Power-law Fluid Research Articles

Simulation of High-Viscosity Generalized Newtonian Fluid Flows in the Mixing Section of a Screw Extruder Using the Lattice Boltzmann Model.

The mixing quality of polymer melts in the mixing section of a single-screw extruder and an injection molding machine has considerable effects on the properties of the molded products. Therefore, the study of the flow field of polymer melts in the mixing section is of great importance. The lattice Boltzmann method (LBM) exhibits unique advantages in simulating non-Newtonian fluids. Many researchers have used LBM to study the flow of medium- and low-viscosity fluids. In their studies, the Reynolds number of fluid flows is generally moderate. However, polymer melts are typical high-viscosity fluids, and their flow Reynolds number is generally very small. The single-relaxation-time lattice Boltzmann method (SRT-LBM) has been used previously to study the flow field of power law fluids in the mixing section. Herein, the flow field of high-viscosity generalized Newtonian fluids in the mixing section of a single-screw extruder is studied using SRT-LBM, the two-relaxation-time lattice Boltzmann method (TRT-LBM), and the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). Through comparison, TRT-LBM has been found to exhibit obvious advantages regarding stability, calculation accuracy, calculation efficiency, and selection of simulation parameters. The TRT-LBM is more suitable for studying high-viscosity generalized Newtonian fluids than SRT-LBM and MRT-LBM. SRT-LBM has low computational efficiency when simulating high-viscosity generalized Newtonian fluids, and instability is easily caused when the fluid has a yield stress. For MRT-LBM, only by studying the relaxation parameters can its advantages be fully utilized. However, optimizing the accuracy and stability of the MRT-LBM via parameter research and linear stability analysis is difficult. For non-Newtonian fluids, it is difficult to optimize the relaxation parameters to make the MRT-LBM more stable and accurate than the TRT-LBM. It is difficult for the MRT-LBM to realize its potential when simulating high-viscosity generalized Newtonian fluids. In addition, we studied the flow pattern in the cross section of the screw channel and compared it to the results reported in previous studies.

Hydrodynamical characteristics of a pair of elliptical squirmers in a channel flow of power-law fluids

Hydrodynamical characteristics of a pair of elliptical squirmers in a channel flow of power-law fluids

Seismic reduction principle and response analysis of variable damping viscous damper system

PurposeA new type of variable damping viscous damper is developed to meet the settings of different damping parameter values at different working stages. Its main principle and design structure are introduced, and the two-stage and multi-stage controllable damping methods are proposed.Design/methodology/approachThe theoretical calculation formulas of the damping force of power-law fluid variable damping viscous damper at elongated holes are derived, aiming to provide a theoretical basis for the development and application of variable damping viscous dampers. For the newly developed variable damping viscous damper, the dynamic equations for the seismic reduction system with variable damping viscous dampers under a multi-degree-of-freedom system are established. A feasible calculation and analysis method is proposed to derive the solution process of time history analysis. At the same time, a program is also developed using Matlab. The dynamic full-scale test of a two-stage variable damping viscous damper was conducted, demonstrating that the hysteresis curve is complete and the working condition is stable.FindingsThrough the calculation and analysis of examples, the results show that the seismic reduction effect of high and flexible buildings using the seismic reduction system with variable damping viscous dampers is significant. The program developed is used to analyze the seismic response of a broadcasting tower using a variable damping TMD system under large earthquakes. The results indicate that the installation of variable damping viscous dampers can effectively control the maximum inter-story displacement response of TMD water tanks and can effectively consume seismic energy.Originality/valueThis method can provide a guarantee for the safe and effective operation of TMD in wind and vibration control.

