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

Purpose The purpose of this study is to solve convective diffusion equation analytically by considering appropriate boundary conditions and using the Taylor-Aris method to determine the solute concentration, the effective and relative axial diffusivities. Design/methodology/approach >An analysis has been conducted on how body acceleration affects the dispersion of a solute in blood flow, which is known as a Bingham fluid, within an artery. To solve the system of differential equations analytically while validating the target boundary conditions, the blood velocity is obtained. Findings The blood velocity is impacted by the presence of body acceleration, as well as the yield stress associated with Casson fluid and as such, the process of dispersing the solute is distracted. It graphically illustrates how the blood velocity and the process of solute dispersion are affected by various factors, including the amplitude and lead angle of body acceleration, the yield stress, the gradient of pressure and the Peclet number. Originality/value It is witnessed that the blood velocity, the solute concentration and also the effective and relative axial diffusivities experience a drop when either of the amplitude, lead angle or the yield stress rises.

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.

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

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.

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...

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.

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.

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.

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.

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...

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 aim of this experimental study is to determine the jet breakup of non-Newtonian, Bingham plastic slurries in air, notably to obtain an experimentally verified formula for the breakup length. The ash-to-water concentration varies between appr. 9% and 57% resulting in Ohnesorge-numbers between 0.0215 and 0.0476 . The Bingham plastic fluid discharge from a circular orifice and the jet exit Weber-numbers were varied between 983 and 46866 . The Hedstrom-numbers are between 172 and 235, the Reynolds-numbers were in the range of 906–7169 and the tested Froude-numbers are between 7.06 and 42.13 at standard temperature and ambient pressure. Most of our experiments fall into the second wind-induced regime. A linearly increasing correlation was found for the dimensionless breakup length as a function of We , the Reynolds-, and the Froude-number. The rheology and the particle size distribution of the (fly and bottom) ash were measured and are reported, respectively.

© 2018 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Supplementary Raw Research Data, is open data under the CC BY license http://creativecommons.org/licenses/by/4.0/ This author accepted manuscript is made available following 24 month embargo from date of publication (October 2018) in accordance with the publisher’s archiving policy, 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.

The linear instability characteristics of a core-annular pipe flow of a Newtonian fluid and a Bingham fluid separated by a mixed region is investigated. The main objective of this study is to investigate the effect of the yield stress of the annular fluid on the stability behaviour. The present linear stability analysis reveals that the corkscrew mode is the most dangerous mode for the parameters considered. The Bingham number seems to destabilise the flow via modifying the velocity profile. The mechanism of instability is found to be inviscid in nature. An energy budget analysis shows that the energy due to the gradient of viscosity perturbation in the radial direction, and the transfer of energy from the basic flow to the perturbation via the “Reynolds stress” term are responsible for the instability observed. The positive contributions of these terms towards instability increases with increasing the yield stress. The critical Reynolds number also decreases with increasing the Bingham number for the corkscrew mode, which indicates the destabilising influence of the yield stress.

A frequently used technological solution for reducing oscillations of rotors excited by imbalance, time-varying forces or ground vibrations consists in inserting damping devices in the rotor supports. To achieve their optimum performance in a wide range of operating speeds their damping effect must be controllable to be possible to adapt it to the current working conditions. This is enabled by application of magnetorheological squeeze film dampers. In mathematical models the magnetorheological oils are represented mostly by Bingham or Herschel–Bulkley theoretical materials. Recent experimental measurements carried out at several working places show that with respect to the shape of the flow curves obtained for different magnitudes of magnetic induction the real magnetorheological fluids behave like a bilinear material. This enables a more accurate implementation of magnetorheological fluids in mathematical models of squeeze film dampers. In addition, unlike the Bingham fluid the flow curve of a bilinear material is continuous which reduces the nonlinear character of the procedures for calculation of the hydraulic forces by which the oil film acts on the shaft journal and the rotor casing. A new developed mathematical model of a short magnetorheological squeeze film damper based on representing the lubricating oil by bilinear material was implemented in the computational procedures for analysis of the steady state response of a Jeffcott rotor loaded by a stationary force and by the weight and imbalance of the disc. The performed computational simulations proved that these procedures were numerically stable and arrived at the solution also in cases when the methods based on representing the magnetorheological oil by Bingham material failed.

