Showing papers on "Herschel–Bulkley fluid published in 2020"

Variations of the Herschel-Bulkley exponent reflecting contributions of the viscous continuous phase to the shear rate-dependent stress of soft glassy materials

Abstract: We explore the flow behavior of concentrated emulsions for which the viscosity of the continuous phase can be significantly varied by changing the temperature. The exponents obtained by fitting the shear rate-dependent stress with the popular Herschel–Bulkley (HB) model display a systematic dependence on the viscosity of the continuous phase, revealing that viscous dissipation via the suspending fluid cannot be neglected in the description of the flow behavior of soft glassy systems. We thus propose a simple constitutive equation that accounts for three distinct dissipation mechanisms: elastic, plastic, and viscous dissipation. This three component model describes the flow behavior of soft glassy materials as accurately as the HB model, albeit maintaining a clear physical insight into the dissipation processes at work.

Viscosity Models for Drilling Fluids—Herschel-Bulkley Parameters and Their Use

Abstract: An evaluation is presented of the practical usage of the Herschel-Bulkley viscosity model for drilling fluids. If data from automatic viscosity measurements exist, the parameters should be selected from relevant shear rate ranges to be applicable. To be able to be used properly, viscosity measurements must be measured with a sufficient accuracy. It is shown that a manual reading of standard viscometers may yield insufficient accuracy. It is also shown that the use of yield point/plastic viscosity (YP/PV) as measured using API or ISO standards normally provide inaccurate viscosity parameters. The use of the Herschel-Bulkley model using dimensionless shear rates is more suitable than the traditional way of writing this model when the scope is to compare different drilling fluids. This approach makes it also easier to make correlations with thermodynamic quantities like pressure and temperature or chemical or mineralogical compositions of the drilling fluid.

A modified Herschel–Bulkley model for rheological properties with temperature response characteristics of poly-sulfonated drilling fluid

Abstract: In the deep oil and gas drilling operations, estimation and prediction of the rheological properties for a drilling fluid are of crucial importance for precisely hydraulic calculating, cuttings car...

Magnetorheological Fluids: Qualitative comparison between a mixture model in the Extended Irreversible Thermodynamics framework and an Herschel–Bulkley experimental elastoviscoplastic model

Abstract: A well-known mixture approach treats magnetorheological materials as mixtures composed of a fluid continuum and an equivalent solid continuum. In the framework of extended irreversible thermodynamics, this obtains a complete physical-mathematical model characterized by interesting evolutionary constitutive equations which, in the pre-yield region, show the co-presence of elastic, viscoelastic, and viscoplastic behaviors. Due to its high computational complexity, it is necessary to find a qualitatively corresponding model that, under the same conditions, provides easy-to-implement evolutionary constitutive equations. In this paper, the authors verify the correspondence of the simple shear flow and thinning behavior of the Herschel–Bulkley plastic component (predominant in the pre-yielding region) from a known experimental model with a reduced computation load with elastoviscoplastic generalization under the framework of generalized standard materials.

Squeeze flow of Bingham, Casson and Herschel-Bulkley fluids with yield slip at the wall by accelerated augmented Lagrangian method

Abstract: The squeeze flow of a viscoplastic material between two parallel coaxial disks with yield slip condition at the wall is examined. The governing equations are solved employing the accelerated augmented Lagrangian method for both the viscoplastic model and the yield slip equation. We compute the shape of the yield surface, the velocity and stress fields using the finite difference method. The effect of squeeze flow parameters was studied. We confirm numerically the recently obtained by Muravleva (2017, 2019) asymptotic solutions. Depending on the ratio of two dimensionless parameters, partial slip (stick-slip) or full slip at the wall are possible.

