Herschel-Bulkley Fluid Research Articles

Observations of Blood Flow in an Inclined Improved Generalized Multiple ConstrictedArtery Influenced by a Magnetic Field

This mathematically designed model explores the facts about the velocity of blood flow in an inclined artery as well as in the presence of a magnetic field. This model conjointly reveals regarding core velocity, shear stress on the wall of artery and volumetric rate of flow under constricted condition. Here we are describing blood as Herschel-Bulkley fluid through an inclined artery which is multiple stenosed at equally spaced and distanced. By using appropriate boundary conditions, analytic expressions for these flow characteristics are administered. The results are shown numerically and diagrammatically still as compared with the prevailing results. This data could also be valuable within the progress of the most recent diagnosing tools for solidifying hardening of the arteries.

The effect of salts and haematite on carboxymethyl cellulose\u2013bentonite and partially hydrolyzed polyacrylamide\u2013bentonite muds for an effective drilling in shale formations

A common issue encountered by drilling engineers during drilling operation in oil and gas industries is that simple water-based muds are not suitable for deeper depth and certain clay-swelling formations. Another option as to increasing the density of the drilling mud which brings about an increase in filtration loss, additives may be added to improve the fluid properties. This paper aims on determining the effectiveness of common salts, sodium chloride (NaCl) and potassium chloride (KCl), and haematite on the rheological properties of optimized carboxymethyl cellulose (CMC)–bentonite and partially hydrolyzed polyacrylamide (PHPA)–bentonite muds. Both CMC and PHPA polymer act as fluid loss-reducing agents and viscosifiers for normal bentonite water-based mud. The mud is further enhanced to counter certain swelling formations such as shale through the addition of NaCl and KCl. These salts inhibit the shale formation from swelling through its ions by entering the lattice of the drilling mud or formation instead of the water ions. Haematite, on the other hand, basically functions to increase mud density and acts as a substitute for barite. The effect of haematite on drilling fluid was studied because it gives higher degree of rheological parameters and increases density as compared to barite. So, an optimized concentration of additives was determined for both CMC–bentonite and PHPA–bentonite mud systems, respectively. Three grams of KCl and 3 g haematite were used for CMC–bentonite mud, while 3 g KCl and 1 g haematite were added into PHPA–bentonite mud. Both these muds have shown swelling reduction as compared to those without the use of additives. Moreover, they exhibited Herschel–Bulkley fluid behaviour according to the power law model where their ‘n’ value was less than 1, while their yield points were more than zero. Since shale sloughing is a major problem faced during drilling operation, it leads to major complications in drilling. So, finally, both the formulated drilling fluids are tested to analyse their effect in shale formations by static immersion test. The shale rock was collected from Champhai District of Mizoram. Both the formulated muds exhibited great results as swelling in shale rock was reduced for both muds and optimum rheological values were maintained.

Enhanced electroosmotic flow of Herschel-Bulkley fluid in a channel patterned with periodically arranged slipping surfaces

In this paper, we consider the electroosmotic flow (EOF) of a viscoplastic fluid within a slit nanochannel modulated by periodically arranged uncharged slipping surfaces and no-slip charged surfaces embedded on the channel walls. The objective of the present study is to achieve an enhanced EOF of a non-Newtonian yield stress fluid. The Herschel-Bulkley model is adopted to describe the transport of the non-Newtonian electrolyte, which is coupled with the ion transport equations governed by the Nernst-Planck equations and the Poisson equation for electric field. A pressure-correction-based control volume approach is adopted for the numerical computation of the governing nonlinear equations. We have derived an analytic solution for the power-law fluid when the periodic length is much higher than channel height with uncharged free-slip patches. An agreement of our numerical results under limiting conditions with this analytic model is encouraging. A significant EOF enhancement and current density in this modulated channel are achieved when the Debye length is in the order of the nanochannel height. Flow enhancement in the modulated channel is higher for the yield stress fluid compared with the power-law fluid. Unyielded region develops adjacent to the uncharged slipping patches, and this region expands as slip length is increased. The impact of the boundary slip is significant for the shear thinning fluid. The results indicate that the channel can be cation selective and nonselective based on the Debye layer thickness, flow behavior index, yield stress, and planform length of the slip stripes.