Computer simulation of two phase power-law nanofluid of blood flow through a curved overlapping stenosed artery with induced magnetic field: entropy generation optimization

PurposeThe purpose of this study is to determine the impact of two-phase power law nanofluid on a curved arterial blood flow under the presence of ovelapped stenosis. Over the past couple of decades, the percentage of deaths associated with blood vessel diseases has risen sharply to nearly one third of all fatalities. For vascular disease to be stopped in its tracks, it is essential to understand the vascular geometry and blood flow within the artery. In recent scenarios, because of higher thermal properties and the ability to move across stenosis and tumor cells, nanoparticles are becoming a more common and effective approach in treating cardiovascular diseases and cancer cells.Design/methodology/approachThe present mathematical study investigates the blood flow behavior in the overlapped stenosed curved artery with cylinder shape catheter. The induced magnetic field and entropy generation for blood flow in the presence of a heat source, magnetic field and nanoparticle (Fe3O4) have been analyzed numerically. Blood is considered in artery as two-phases: core and plasma region. Power-law fluid has been considered for core region fluid, whereas Newtonian fluid is considered in the plasma region. Strongly implicit Stone’s method has been considered to solve the system of nonlinear partial differential equations (PDE’s) with 10–6 tolerance error.FindingsThe influence of various parameters has been discussed graphically. This study concludes that arterial curvature increases the probability of atherosclerosis deposition, while using an external heating source flow temperature and entropy production. In addition, if the thermal treatment procedure is carried out inside a magnetic field, it will aid in controlling blood flow velocity.Originality/valueThe findings of this computational analysis hold great significance for clinical researchers and biologists, as they offer the ability to anticipate the occurrence of endothelial cell injury and plaque accumulation in curved arteries with specific wall shear stress patterns. Consequently, these insights may contribute to the potential alleviation of the severity of these illnesses. Furthermore, the application of nanoparticles and external heat sources in the discipline of blood circulation has potential in the medically healing of illness conditions such as stenosis, cancer cells and muscular discomfort through the usage of beneficial effects.

Inelastic Solution for Power Law Fluid with Taylor Galerkin-Pressure Correction Finite Element Method: Axisymmetric Contraction Flows

In this study we examine the flow of inelastic fluids with various shear properties in axisymmetric contractions with various contraction ratios are selected as 4:1, 6:1 and 8:1 with both rounded-corner and sharp. Particular attention is paid to the effect of shear thickening and shear thinning upon the solution behavior. Power-law inelastic model is employed coupling with the conservation of momentum equation and continuity equation. The numerical simulation of such fluid is performed by using the Taylor Galerkin pressure correction (T-G/P-C) finite element algorithm. The effects of geometry structure and many factors such as Reynolds number (Re) and the parameters of power law model are presented in this study. Particularly, in this study we are focused on the influence of these factors on the solution components and the level of convergence. This research was a comparative study between sharp and rounded-corner contraction geometries with a ratio of 4:1, and to another comparative study among sharp contraction geometries with ratios of 4:1, 6:1, and 8:1. The practical implications of this study focused on vortex length and the impact of varying the parameters of the power law model and the Reynolds number (Re) on it for 4:1 contraction flow. The study dealt with the effect of different geometries on the rates of convergence of velocity and pressure as well as the characteristics of axial velocity and pressure on the axis of symmetry.

New Simple Analytical Surge/Swab Pressure Model for Power-Law and Modified Yield-Power-Law Fluid in Concentric/Eccentric Geometry

The axial movement of pipe in and out of the well generates positive (surge) and negative (swab) pressures that will impact the well pressure. When the swab and surge effects cause well pressures outside the allowable operational limits, wellbore instability (well collapse/well fracture), kick, and induced drill string sticking issues will occur. The problems increase the operational and nonproductive time-related costs. Consequently, the drilling budget rises significantly. It is therefore, imperative to predict the differential pressures in order to mitigate the problems. Even though several models have been developed in the past, models work for the considered experimental setup and conditions. In this paper, a simple analytical model was derived for eccentric/concentric annuli. The fluid rheological behaviors were assumed to be described by power law and yielded power-law. The model is derived based on a steady state condition, and the effects of tripping speed, the power-law fluids, the yield-power-law fluids rheological parameters, and well geometries are considered. The model is compared with experimental data from the literature and with the existing model. Parametric sensitivity studies have been conducted. Results show that the model prediction exhibited quite good performance, with an average percentile error deviation of 9.9% and 6.2% for the power-law and yield-power-law fluids, respectively. However, more testing is required to determine the model’s limitations and application.