In this paper, we describe our study of the mixed convection of a Boussinesquian Bingham fluid in a vertical channel in the absence and presence of an external uniform magnetic field normal to the walls. The velocity, the induced magnetic field, and the temperature are analytically obtained. A detailed analysis is conducted to determine the plug regions in relation to the values of the Bingham number, the buoyancy parameter, and the Hartmann number. In particular, the velocity decreases as the Bingham number increases. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of diagrams illustrating the influence of various parameters involved in the problem is presented and discussed.

This work aims to explore the T-channel momentum and heat transfer characteristics with the combined effect of Bingham plastic fluids (0.01 ≤ Bn ≤ 20) behavior and geometrical variation in terms of branching angle (30 deg ≤ α ≤ 90 deg). The problem has been solved over a wide range of Reynolds number (50 ≤ Re ≤ 300) and Prandtl number (10 ≤ Pr ≤ 50). For the momentum flow, qualitative and quantitative features are analyzed in terms of streamlines, structure of yielded/unyielded regions, shear rate contours, plug width and length variation, and local pressure coefficient. These features have been represented in terms of isotherm patterns, temperature profile, Nusselt number, and its asymptotic value for heat transfer characteristics. The recirculating flows have been presented here in the vicinity of T-junction, which promote mixing and heat transfer. Broadly, the size of this zone bears a positive dependence on Re and α. However, fluid yield stress tends to suppress it. The critical Reynolds and Bingham numbers were found to be strong functions of the pertinent parameters like α. The inclination angle exerts only a weak effect on the yielded/unyielded regions and on the recirculation length of main branch. Results show a strong relationship of the plug width and length with key parameters and branches. The Nusselt number exhibits a positive relationship with α, Bn, and Re but for lower Pr in the T-junction vicinity for both branches. Such length indicates the required optimum channel length for thermal mixing.

Laminar Bingham fluid flow in the entrance region of a circular pipe is investigated using a momentum integral model. The fully developed flow is uniform in the core region, while the velocity changes in the annular part of the cross section of the pipe. The inlet-filled region concept is adopted. In the inlet region, the boundary layer thickness increases until the size of the plug flow area reaches the fully developed flow size. The model converges to the fully developed solution in the filled region. The model provides the velocity, pressure drop, and skin friction coefficient profiles. The pressure drop results are in good agreement with published experimental data. The flow results asymptotically converge to the fully developed values. In addition, the results are consistent with published Newtonian fluid flow experimental data and theoretical results for the boundary layer thickness, pressure drop, and centerline velocity for small values of the Bingham number.

In the present paper, the non-iterative PISO algorithm and finite volume method are employed to solve the exact Bingham fluid flow. The OpenFOAM solver, i.e., icoFoam, is modified to achieve this goal. The accuracy of numerical procedures is obtained by reproducing the results of Chupin and Dubois (Comput Math Appl 72:1263–1286, 2016. doi:10.1016/j.camwa.2016.06.026). Then, the Bingham fluid flow in a cylindrical enclosure with the rotating top wall is numerically studied by the modified solver for the following ranges of conditions: Reynolds number, $$ 1 \le \text{Re} \le 1000 $$, Bingham number, $$ 0 \le {\text{Bn}} \le 1000 $$ and aspect ratio (AR) of 1, 1/2, 1/4, 1/8 and 1/16. The variation of yielded regions percentage with Re and Bn is plotted for AR = 0.5 and 1. It is found that Reynolds number change in the range $$ 1 \le {\text{Re}} \le 10{\text{Bn}} $$ has no significant effect on the size and shape of the unyielded regions for constant Bn and AR = 1. The effect of Re, Bn and AR on the primary ($$ Q_{p}^{*} $$) and secondary ($$ Q_{s}^{*} $$) volumetric flow rate is also discussed. A correlation is proposed in terms of Re and Bn to approximate the torque coefficient ($$ C_{\text{T}} $$) for $$ 1\le {\text{Re}} \le 1 0 0,\,\, 0\le {\text{Bn}} \le 1000\, $$ and different aspect ratios.