Flow rate based framework for solving viscoplastic flow with slip

In this work, laminar flow through a slit between parallel plates has been analyzed. The flow rate based formulation for such flows, with slip and yield, has been established. The method has been verified for both the Bingham and Herschel–Bulkley fluids. Then, the method has been applied to the Herschel–Bulkley model with slip, and the Bingham–Papanastasiou and Windhab models. Moreover, the method has calculated velocity of the Carreau fluid with slip and yield, which has been found to be consistent with the velocity by the conventional method.

CFD Modeling of Hydraulic Behavior of Oil- and Water-Based Drilling Fluids in Laminar Flow

Summary In recent years, drilling fluids have become more complex in nature to satisfy diverse requirements in drilling operations. Accurate prediction of the frictional pressure losses while drilling is complex because of a combination of various drilling parameters. In the present study, a computational–fluid–dynamics (CFD) analysis is performed to investigate the hydraulics of solids–free non–Newtonian drilling fluids with an eccentric annulus coupled with a rotating drillstring. The Herschel-Bulkley fluid model is used to describe the non-Newtonian fluid behavior of the drilling fluid. Annular inlet fluid velocities are varied from 0.5 to 1.2 m/s (laminar flow). Simulation results are compared with the experimental data from the in–house flow–loop results. The flow loop has a 10–m–long annulus section with a 100–mm–inner–diameter (ID) wellbore and 50–mm–outer–diameter (OD) fully eccentric drillstring. Pressure–drop results from the flow–loop experiments at various flow velocities with and without drillstring rotation are reported. Experimental results show that the pressure drop increases with the drillstring rotation in an eccentric annulus. Pressure–drop predictions from CFD analysis are in close agreement with the experimental results. Also, it has been observed that drilling fluids with similar viscosity profiles measured according to API RP 13D (2017) can have significantly different hydraulic and cuttings–transport behavior. As observed from experimental results, drilling fluids with similar viscosity profiles and density have different pressure drops. This study will contribute to a better understanding of the hydraulic behavior of drilling fluids.

On the blocking limit of steady-state flow of Herschel–Bulkley fluid

On the blocking limit of steady-state flow of Herschel–Bulkley fluid

Rheological behaviors of sugar alcohols for low-to-medium temperature latent heat storage: Effects of temperature in both the molten and supercooled liquid states

As potential candidates of solid−liquid phase change materials (PCM) for latent heat storage in the low-to-medium temperature range (80–250 °C), the temperature-dependent rheological behaviors of five select sugar alcohols were characterized over a wide range of shear rates from 10−3 s−1 to 104 s−1. It was found that the four linear-structured sugar alcohols, i.e., xylitol, erythritol, d-mannitol, and d-dulcitol, are Newtonian fluids above their respective critical shear rates, in both the molten and supercooled liquid states, and that they exhibit typical shear thinning behaviors below the critical shear rates. In particular, d-mannitol and d-dulcitol, with relatively higher melting points, behave like Herschel-Bulkley fluids, which experience slight yield under small yield stresses (0.0001–0.0099 Pa s and 0.0078–0.0528 Pa s for d-mannitol and d-dulcitol, respectively). Inositol, the only cyclic-structured sugar alcohol with the highest melting point (497.65 K), also behaves like a Herschel-Bulkley fluid in both the molten and supercooled liquid states. The dynamic viscosity curves of inositol were found to agree with the Cross model, leading to determination on its zero shear and infinite shear viscosities. An Arrhenius-type dynamic viscosity-temperature curve was observed for inositol over the entire temperature range at the highest shear rate of 104 s−1.

FDM analysis on pulsatile two-phase MHD rheology of blood in tapered stenotic blood vessels

The pulsatile two-phase flow of blood in a tapered narrow artery with overlapping stenosis in the presence of magnetic field is analysed, modelling the suspension of all the erythrocytes in the inner phase region as Herschel-Bulkley fluid and the cell depleted plasma in the outer-phase region as Newtonian fluid. Explicit finite difference method is employed to obtain the numerical solution to various flow measurements from the modelled initial boundary value problem. It is found that when the magnetic field parameter increases, the velocity increases and wall shear stress and longitudinal impedance to flow increase. The estimates of the increase in the longitudinal impedance to flow for the two-phase H-B fluid model is higher than that of the single-phase H-B fluid model.