A universal rescaling law for the maximum spreading factor of non-Newtonian droplets with power-law fluids

The maximum spreading diameter of non-Newtonian fluid droplets impacting on the solid surface is a key concern in a variety of industrial and medical applications. In this work, we focus on the effect of the shear-thinning, one of the most important non-Newtonian properties, on the spreading dynamics of impacting droplets. A finite element scheme combined with a phase field method and dynamic contact angle model has been employed to perform extensive studies on the spreading process of power-law fluid droplets on solid surfaces with various rheological parameters, impact conditions and surface wettability. The simulation results show that on both hydrophilic and hydrophobic surfaces, impacting droplets exhibit two typical morphologies at the maximum spreading state: a spherical cap in the low-Weber-number range (capillary regime) and a thin-film form in the high-Weber-number range (viscous regime). The maximum spreading factor βmax, of droplets with different degrees of shear-thinning converges to the equilibrium spreading state for a droplet with U0=0 at the low-Weber-number limit. Furthermore, a theoretical relationship of βmax∼We1/2 has been derived in the capillary regime. In contrast, the effect of the shear-thinning property becomes significant in the high-Weber-number regime. We discussed the influence of the power-law coefficients K and n on the spreading process and βmax independently. Specifically, as the power-law index n decreases, the morphology of the shear-thinning droplet at the maximum spreading state tends to change from a spherical cap to a thin-film form. Considering the non-uniform distribution of shear rates in the spreading shear-thinning droplet, a new scaling relationship of βmax∼ln(Ren1/(2n+3)) has been proposed based on theoretical derivation and numerical simulations. By introducing an interpolation function on the scaling relationships between the capillary and viscous regimes, we obtained a universal rescaling model that agrees well with numerical and experimental results of non-Newtonian droplets with shear-thinning fluid over a wide range of We numbers, surface wettability and rheological parameters.

Controlling factors of coating thickness of Sisko fluid in blade coating process

Blade coating is a technique for coating the moving substrate with a protective fluid layer through the blade as a common smoothing device. The heat transfer and slip effects of the rheological Sisko fluid model for plane coater are considered under blade coating process. This model combines the power-law and Newtonian fluids and taken as the limiting behavior of a blade coating in the stiff blade limit. The flow of greases is the most significant example of this type of fluid, which is easily found in nature and has many practical uses. To solve the non-linear expressions, LAT (Lubrication Approximation Theory) is applied, and a shooting technique is used for numerical solutions. The impacts of several parameters on flow characteristics, particularly the velocity ratio K, the Sisko fluid parameter b, the power-law index n, and the slip parameter α are investigated. The effects of both shear-thinning and shear-thickening behaviors are also investigated. The lubrication pressure and temperature increase with the Sisko fluid parameter b and decrease with the slip parameter α. As material parameter b increases from (0.001–1), 20.7% reduction in coating thickness and a 53.2% pressure reduction is noted as compared to the Newtonian case.