Single-port laparoscopic surgery (SLS), which utilizes one major incision, can deliver favorable cosmetic outcomes with fewer patient hospitalization stays and less postoperative pain. However, current SLS instruments, which are rigid and slender, have been suffering from several drawbacks, including their inability to provide the optimum articulation required to complete certain SLS tasks. This paper reports on the development of a lightweight smart hydraulic actuation system that is proposed to be embedded at selected joints along current SLS instruments, in order to enhance their adaptability with a higher level of stiffness and degrees-of-freedom. The developed smart actuation system utilizes both conventional hydraulic and magnetorheological (MR) fluid actuation technologies. Electromagnetic finite element analyses were conducted to design the electromagnetic circuit of the smart actuator. A prototype of the developed actuation system was manufactured, and its performance was assessed using a dedicated experimental arrangement, which was found to agree well with the results obtained using a Bingham plastic theoretical model. Finally, the present design of the developed smart actuation system permits an angulation of about 90&deg, and a maximum force output in excess of 100 N, generated under a magnetic excitation of about 1.2 Tesla, which should be sufficient to resist torques of up to 500 mNm.

The stability of neutrally and non-neutrally buoyant particles immersed in a plane Poiseuille flow of a yield-stress fluid (Bingham fluid) is addressed numerically. Particles being carried by the yield-stress fluid can behave in different ways: they might (i) migrate inside the yielded regions or (ii) be transported without any relative motion inside the unyielded region if the yield stress is large enough compared to the buoyancy stress and the other stresses acting on the particles. Knowing the static stability of particles inside a bath of quiescent yield-stress fluid (Chaparian & Frigaard, J. Fluid Mech. , vol. 819, 2017, pp. 311–351), we analyse the latter behaviour when the yield-stress fluid Poiseuille flow is host to two-dimensional particles. Numerical experiments reveal that particles lose their stability (i.e. break the unyielded plug and sediment/migrate) with smaller buoyancy compared to the sedimentation inside a bath of quiescent yield-stress fluid, because of the inherent shear stress in the Poiseuille flow. The key parameter in interpreting the present results is the position of the particle relative to the position of the yield surface in the undisturbed flow (in the absence of any particle): the larger the portion of a particle located inside the undisturbed sheared regions, the more likely is the particle to be unstable. Yet, we find that the core unyielded plug can grow locally to some extent to contain the particles. This picture holds even for neutrally buoyant particles, although they are strictly stable when they are located wholly inside the undisturbed plug. We propose scalings for all cases.

The rheological behavior of many lubricants used in hydrodynamic bearings can reasonably be modeled using the Bingham plastic material model. This behavior is characterized by a strong discontinuity, from a pure solid state to a viscous fluid state depending on the local shear stress. In literature three methods have been presented to model a Bingham plastic lubricated film. A full CFD and thus expensive, numerical simulation has been used. A general Reynolds equation based simulation has been used, however with a less accurate numerical regularization of the material discontinuity. Or a general Reynolds equation based simulation has been used, but with a severe reduction of the geometric complexity. In this paper, an ’exact’ thin film lubrication simulation for a Bingham plastic fluid is presented. The model is said to be exact in the sense that it requires no additional approximations to those used in the derivation of the general Reynolds equation, and requires no numerical regularization of the Bingham plastic fluid model and can still be used on any lubricating film geometry. Simulations on both infinite and finite journal bearings shows that the results of this new method are in good accordance with literature, demonstrating the validity of the method.

We study the stability of laminar Bingham&ndash, Poiseuille flows in a sheet of fluid (open channel) down an incline with constant slope angle &beta, &isin, (0,&pi, /2). This problem has geophysical applications to the evolution of landslides. In this article, we apply to this problem recent results of Falsaperla et al. for laminar Couette and Poiseuille flows of Newtonian fluids in inclined channels. The stability of the basic motion of the generalised Navier&ndash, Stokes system for a Bingham fluid in a horizontal channel against linear perturbations has been studied. In this article, we study the flows of a Bingham fluid when the channel is oblique and we prove a stabilizing effect of the Bingham parameter B. We also study the stability of the linear system with an energy method (Lyapunov functions) and prove that the streamwise perturbations are always stable, while the spanwise perturbations are energy-stable if the Reynolds number Re is less than the critical Reynolds number Rc obtained solving a generalised Orr equation of a maximum variational problem.