Process- and bio-inspired hydrogels for 3D bioprinting of soft free-standing neural and glial tissues

A bio-inspired hydrogel for 3D bioprinting of soft free-standing neural tissues is presented. The novel filler-free bioinks were designed by combining natural polymers for extracellular matrix biomimicry with synthetic polymers to endow desirable rheological properties for 3D bioprinting. Crosslinking of thiolated Pluronic F-127 with dopamine-conjugated (DC) gelatin and DC hyaluronic acid through a thiol–catechol reaction resulted in thermally gelling bioinks with Herschel–Bulkley fluid rheological behavior. Microextrusion 3D bioprinting was used to fabricate free-standing cell-laden tissue constructs. The bioinks exhibited flattened parabolic velocity profiles with tunable low shear regions. Two pathways were investigated for curing the bioink: chelation and photocuring. The storage modulus of the cured bioinks ranged from 6.7 to 11.7 kPa. The iron (III) chelation chemistry produced crosslinked neural tissues of relatively lower storage modulus than the photocuring approach. In vitro cell viability studies using the 3D bioprinted neural tissues showed that the cured bioink was biocompatible based on minimal cytotoxic response observed over seven days in culture relative to control studies using alginate hydrogels. Rodent Schwann cell-, rodent neuronal cell-, and human glioma cell-laden tissue constructs were printed and cultured over seven days and exhibited comparable viability relative to alginate bioink controls. The ability to fabricate soft, free-standing 3D neural tissues with low modulus has implications in the biofabrication of microphysiological neural systems for disease modeling as well as neural tissues and innervated tissues for regenerative medicine.

An experimental study on flow and heat transfer characteristics of binary hydrate slurries in a horizontal tube

Fluid flow and heat transfer characteristics of two kinds of binary hydrate slurries CO2-TBAB and CO2-THF in a horizontal tube are investigated experimentally. It is found that CO2-TBAB hydrate slurry shows Herschel-Bulkley (H–B) fluid characteristics at low flow velocity (<0.35 m/s) and as a dilatants fluid at high flow velocity (>0.45 m/s). On the other hand, CO2-THF hydrate slurry exhibits dilatant fluid properties in the flow velocity range of 0.1–0.8 m/s. Moreover, heat transfer characteristics of CO2-TBAB slurry are studied at different TBAB initial concentrations, flow velocities and heating powers. The local convective heat transfer coefficient decreases in the slurry region and then increases in the aqueous solution region. The hydrate slurry produced with 15 wt% initial concentration of TBAB shows a longer slurry region and a shorter solution region. The local convective heat transfer coefficient of CO2-TBAB hydrate slurry with 5 wt% TBAB is in a range of 4413–5397 W/m2K and its phase change zone is at a temperature of 12–14 °C.

Lubrication solution of the flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters in an asymmetric channel

The lubrication flow of a Herschel-Bulkley fluid in a long asymmetric channel, the walls of which are described by two arbitrary functions h1(x) and h2(x) such that h1(x) &amp;lt; h2(x) and h1(x) + h2(x) are linear, is solved extending a recently proposed method, which avoids the lubrication paradox approximating satisfactorily the correct shape of the yield surface at zero order [P. Panaseti et al., “Pressure-driven flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters,” Phys. Fluids 30, 030701 (2018)]. Both the consistency index and the yield stress are assumed to be pressure-dependent. Under the lubrication approximation, the pressure at zero order is a function of x only, is decoupled from the velocity components, and obeys a first-order integro-differential equation. An interesting feature of the asymmetric flow is that the unyielded core moves not only in the main flow direction but also in the transverse direction. Explicit expressions for the two yield surfaces defining the asymmetric unyielded core are obtained, and the two velocity components in both the yielded and unyielded regions are calculated by means of closed-form expressions in terms of the calculated pressure and the two yield surfaces. The method is applicable in a range of Bingham numbers where the unyielded core extends from the inlet to the outlet plane of the channel. Semi-analytical solutions are derived in the case of an asymmetric channel with h1 = 0 and linearly varying h2. Representative results demonstrating the effects of the Bingham number and the consistency-index and yield-stress growth numbers are discussed.

