bingham plastics show the shape of the free surface in quasi-steady-state simulations, and its effect on the yielded/unyielded regions and the squeeze force. The present simulation results are obtained for both planar and axisymmetric geometries as in our previous paper [A. Matsoukas, E. Mitsoulis, Geometry effects in squeeze flow of Bingham plastics, J. Non-Newtonian Fluid Mech. 109 (2003) 231–240] and for aspect ratios ranging from 0.01 to 1. Bigger aspect ratios produce more free surface movement relative to the disk radius or plate length, but less movement relative to the gap. Planar geometries give more free surface movement than axisymmetric ones. Viscoplasticity serves to reduce the free surface movement and its deformation. In some cases of planar geometries and big aspect ratios, unyielded regions appear at the free surface, while the small unyielded regions near the center of the disks or plates are not affected. Including the free surface in the calculations of the squeeze force adds a small percentage to the values depending on aspect ratio and Bingham number. The previously fitted easy-to-use equations are corrected to account for that effect. [Copyright &y& Elsevier]

Abstract: We solve the one-dimensional cessation Couette and Poiseuille flows of a Bingham plastic using the regularized constitutive equation proposed by Papanastasiou and employing finite elements in space and a fully implicit scheme in time. The numerical calculations confirm previous theoretical findings that the stopping times are finite when the yield stress is nonzero. The decay of the volumetric flow rate, which is exponential in the Newtonian case, is accelerated and eventually becomes linear as the yield stress is increased. In all flows studied, the calculated stopping times are just below the theoretical upper bounds, which indicates that the latter are tight. [Copyright &y& Elsevier]

Abstract: We study the mobilization and subsequent flow in a porous medium of a fluid with a yield stress, modeled as a Bingham plastic. We use single-capillary expressions for the mobilization and flow in a pore-throat, and a pore-network model that accounts for distributed yield-stress thresholds. First, we extend the statistical physics method of invasion percolation with memory, which models lattice problems with thresholds, to incorporate dynamic effects due to the viscous friction following the onset of mobilization. Macroscopic relations between the applied pressure gradient and the flow rate for single-phase flow are proposed as a function of the pore-network microstructure and the configuration of the flowing phase. Then, the algorithm is applied to model the displacement of a Bingham plastic by a Newtonian fluid in a porous medium. The results find application to a number of industrial processes including the recovery of oil from oil reservoirs and the flow of foam in porous media. [Copyright &y& Elsevier]

Abstract: Fully developed laminar flows of water-based magneto-rheological (MR) fluids in microtubes at various Reynolds and Hedsrom numbers have been numerically simulated using finite difference method. The Bingham plastic constitutive model has been used to represent the flow behavior of MR fluids. The combined effects of wall roughness and shear yield stress on the flow characteristics of MR fluids, which are considered to be homogeneous by assuming the small particles with low concentration in the water, through microtubes have been numerically investigated. The effect of wall roughness on the flow behavior has been taken into account by incorporating a roughness–viscosity model based on the variation of the MR fluid apparent viscosity across the tube. Significant departures from the conventional laminar flow theory have been acquired for the microtube flows considered. [Copyright &y& Elsevier]

The creeping drag flow of a Bingham plastic past a circular cylinder kept symmetrically between parallel plates was analyzed via numerical simulations with the finite element method. Different gap/cylinder diameter ratios have been studied ranging from 2:1 to 50:1. The Bingham constitutive equation is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coefficient for a wide range of Bingham numbers. The present results extend previous analyses for creeping drag flow past a cylinder in an infinite medium based on variational principles and provide calculations of the drag coefficient around a cylinder in the case of wall effects. [Copyright &y& Elsevier]

We investigate numerically the interactions of two-dimensional jets of Bingham plastic and Herschel–Bulkley fluids with a vertical surface at a distance from the die exit. This problem simulates the early stages of filling of a planar cavity. Our main objective is to explain the flow instabilities observed during the processing of semisolid materials. The effects of the Reynolds and Bingham numbers and of the inlet boundary conditions on both the filling and the stability of the jet are established by means of numerical time-dependent calculations. [Copyright &y& Elsevier]

Squeeze flow of Bingham plastics shows small unyielded regions confined only near the center of the disks. Previous simulation results on axisymmetric coaxial disks are extended to aspect ratios ranging from 0.01 to 1, and to planar parallel plates of infinite width. New results are given for a wide range of Bingham numbers using the continuous modification of Papanastasiou for the Bingham model. Axisymmetric geometries give smaller unyielded regions than planar ones, while big aspect ratios give larger unyielded regions than small ones for the same Bingham number. Calculations of the squeeze force along disks or plates for different aspect ratios are also given and fitted to easy-to-use equations. [Copyright &y& Elsevier]