Nowadays, development of heavy oil usually demands massive hot water injection and meanwhile produces considerable carbon footprint. Radiofrequency (RF) heating, as a “Non-aqueous” method, has potentials to be a cleaner and efficient way for heavy oil development in near future. In this paper, we presented a novel numerical model for simulating non-Newtonian Bingham fluid flow in heavy oil reservoirs based on RF heating. Compared to previous studies, this paper focuses on issues including: (1) Application of RF heating in heavy oil reservoir; (2) Non-Darcy flow induced by threshold pressure gradient (TPG) of Bingham fluid; (3) Temperature dependent TPG and viscosity; (4) Two-way coupling between non-Darcy flow, transient heat transfer and electromagnetic (EM) field. To incorporate TPG in numerical analyses, an effective method was utilized by modifying the gravitational acceleration vector in Darcy's law. This method was verified with analytical solution. By doing this, the induced moving boundary by TPG can be simulated, and pressure-disturbed area can be determined. Results show that RF heating significantly mitigates the impediment induced by TPG and high viscosity near well. The moving boundary stops motion at around 1000th day of production and the extreme disturbed distance is 63 m. Besides, it is found that no matter whether TPG is considered or not, RF heating has a positive impact on the reservoir development. However, for the production time less than 1000 days, RF heating is more effective when TPG is considered. Finally, we also found it very necessary to incorporate TPG in the simulations to determine optimal well spacing. If TPG is neglected in kinematic equation, the optimal well spacing would be overestimated by over 50%. At the same time, the change of TPG value with temperature cannot be ignored. Otherwise, the optimal well spacing would be underestimated by 15%. This paper reveals the potentials of RF heating method for non-Newtonian Bingham fluid production and provides an alternative way for clean, environmental, and highly efficient development of heavy oil reservoir.

Dense granular materials are universal in nature and some common examples of this kind of materials in our daily lives are sand, rice, sugar etc. Research in this area is motivated by numerous applications encountered in industrial processes, such as hopper discharge, chute flow, moving beds, sandpipe flow, etc. and also in geophysics for the description and prediction of natural hazards like landslide and rock avalanches. Here, a continuum description of these granular flows is appropriate. Granular materials in liquid-like state show strong non-Newtonian behavior, which is typically described by phenomenological constitutive laws with local rheology. Very often, fluidization and flows of granular materials are localized in thin shear bands, whereas the granular material remains in solid-like state outside these bands. In this paper we establish a benchmark problem for granular materials, namely as Couette flow which is a very common example for granular materials in industrial application. We formulate the rheology for the continuum approach in the framework of the regularized version of a Bingham fluid and use advanced numerical methods regarding discretization as well as solution aspects, so that we can provide mesh independent results with two different software packages, Featflow and Openfoam, which can be used for validation and evaluation of the different methods and approaches. The authors thank the German Research Foundation DFG for funding under the grants TU 102/44-1 and SCHW 1168/6-1 within the pilot for transnational cooperation of the Dutch Technology Foundation STW and the DFG. This work was also supported by DAAD.

We study material flow in the vicinity of single shear bands in high strain-rate (10(4) -10(5) per second) deformation of metals. Shear band plastic flow, in three different materials, is shown to resemble unsteady planar Couette flow (Stokes first problem) of a Bingham fluid. Equivalent shear band viscosities and yield stresses are obtained, with the former similar to liquid metal viscosities and the latter being similar to 0.5 times the band nucleation stress. Reynolds and Bingham numbers, computed based on the shear band displacement measurements, are suggestive of boundary layer formation, consistent with the severe localization of deformation within shear bands. (C) 2018 Elsevier Ltd. All rights reserved.

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.

The theory of slow viscous flow around a slender body is generalized to the situation where the ambient fluid has a yield stress. The local flow around a cylinder that is moving along or perpendicular to its axis, and rotating, provides a first step in this theory. Unlike for a Newtonian fluid, the nonlinearity associated with the viscoplastic constitutive law precludes one from linearly superposing solutions corresponding to each independent component of motion, and instead demands a full numerical approach to the problem. This is accomplished for the case of a Bingham fluid, along with a consideration of some asymptotic limits in which analytical progress is possible. Since the yield stress of the fluid strongly localizes the flow around the body, the leading-order slender-body approximation is rendered significantly more accurate than the equivalent Newtonian problem. The theory is applied to the sedimentation of inclined cylinders, bent rods and helices, and compared with some experimental data. Finally, the theory is applied to the locomotion of a cylindrical filament driven by helical waves through a viscoplastic fluid.