Effect of varying viscosity on two-fluid model of pulsatile blood flow through porous blood vessels: A comparative study

Present work concerns the pulsatile blood flow of two-fluid model through porous blood vessels under the effect of radially varying viscosity. Blood is modeled as two-phase fluid model consisting a core region by non-Newtonian (Herschel-Bulkley) fluid and a plasma region modeled as Newtonian fluid. No slip condition has been used on wall and pressure gradient is taken as periodic function of time. Up to first order approximate solutions of governing equations are obtained using perturbation approach. A comparative analysis for relative change in flow resistance between our model and previously studied single and two-fluid models without porous layer near wall has also been done. The wall of the blood vessel is composed by a thin Brinkman (porous) layer. The stress jump condition has been imposed on fluid-porous interface. Analytical expressions for the velocity profile, flow rate, wall shear stress and flow resistance have been obtained for different regions and the effect of plasma layer thickness, varying viscosity, yield stress, permeability and viscosity ratio parameter on the flow variables are pictorially discussed. It is perceived that values of flow rate for two-fluid model with porous region near wall is higher in comparison to two-fluid model without porous region near wall. Present study reveals a significant impact of glycocalyx layer on blood flow through blood vessels with a porous layer near wall.

A modified LBM for non-Newtonian effect of cement paste flow in 3D printing

Purpose The screw extruder is applied in cement-three-dimensional (3D) printing. The cement paste flow in 3D printing is the typical Herschel–Bulkley fluid. To understand the flow in the channel, the improved lattice Boltzmann method (LBM) is proposed. Design/methodology/approach For Herschel–Bulkley flow, an improved LBM is presented to avoid the poor stability and accuracy. The non-Newtonian effect is regard as a special forcing term. The Poiseuille flow is taken to discuss the detailed process of the method. With the method, the analytical solution and numerical solution are obtained and compared. Then, the effect of the initial yield stress on the numerical solution is both explored by the shear-thickening fluid and the shear-thinning fluid. Moreover, the variations of the relative errors under different lattice nodes and different power-law indexes are analyzed. Finally, the method is applied into the simulation of the flow in the extruder of cement-3D printing. Findings The results show that the improved method is effective for Herschel–Bulkley fluids, which can simulate the flow in the extruder stably and accurately. Practical implications The simulation can contribute to understand the cement paste flow in the screw extruder, which helps to optimize the structure of the extruder in the following periods. Originality/value The improve method provide a new way to analyze the flow in the extruder of cement-3D printing. Also, in the past research, LBM for Herschel–Bulkley fluid is ignored, whereas the study can provide the reference for the numerical simulation.

Effect of varying viscosity on a two-layer model of the blood flow through porous blood vessels

The present work concerns the effect of radially varying viscosity on blood flow through blood vessels with porous walls. Blood is assumed as a two-fluid model consisting of a core region of suspension of all red cells constituted by the Herschel-Bulkley fluid and a peripheral layer of plasma free from the cells modeled as a Newtonian fluid. No slip condition has been used on the wall and the pressure gradient has been taken as constant. The wall of the blood vessel is composed of a thin porous (Brinkman) layer representing the glycocalyx layer. On the fluid interface the stress jump boundary condition as suggested by Ochoa-Tapia and Whitaker has been used. Analytical expressions for velocity profile, wall shear stress, rate of flow and resistance to flow have been obtained for different regions and the effects of plasma layer thickness, varying viscosity, yield stress, permeability and viscosity ratio parameter on the hemodynamical quantities are discussed and depicted graphically. A comparative analysis for a relative change in flow resistance between our model and the previously studied single and two-fluid models without porous walls has been done. The effects of various parameters on hematocrit and Fahraeus effect have also been analyzed and results of earlier works have been established as special limiting cases of the present study. A novel observation is that a decreasing viscosity ratio parameter ( $\lambda_{1}$ ) leads to decay in average concentration of RBCs leading to decay in hematocrit (Ht). It is concluded that a thick porous layer with high porosity at wall due to either a glycocalyx layer or the deposition of fatty plaques of cholesterol may lead to significant decay in hematocrit Ht and may lead to anemia.