Mesoscopic CUDA 3D MRT-LBM Simulation of Natural Convection of Power-Law Fluids in a Differentially Heated Cubic Cavity with a Machine Learning Cross-Validation

Mesoscopic CUDA 3D MRT-LBM Simulation of Natural Convection of Power-Law Fluids in a Differentially Heated Cubic Cavity with a Machine Learning Cross-Validation

Free convection of thermodependent non-Newtonian fluids in a square enclosure partially heated at one side

This article exhibits a numerical analysis on free convection cooling of a heater located on the left side of a square enclosure using thermodependent power-law fluids. The temperature of the right sidewall is maintained relatively cold, while the unheated portions of the left wall and the horizontal ones are thermally insulated. The governing differential equations are numerically solved using a finite volume technique based on the iterative Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. The objective of this article is to analyze the impacts of the Rayleigh number, the Pearson number, the power-law index, and the location and length of the heat source on the fluid structure and temperature patterns, and to subtract the impact of these control parameters on the cooling efficiency of the cavity. The results reveal that rising the heater size and the Rayleigh number improves free convection inside the cavity. Moreover, using shear-thinning fluids (i.e. n < 1) with high value of the Pearson number enhances the thermal performance of the enclosure. The findings also point to the existence of a peak in the average Nusselt number variation, corresponding to an optimal heater location.

A Novel Prediction Model of the Drag Coefficient of Irregular Particles in Power-Law Fluids

The settlement drag coefficient of irregular particles in power-law fluids is a crucial parameter in the field of petroleum engineering. However, the irregular shape of the particle and the non-Newtonian rheological properties of the fluid make it challenging to predict the settlement drag coefficient. In this study, the spherical and irregular particle sedimentation processes in power-law fluids have been analyzed using a visual device and a high-speed camera system. A mechanical model dependent on the force balance of settlement particles was adopted to conduct a detailed statistical analysis of 114 spherical particle experimental results, and a prediction model of the drag coefficient of spherical particles in the power-law fluid was established with a mean relative error of 3.85%. On this basis, considering the influence of geometric shape on the law of particle sedimentation, a new irregular particle sedimentation resistance coefficient model in power-law fluid is established via the incorporation of the parameter circularity of 2D shape description c into the spherical particle sedimentation resistance coefficient predictive model. The parameters in the new irregular particle sedimentation resistance coefficient predictive model can be obtained via nonlinear data fitting of the 211 groups of irregular particles using experimental results in the power-law fluid. The model has high prediction accuracy for the drag coefficient of irregular particles in power-law fluid, with a mean relative error of 4.47, and expands the scope of engineering applications, which is of great significance for fracturing scheme design and wellbore cleaning.

Pore-scale hydrodynamics of non-Newtonian power-law fluids across a partially blocked porous medium in a confined channel

Transport of non-Newtonian fluids in porous media is pervasive in many natural and industrial applications. However, capturing the rheological behaviors of fluids by direct experimental techniques is challenging at the pore-scale. This paper outlines the pore-scale hydrodynamic interactions of non-Newtonian power-law fluids across a partially blocked porous medium in the laminar flow regime by computational fluid dynamics. The porous medium consists of an array of uniformly arranged square pillars. We explore the complex interplay of power-law rheology and Reynolds number on the microscopic flow field at the pore-scale. We capture the momentum transfer at the permeable interface between the porous and non-porous regions through stream-wise and span-wise velocity components and average volumetric flow rates at each pore-throat. Our results unveil a significant augmentation in stream-wise momentum by shear-thinning behavior and a diminution in momentum by shear-thickening behavior of the fluid through the porous medium. Further, the flow-leakage at the top interface purely depends on the combined effects of Reynolds number and power-law index. The channel pressure drop between the windward and leeward faces of the porous medium increases with the power-law index at low Reynolds number, while it decreases at high Reynolds number. Moreover, we provide a simple numerical framework to comprehend how the power-law behavior of the fluid dynamically regulates the flow field at the pore-scale.