Analysis of the flow properties of a Herschel–Bulkley fluid using short back extrusion viscometry and considering time-dependent and stress growth behaviors

Abstract: The recently proposed short back extrusion (SBE) method is an improved immersed-type BE method. A translational concentric cylinder rheometer is used. As the measurement position is inside the sample, the upflow in the annular space is smooth even over a short distance (5 to 15 mm). Measurement over a short distance decreases the amount of sample adhering to the plunger; this facilitates repeated measurements, as the removal of the adhering sample after each measurement is not needed. The rheometer analysis program can perform automated Newtonian, power-law, and Herschel–Bulkley flow analyses by introducing novel mathematical solutions and obtaining constitutive equations for the various flow types. Herschel–Bulkley fluids exhibit semisolid properties and thixotropic flow characteristics, specifically, stress growth or time-dependent behavior. Currently, SBE viscometry is the only available method to evaluate viscosity and yield stress simply and simultaneously and this study presented the results compared with rotational cone-plate viscometry.

Evaluation of the Behavioral Characteristics in a Gas and Heavy Oil Stratified Flow According to the Herschel–Bulkley Fluid Model

Abstract: At present, most researches on gas-liquid two-phase flow use a power-law fluid model. However, with the development of unconventional petroleum resources and the restarting of heavy oil, the fluid showed strong yield characteristics. The power-law constitutive will not be able to express the yield-pseudoplastic fluid rheological properties. In order to make the study applicable to a larger range of shear rates, this study used the Herschel-Bulkley fluid model to discuss the gas-liquid flow characteristics. Based on the Herschel-Bulkley fluid constitutive, a two-fluid model, combined with dimensionless and iterative calculation methods, was used to theoretically derive the prediction model of liquid holdup and pressure drop for gas-liquid stratified flow. The effects of non-Newtonian fluid rheological parameters, flow conditions, and pipeline geometry on Herschel-Bulkley fluid and gas stratified flow were further analyzed. The results show that the power-law index n and the yield stress τ0 (characterizing the rheological characteristics of the liquid phase) have significant effects on the gas-liquid two-phase stratified flow. Specifically, the enhanced liquid yield and shear thinning characteristics will lead to an increase in liquid holdup and a decrease in pressure drop. Comparing with the experimental data, the calculation model proposed in this work has a good prediction effect and provides new insights into the flow behavior of gas and waxy heavy oil with yield stress.

Linear instability driven by an electric field in two-layer channel flow of Newtonian and Herschel–Bulkley fluids

Abstract: We investigate the linear stability characteristics of a pressure-driven two-layer channel flow of immiscible Newtonian and Herschel–Bulkley fluids subjected to an applied electric field normal to the flow. The linear stability equations are derived and solved using an accurate spectral Chebyshev collocation method. It is found that the electric field can stabilise or destabilise the flow depending on the electrical properties of the fluids. We also observe that increasing the electric permittivity ratio and decreasing the electrical conductivity ratio, while keeping the rest of the parameters constant, enhances the growth rate of the disturbances. The “Reynolds stress” of the Newtonian layer and the work done by the velocity and stress disturbances tangential to the interface are found to be the mechanism of the instability observed due to the applied electric field. A parametric study is also conducted by varying the thickness of the bottom layer, Bingham number and flow index of the Herschel–Bulkley fluid. Increasing Bingham number is found to be stabilising or destabilising depending on the thickness of the non-Newtonian layer and the maximum disturbance growth occurs at an optimum value of non-Newtonian layer thicknesses. Increasing the shear-thinning and shear-thickening nature is shown to destabilise the flow. Our study is relevant in many microfluidic and electronic cooling applications.

Unidirectional flows of a Herschel–Bulkley fluid with pressure-dependent rheological moduli

Abstract: In this paper we study the planar channel flow of a Herschel–Bulkley fluid with pressure-dependent consistency index and yield stress. In particular we consider unidirectional flows in which the velocity is directed along the longitudinal direction of the channel. We show that unidirectional flows are possible only if the dependence on the pressure is linear, since in the nonlinear case secondary flow may appear. We determine constraints that ensure the existence of unyielded regions and constraints that guarantee that the flow does not come to a stop. Analytical solutions for the velocity field and the pressure are determined, and numerical examples that show the dependence on the physical parameters of the model are provided.