Investigation of numerical simulation of non-Newtonian flows dam break and dam breach in open channels using modified VOF method

This paper concerns modelling dam break flows of non-Newtonian Herschel-Bulkley (HB) fluid by using the volume of fluid (VOF) method and high resolution advection schemes. The VOF method is based on the fact that two or more fluids (or phases) are not interpenetrating. In the present study, a modified approach is used to overcome this problem. The OpenFoam software is employed and inter-Foam solver is used in two and three-dimensional model with non-Newtonian fluid. The numerical results of the present study are compared with analytical, numerical and experimental results found in literature. The numerical code which is used showed better agreement with the experimental data than those using shallow water equations and PLIC method.

Sensitivity Analysis of a Wall Boundary Condition for the Turbulent Pipe Flow of Herschel–Bulkley Fluids

This article follows from a previous study by the authors on the computational fluid dynamics-based analysis of Herschel–Bulkley fluids in a pipe-bounded turbulent flow. The study aims to propose a numerical method that could support engineering processes involving the design and implementation of a waste water transport system, for concentrated domestic slurry. Concentrated domestic slurry results from the reduction in the amount of water used in domestic activities (and also the separation of black and grey water). This primarily saves water and also increases the concentration of nutrients and biomass in the slurry, facilitating efficient recovery. Experiments revealed that upon concentration, domestic slurry flows as a non-Newtonian fluid of the Herschel–Bulkley type. An analytical solution for the laminar transport of such a fluid is available in literature. However, a similar solution for the turbulent transport of a Herschel–Bulkley fluid is unavailable, which prompted the development of an appropriate wall function to aid the analysis of such flows. The wall function (called ψ 1 hereafter) was developed using Launder and Spalding’s standard wall function as a guide and was validated against a range of experimental test-cases, with positive results. ψ 1 is assessed for its sensitivity to rheological parameters, namely the yield stress, the fluid consistency index and the behaviour index and their impact on the accuracy with which ψ 1 can correctly quantify the pressure loss through a pipe. This is done while simulating the flow of concentrated domestic slurry using the Reynolds-Averaged Navier–Stokes (RANS) approach for turbulent flows. This serves to establish an operational envelope in terms of the rheological parameters and the average flow velocity within which ψ 1 is a must for accuracy. One observes that, regardless of the fluid behaviour index, ψ 1 is necessary to ensure accuracy with RANS models only in flow regimes where the wall shear stress is comparable to the yield stress within an order of magnitude. This is also the regime within which the concentrated slurry analysed as part of this research flows, making ψ 1 a requirement. In addition, when the wall shear stress exceeds the yield stress by more than one order (either due to an inherent lower yield stress or a high flow velocity), the regular Newtonian wall function proposed by Launder and Spalding is sufficient for an accurate estimate of the pressure loss, owing to the relative reduction in non-Newtonian viscosity as compared to the turbulent viscosity.

Viscoplastic fluids in 2D plane squeeze flow: A matched asymptotics analysis

A matched asymptotic expansions approach is used to determine the flow behaviour of Casson and Herschel–Bulkley fluids between two parallel plates that are approaching each other with a constant velocity. The present study is based on the earlier work of Muravleva (2015), who has analyzed the squeeze flow of a Bingham fluid using the method of matched asymptotic expansions. A naive application of classical lubrication theory leads to a kinematic inconsistency in the predicted plug region - the well known “squeeze flow paradox” for a viscoplastic fluid. The objective of this work is to determine a consistent solution for the aforementioned constitutive equations. Based on the technique of matched asymptotic expansions, the solution is formulated in terms of separate expansions in the regions adjacent to the two plates where the shear stress is dominant, and a central pseudo-plug (plastic) region where the normal stresses become comparable to the shear stress; the two regions being separated by a pseudo-yield surface. In this manner, a complete asymptotic solution is developed for the squeeze flow of both Casson and Herschel–Bulkley fluid models. Using this solution, we derive expressions for the velocity, pressure and stress fields, and the squeeze force acting to retard the plates. The effect of the yield threshold on the pseudo-yield surface that separates the sheared and plastic zones, pressure distribution and squeeze force is investigated.