The Folgar–Tucker fiber orientation model coupled with weakly compressible Smoothed Particle Hydrodynamics is used to simulate the process of casting of fiber reinforced concrete and to predict the spatial-temporal evolution of the probability density function of fiber orientation. The flowable concrete-fiber mix is modeled as a viscous Bingham-type fluid. Model predictions qualitatively agree with fiber orientations observed in an L-box test with fibers suspended in transparent gel. Important factors and assumptions regarding the fiber flow are reviewed and conclusions are drawn based on numerical experiments.

Buoyant miscible displacement flow of a Bingham fluid by a Newtonian fluid along a vertical plane-channel is studied, in the high Peclet number regime. The displacing fluid is lighter than the displaced fluid and the flow direction is upwards, hence density-unstable. The flow is effectively governed by 4 dimensionless parameters: the Newtonian Bingham number (BN), the viscosity ratio (m), the Reynolds number (Re), and modified Froude number (Fr). This is a simple model for micro-annulus formation in the primary cementing of oil and gas wells. The micro-annulus layers correspond to residual drilling mud that remains on the walls after displacement. Here we show that in density unstable situations static residual wall layers can exist for yield stresses below the minimum for density stable regimes. The layers are partially static and may also be thicker than the fully static layers encountered in density stable flows. Adverse buoyancy gradients (represented here by large χ = 2 R e F r 2 ), also seems to promote instability of the flow. These instabilities are various, ranging from Rayleigh–Taylor type frontal instabilities, through to Kelvin–Helmholz type inertial waves, and more viscous-controlled inverse bamboo and mushroom morphologies. We present an overview of flow regimes within our parameter space and approximate onset criteria. It is unclear whether or not the instabilities observed result in improved fluid displacement efficiency.

Purpose This paper is concerned with the peristaltic transport of an incompressible non-Newtonian fluid in a porous elastic tube. The impacts of slip and heat transfer on the Herschel-Bulkley fluid are considered. The impacts of relevant parameters on flow rate and temperature are examined graphically. The examination incorporates Newtonian, Power-law and Bingham plastic fluids. The paper aims to discuss these issues. Design/methodology/approach The administering equations are solved utilizing long wavelength and low Reynolds number approximations, and exact solutions are acquired for velocity, temperature, flux and stream functions. Findings It is seen that the flow rate in a Newtonian fluid is high when contrasted with the Herschel-Bulkley model, and the inlet elastic radius and outlet elastic radius have opposite effects on the flow rate. Originality/value The analysis carried out in this paper is about the peristaltic transport of an incompressible non-Newtonian fluid in a porous elastic tube. The impact of slip and heat transfer on a Herschel-Bulkley fluid is taken into account. The impacts of relevant parameters on the flow rate and temperature are examined graphically. The examination incorporates Newtonian, Power-law and Bingham plastic fluids.

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.

This study is conducted to investigate the Bingham—Papanastasiou fluid flow driven by a rotating infinite disk. The Bingham—Papanastasiou model is a modification of the Bingham plastic model, which is developed by introducing a continuation parameter to overcome its discontinuity. The von K´arman similarity solution is used to transform the flow equations from ordinary differential equations to a nonlinear system of partial differential equations, which is solved numerically. The effect of the Bingham flow parameters on the radial, tangential, and axial velocities, pressure, and radial and tangential skin friction coefficients is discussed.

The linear stability of thermocapillary liquid layer of a Bingham-plastic fluid is studied. Due to the yield stress of Bingham fluid, there is a plug region in the flow, which divides the yielded flow into two regions. When the flow is subjected to a small perturbation, the velocity perturbation below the upper surface of plug region is negligible, while the temperature perturbation can be found in all flow regions at moderate and small Prandtl numbers (Pr). The perturbation amplitude of the upper surface of plug region decreases rapidly with the increase of Pr. The preferred modes are the upstream oblique wave and the downstream streamwise wave at small and large Pr, respectively. The effects of the yield stress, gravity and the interfacial heat transfer on the flow stability are discussed. The perturbation amplitude only appears above the plug region, which differs from the cases in the plane Bingham–Poiseuille flow and the thermocapillary liquid layer of a Carreau fluid.