The present study concentrates on the effects of viscous dissipation and the yield shear stress on the asymptotic behaviour of the laminar forced convection in a circular duct for a Bingham fluid. It is supposed that the physical properties are constant and the axial conduction is negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial distributions of wall heat flux which yield a thermally developed region. It is shown that if the asymptotic value of wall heat flux distribution is vanishes, the asymptotic value of the Nusselt number is zero. The case of the asymptotic wall heat flux distribution non-vanishing giving a value of the Nusselt number dependent on the Brinkman number and on the dimensionless radius of the plug flow region was also analysed. For an infinite asymptotic value of wall heat flux distributions, the asymptotic value of the Nusselt number depends on the dimensionless radius of the plug flow region and on the dimensionless parameter which depends on the asymptotic behaviour of the wall heat flux. The condition of uniform wall temperature and convection with an external isothermal fluid were also considered. The comparison with other existing solutions in the literature in the Newtonian case is analysed. [Copyright &y& Elsevier]

Numerical simulations have been undertaken for the creeping pressure-driven flow of a Bingham plastic past a cylinder kept between parallel plates. Different gap/cylinder diameter ratios have been studied ranging from 2:1 to 50:1. The Bingham constitutive equation is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both the yielded and practically unyielded regions. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coefficient for a wide range of Bingham numbers. The present results extend previous simulations for creeping flow of a cylinder in an infinite medium and provide calculations of the drag coefficient around a cylinder in the case of wall effects. [Copyright &y& Elsevier]

In this study, a new approach is developed to determine the starting pressure head gradient and flowrate of a Bingham plastic through a fractal fracture network. The trace length of fracture is assumed to follow a power-law fractal distribution. The aperture of the fracture is related to the trace length by a scaling relationship. Flow in each fracture is treated as rectangular channel-type flow. A dimensionless flowrate ratio is defined by the average fracture flowrate of Bingham plastic over the flowrate of Newtonian fluid in the smallest fracture. The impact of the input parameters that define the fractal characteristics of the network, the pressure head gradient condition and the Bingham plastic properties is quantified and discussed. It is found that the flowrate ratio significantly decreases with the fractal dimension of trace length as the contrast of fracture lengths in the fractal network decreases with the fractal dimension. The flowrate significantly increases with the maximum over minimum trace length ratio in the network. The scaling exponent dramatically enhances the flowrate in the scaled fractal network. The dimensionless flowrate ratio increases with the pressure head gradient in a non-linear fashion. When the Bingham number is small enough, the dimensionless flowrate ratio does not depend on the pressure head gradient. After flows in more fractures have been activated due to the increase in the pressure head gradient, the Bingham plastic flowrate dramatically increases with the pressure head gradient compared to the Newtonian fluid counterpart. • New solution is developed for starting pressure gradient and Bingham plastic flowrate in a fractal network. • The aperture of the fracture is related to trace length by a scaling relationship. • The trace length of fracture follows a power-law fractal distribution. • Flowrate significantly decreases with fractal dimension of the trace length. • Scaling exponent dramatically enhances the flowrate in the fractal network. [ABSTRACT FROM AUTHOR]

• The poiseuille flow of a bingham plastic in a tube of variable radius is considered. • A lubrication solution is derived at zero order. • The lubrication paradox is avoided at zero order. • The lubrication solution is validated against an approximate analytical solution. • It is demonstrated that the perturbation solution exists only for small variations of the tube radius. We extend a method developed by Fusi and Farina (Appl. Math. Comp. 320, 1–15, 2018) to obtain semi-analytical lubrication-approximation solutions for the flow of a Bingham-plastic in a tube of variable radius. The proposed method is applicable provided that the unyielded core extends continuously from the inlet to the outlet. It turns out that the variable radius of the latter core obeys a stiff integral-algebraic equation which is solved both numerically and asymptotically. The pressure distribution is then obtained integrating a 1st-order ODE and the velocity components are computed using analytical expressions. Converging or diverging either linearly or exponentially, undulating and stenosed tubes are considered. The effects of the shape of the wall on the yield surface which separates the yielded region from the unyielded core and on the pressure difference required to drive the flow are investigated and discussed. The results show that the effect of the wall variation amplitude is greatly amplified as the volumetric flow rate (or, equivalently, the imposed pressure difference driving the flow) increases. It is also demonstrated that the pressure difference needed to achieve a given volumetric flow rate in a converging pipe is always higher than that for a diverging one. [ABSTRACT FROM AUTHOR]

• Introduction of the concept of a rheological texture. • New bearing concepts based on a rheological texture. • The rheological texture enhances the bearing performance and significantly changes the pressure distribution in the bearing. • The texture adds an extra dimension in the design space of bearings and can be controlled actively, realizing a smart bearing. • A new hybrid journal bearing configuration where both hydrostatic and hydrodynamic working regimes are not compromised. • Herringbone bone bearing that uses the rheological texture in a v-shaped pattern. This paper discusses a new type of hybrid journal bearing in which a magnetorheological fluid is used in combination with local magnetic fields, such that the hydrodynamic and hydrostatic working regimes are not compromised. This demonstrates the potential of using the concept of rheological texture in bearings. The performance of this new type of bearing is assessed via Finite Element Modelling (FEM) in which the behaviour of the fluid film is described by the ideal Bingham plastic fluid model. Both the yield stress and the viscosity increase as a function of the magnetic field. [ABSTRACT FROM AUTHOR]