A Numerical Study on Unsteady Flow of Herschel–Bulkley Nanofluid Through an Inclined Artery with Body Acceleration and Magnetic Field

The present paper deals with the mathematical model for pulsatile flow of Herschel–Bulkley fluid through an inclined artery with stenosis and tapering. The governing equations of Herschel–Bulkley nanofluid are highly non-linear which are simplified in the case of artery having mild stenosis and slightly tapering. The effects of heat and mass transfer have been considered in the model. The solutions for velocity profile, wall shear stress distribution, flow impedance, temperature and concentration profiles are evaluated numerically using finite difference schemes for different values of the parameters associated with the model. The obtained results are represented graphically and the influences of involved parameters on the flow of nanofluid are discussed in detail. It is observed from the computed numerical results that the velocity profile enhances with increase in Grashof numbers. The magnitude of shear stress at the arterial wall increases with increase in stenotic height and Hartmann number and decreases with increase in Grashof numbers. The value of flow resistance enhances with increase in stenotic height, Hartmann number, time and thermophoresis parameter and decreases with increase in inclination parameters, Grashof numbers, Brownian motion parameter and Prandtl number. The combined effects of rheology of blood and parameters associated with heat and mass transfer on flow resistance have been analysed from which the significance of rheology of blood can be understood.

Evaluation of bioink printability for bioprinting applications

Three-dimensional (3D) bioprinting, as a freeform biomedical manufacturing approach, has been increasingly adopted for the fabrication of constructs analogous to living tissues. Generally, materials printed during 3D bioprinting are referred as bioinks, which may include living cells, extracellular matrix materials, cell media, and/or other additives. For 3D bioprinting to be an enabling tissue engineering approach, the bioink printability is a critical requirement as tissue constructs must be able to be printed and reproduce the complex micro-architecture of native tissues in vitro in sufficient resolution. The bioink printability is generally characterized in terms of the controllable formation of well-defined droplets/jets/filaments and/or the morphology and shape fidelity of deposited building blocks. This review presents a comprehensive overview of the studies of bioink printability during representative 3D bioprinting processes, including inkjet printing, laser printing, and micro-extrusion, with a focus on the understanding of the underlying physics during the formation of bioink-based features. A detailed discussion is conducted based on the typical time scales and dimensionless quantities for printability evaluation during bioprinting. For inkjet printing, the Z (the inverse of the Ohnesorge number), Weber, and capillary numbers have been employed for the construction of phase diagrams during the printing of Newtonian fluids, while the Weissenberg and Deborah numbers have been utilized during the printing of non-Newtonian bioinks. During laser printing of Newtonian solutions, the jettability can be characterized using the inverse of the Ohnesorge number, while Ohnesorge, elasto-capillary, and Weber numbers have been utilized to construct phase diagrams for typical non-Newtonian bioinks. For micro-extrusion, seven filament types have been identified including three types of well-defined filaments and four types of irregular filaments. During micro-extrusion, the Oldroyd number has been used to characterize the dimensions of the yielded areas of Herschel-Bulkley fluids. Non-ideal jetting behaviors are common during the droplet-based inkjet and laser printing processes due to the local nonuniformity and nonhomogeneity of cell-laden bioinks.

The influence of seawater on magnetite tailing rheology

It is well known that seawater affects mineral beneficiation, especially in the presence of fine particles. In the present paper, the effect of seawater fraction on the rheology of unflocculated fine magnetite tailings has been studied. Slurry data has been interpreted as both Bingham and Herschel-Bulkley fluids. To relate the experimental results with surface physicochemical properties, zeta potential measurements have been performed to the samples. Results show that besides the well known result that the yield stress and Bingham viscosity have a strong dependency on the particle concentration, the yield stress has been found highly sensitive to the seawater fraction. In contrast, the plastic viscosity observed a comparatively weaker dependency on this variable.