Analysis of a two-fluid Taylor-Couette flow with one non-Newtonian fluid

Abstract: We study the dynamic behaviour of two viscous fluid films confined between two concentric cylinders rotating at a small relative velocity. It is assumed that the fluids are immiscible and that the volume of the outer fluid film is large compared to the volume of the inner one. Moreover, while the outer fluid is considered to have constant viscosity, the rheological behaviour of the inner thin film is determined by a strain-dependent power-law. Starting from a Navier--Stokes system, we formally derive evolution equations for the interface separating the two fluids. Two competing effects drive the dynamics of the interface, namely, the surface tension and the shear stresses induced by the rotation of the cylinders. When the two effects are comparable, the solutions behave, for large times, as in the Newtonian regime. We also study the regime in which the surface tension effects dominate the stresses induced by the rotation of the cylinders. In this case, we prove local existence of positive weak solutions both for shear-thinning and shear-thickening fluids. In the latter case, we show that interfaces which are initially close to a circle converge to a circle in finite time and keep that shape for later times.

Identification of the pore size distribution of a porous medium by yield stress fluids using Herschel-Bulkley model

Abstract: In this paper, we present a new method to determine the pore-size distribution (PSD) in a porous medium. This innovative technique uses the rheological properties of non-Newtonian yield stress fluids flowing through the porous sample. In a first approach, the capillary bundle model will be used. The PSD is obtained from the measurement of the total flow rate of fluid as a function of the imposed pressure gradient magnitude. The mathematical processing of the experimental data, which depends on the type of yield stress fluid, provides an overview of the pore size distribution of the porous material. The technique proposed here was successfully tested analytically and numerically for usual pore size distributions such as the Gaussian mono and multimodal distributions. The study was conducted for yield stress fluids obeying the classical Bingham model and extended to the more realistic Herschel-Bulkley model. Unlike other complex methods, expensive and sometimes toxic, this technique presents a lower cost, requires simple measurements and is easy to interpret. This new method could become in the future an alternative, non-toxic and cheap method for the characterization of porous materials.

Spreading Kinetics of Herschel-Bulkley Fluids over Solid Substrates

Abstract: The spreading kinetics of Herschel-Bulkley fluids on horizontal solid substrates was studied theoretically. The evolution equations of film thickness were established in both gravitational and capillary regimes and the dynamic contact angles were derived. Finally, the results were compared with known references. The results show that the yield behavior of the fluids is considered to have a significant impact on the spreading kinetics in both cases. Only when stress is larger than yield stress, the significant flow will occur above the substrate. Spreading zone will be divided into two parts by yield surface: sheared zone and yield zone, which is different from the common Newtonian fluids or power-law non-Newtonian fluids extremely. Below the yield surface (z

Particle Settling in Sheared non-Newtonian Fluids

Abstract: A key unanswered question is how the settling rate of large particles is related to the rheology of the fluid and the local shear in the particle vicinity. In this study, a numerical investigation of large particle settling in un-sheared and sheared non-Newtonian fluids is presented. The particle settling rate increases with increasing imposed shear and with increasing shear thinning. For power-law and Herschel-Bulkley fluid rheology model, a criterion proposed for estimating the settling velocity under shear that can be used to provide estimates of particle settling under transport and the likely distance before complete stratification under laminar flow.

Effects of viscous dissipation and axial heat conduction on forced convection flow of herschel-bulkley fluid in circular duct with axially variable wall heat flux

Abstract: The present study focuses on the effects of viscous dissipation and axial heat conduction on the asymptotic behavior of the laminar forced convection in a circular duct for a Herschel-Bulkley fluid with variable wall heat flux. Analytical asymptotic solutions are presented for the case of axial variations of the wall heat flux, with finite non-vanishing values at infinity along the flow direction. The asymptotic bulk and mixing Nusselt numbers and the asymptotic bulk and mixing temperature distributions are evaluated analytically in the case of axially variable wall heat flux for which polynomial and logarithmic functions are considered as examples. It is shown that the asymptotic bulk Nusselt number depends on the dimensionless radius of the plug flow region a, on the power-law exponent n, on the Peclet number Pe and the asymptotic Brinkman number BBBB∞. The effects of yield stress, Peclet number, and Brinkman number on the asymptotic bulk Nusselt number are discussed.