Experimental data for the pressure-driven flow of concentrated lignocellulosic biomass (corn stover) in a circular pipe are presented. A positive curvature was observed in the pressure profile at steady state, both when the biomass was flowing, and for several minutes after the flow had stopped. After the flow into the pipe was stopped, biomass continued to be expelled for at least five minutes, suggesting that the material is compressible. Occasionally, the pressure and outlet flow rate exhibited rapid, transient fluctuations. The fluctuations would cease when dryer-than-average heterogeneities exited the pipe. A mathematical model is developed to treat the biomass as a compressible Bingham fluid with a density-dependent yield stress. This model quantitatively reproduces steady-state pressure profiles for both flowing and nonflowing states, and captures the transition between the two states after the inlet flow rate is set to zero. Our model cannot predict the rapid pressure fluctuations that appear to be associated with heterogeneities in composition.Experimental data for the pressure-driven flow of concentrated lignocellulosic biomass (corn stover) in a circular pipe are presented. A positive curvature was observed in the pressure profile at steady state, both when the biomass was flowing, and for several minutes after the flow had stopped. After the flow into the pipe was stopped, biomass continued to be expelled for at least five minutes, suggesting that the material is compressible. Occasionally, the pressure and outlet flow rate exhibited rapid, transient fluctuations. The fluctuations would cease when dryer-than-average heterogeneities exited the pipe. A mathematical model is developed to treat the biomass as a compressible Bingham fluid with a density-dependent yield stress. This model quantitatively reproduces steady-state pressure profiles for both flowing and nonflowing states, and captures the transition between the two states after the inlet flow rate is set to zero. Our model cannot predict the rapid pressure fluctuations that appear to b...

In this study, we report the theoretical resistance force of a magneto-rheological (MR) shock absorber. We use the Bingham plastic model to theoretically represent the dynamic behavior of MR fluid flow in a circular pipe under the effect of a magnetic field. Because an MR fluid has yield stresses, the flow is divided into two regions: shear flow and plug flow. We reveal the relation between the resistance force of the MR shock absorber and the applied magnetic field. We conduct experiments and compare the experimental and analytical results to verify the theoretical approach.

The thermal performance of helical-coil heat exchangers can be significantly enhanced when operated with ice slurry as a phase-change refrigerant. It is essential to also consider the hydrodynamics of ice slurry flow to determine the overall performance of the heat exchanger. This study presents a detailed numerical investigation of the thermo-hydrodynamic performance of a helical coil heat exchanger operated with a laminar and non-Newtonian flow of ethyl-alcohol ice slurry subject to phase change. The Bingham plastic model is used to reflect the non-Newtonian behavior of ice slurry. The phase change of ice slurry is modelled using the enthalpy-porosity method. The pressure drop and heat transfer of ice slurry in a double-turn helical coil are determined in terms of ice mass fraction and Dean number. The results show that an increase in the ice mass fraction and Dean number results in an increase of the heat transfer rate. This is, however, associated with an increase in pressure drop. The entropy generation analysis is introduced to evaluate the overall performance of the heat exchanger, taking into account the opposing effects of heat transfer and pressure drop. It is evident that, at certain ice mass fractions, there exists an optimal value of the Dean number that leads to minimum irreversibility and maximum overall performance.

In this study, applicability of peristaltic waves as an efficient means for bio-particle manipulation is numerically investigated using the lattice Boltzmann method (LBM). The analysis is carried out in a flow configuration which comprises a two-dimensional, closed-ended, vertical cavity filled with a Bingham fluid and equipped with two flexible side walls and two rigid upper and lower plates. It is shown that by judicially adjusting the working parameters of the peristaltic waves (e.g., wavelength, amplitude, speed, and/or phase lag) it is possible to control the dynamics/trajectory of a large, circular bio-particle immersed in the fluid. It is also shown that a suspending circular particle moves faster if the surrounding fluid possess a yield-stress. Based on our obtained numerical results, for a given cross-sectional area, circular particles move faster than elliptical particles when excited peristaltically.

In this paper, double-diffusive natural convection, studying Soret and Dufour effects and viscous dissipation in a square cavity filled with Bingham fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM). In addition, entropy generations through fluid friction, heat transfer, and mass transfer has been studied. The problem has been solved by applying the regularised Papanastasiou model. This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 103,104 and 105), Bingham number (Bn), Lewis number (Le = 2.5, 5 and 10), Dufour parameter (Df) = 0, 1, and 5), Soret parameter (Sr) = 0, 1, and 5), Eckert number (Ec = 0, 0.001, and 0.01), inclined angle (Θ = 0, 40, 80, and 120) and the Buoyancy ratio (N = −1, 0.1, 1). Results indicate that the increase in Rayleigh number enhances heat and mass transfer for various Bingham numbers and inclined angles. The alteration of the inclined angle changes heat and mass transfer. In addition, the rise of the inclined angle alter the unyielded zones. The increase in the Lewis number augments mass transfer in different inclined angles while it causes heat transfer to drop marginally at Θ = 0, 40, and 120. The heat transfer increases with the rise of the Dufour parameter and the mass transfer enhances as the Soret parameter increases for different Bingham numbers and Rayleigh numbers. In some cases, the augmentation of Soret and Dufour parameters alter the behavior of heat and mass transfer against the alteration of the inclined angle. The addition of Soret and Dufour parameters and Lewis numbers do not affect the unyielded zone considerably. The augmentation of the buoyancy ratio number enhances heat and mass transfer. The rise of buoyancy ratio number alters the unyielded section significantly. The increase in Eckert number declines heat transfer, but it has a marginal effect on mass transfer. The augmentation of Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the Bingham number provokes various irreversibilities to drop significantly. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The rise of Eckert number alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters.

The evolution equations for the particle distribution functions are written in a divergence form applicable in three dimensions. From this set, it is shown that the continuity equation and the equations of motion are satisfied in Cartesian, cylindrical and spherical coordinates for all fluids when additional source terms are added to the equations of evolution in the latter two coordinate systems. If the body forces are present, a new set of source functions is required in each coordinate system and these are described as well. Next, the energy equation is derived by using a separate set of particle distribution functions. Modifications of the relevant equations to be applicable to incompressible fluids is described. The incorporation of boundary conditions and the description of the numerical scheme for the simulation of the flows employing the new approach is given. Validation results obtained through the modelling of a mixed convection flow of a Bingham fluid in a lid-driven square cavity, and the steady flow of a Bingham fluid in a pipe of square cross-section are presented. Next, using the cylindrical coordinate version of the evolution equations, numerical modelling of the steady flow of a Bingham fluid and the Herschel–Bulkley fluid in a pipe of circular cross-section have been performed and compared with the simulation results using the augmented Lagrangian method as well as the analytical solutions for the velocity field and the flow rate. Finally, some comments on the theoretical differences between the present approach and the existing formulations regarding Lattice Boltzmann Equations are offered.

The unclassified tailings paste (UTP) is a typical non-Newtonian fluid with a mass fraction over 70%, and the UTP disposal technology is of great significance to solve the disaster of tailings ponds and underground voids. The widely used Buckingham equation for predicting the pressure gradient of UTP in pipe flow does not consider the effect of wall slip drag reduction and the prediction accuracy is relatively low. To this end, a theoretical derivation based on the apparent wall slip equations established by previous scholars, sedimentation tests, loop tests and rheological tests were carried out. When the UTP is a Bingham fluid, the proposed new pressure gradient model which considers the wall slip effect is composed of the Buckingham equation and a dimensionless wall slip correction coefficient. The correction coefficient decreases with increases in either slip layer thickness and plastic viscosity of UTP, and increases with increases in either pipe diameter and slip layer viscosity. In this study, the dimensionless correction coefficient is 0.83∼0.85. When using the new pressure gradient model, the ratio of solids volume fraction to the maximum packing volume fraction of UTP (the filling degree) is at least 0.76. Compared with the measured pressure gradient from the loop tests in this study and the literature, the average error of the new pressure gradient model is 11.3%, whereas the average error of the Buckingham equation is 29.8%. The advantages of the new pressure gradient model are that the required parameters are easy to obtain, the model is easy to solve, and the prediction accuracy is better than the Buckingham equation. When the UTP is a Herschel-Bulkley fluid, the reliability of the pipe pressure gradient model which considers the wall slip effect still needs to be verified.