Effect of aiding buoyancy on heat transfer from an isothermal square cylinder in power-law fluids

Effect of aiding buoyancy on heat transfer from an isothermal square cylinder in power-law fluids

A Review of the Settling Law of Drill Cuttings in Drilling Fluids

During the drilling process, cuttings settle under the action of gravity, which easily results in the formation of a cuttings bed, which then results in wellbore cleaning problems. The settling law of cuttings in drilling fluid is essentially a problem of solid–liquid two-phase settling. This study analyzes and summarizes the effects of the wall effect, the rheology of the fluid, particle shape irregularity, and particle concentration on the settling rate of particles and clarifies the problems faced by current research on the settling rate of particles and the development direction. Studies have shown that walls exert additional blocking effects on particles, thus reducing their settling velocity. The shear thinning effect of non-Newtonian fluids such as power-law fluids and Herschel–Bulkley fluids will reduce the viscosity of the liquid, thus increasing the settling velocity of the particles. Compared with spherical particles, irregular particles will obtain higher resistance in the fluid, leading to a decline in the particle settling velocity. The mutual interference between particles will result in an increase in the drag force on the particles and a decline in the settling velocity. However, when the particles are aggregated, the settling velocity will increase. This study can provide theoretical guidance for predicting the migration law of cuttings during the drilling of horizontal wells, and it has important significance for enriching the theory of solid–liquid two-phase flow.

A non-Newtonian thermal lattice Boltzmann method for simulation of Rayleigh–Bénard convection of power-law fluids

Despite the widespread popularity of the Bhatnagar–Gross–Krook lattice Boltzmann (BGK-LB) model due to its simplicity and efficiency, its application in heat transfer involving non-Newtonian fluids (NNFs) has been limited by inherent constraints. This paper proposes a numerically stable BGK-LB model for the thermal flow of NNFs. The modified model incorporates the local shear rate into the equilibrium distribution function of the velocity field and addresses the numerical instability problems encountered in the traditional BGK-LB model under low viscosity conditions by introducing an additional parameter. In addition, a temperature evolution equation that can accurately recover the convective diffusion equation is adopted. The accuracy of the current method is validated by performing simulations of Rayleigh–Bénard convection (RBC) in a square cavity filled with Newtonian fluids and NNFs. Subsequently, simulations are conducted to investigate the behavior of RBC in power-law fluids. The analysis focuses on examining the impact of the Rayleigh number (Ra = 5 × 103 − 105) and the power-law index (n = 0.8–1.3) on the convective structure and heat transfer characteristics while maintaining a fixed Prandtl number (Pr = 7) and aspect ratio (L/H = 2). It is discovered that, for a given n value, the convection intensity and heat transfer rate increase with increasing Ra, which is supported by the increasing trend of the mean Nusselt number (Nū) with Ra. Furthermore, compared to NFs, pseudo-plastic fluids display a higher Nū value due to an augmented heat transfer rate, while dilatant fluids exhibit a lower Nū value owing to a diminished heat transfer rate.

Vertical cementing displacement flows of shear-thinning fluids

We present a comprehensive study on the displacement flows of shear-thinning (power-law) fluids in a vertical eccentric annulus, employing both experimental and computational methods. This is a sequel to our previous studies [R. Zhang and I. Frigaard, J. Fluid Mech. 947, A32 (2022); R. Zhang and I. Frigaard, J. Fluid Mech. 972, A38 (2023)], which primarily discussed about the dispersive effects for the displacement flow of two Newtonian fluids. The same set of criteria has been applied to determine a steady/unsteady and dispersive/non-dispersive front. The overall classification map broadly aligns with findings from the Newtonian study, while also offering additional information due to the extreme viscosity ratio present. Our observations reveal that the flow behavior is significantly influenced by both the buoyancy force (b) and the viscosity ratio (M). Specifically, higher values of either b or M tend to induce a more steady and non-dispersive regime. Moreover, we have examined intriguing viscosity effects including viscosity dominant flows and viscous driven instabilities. Shear-thinning effects have also been observed and investigated in this study.

Retraction: Mixed convective heat transfer in a power-law fluid in a square enclosure: higher order finite element solutions

Retraction: Mixed convective heat transfer in a power-law fluid in a square enclosure: higher order finite element solutions

Numerical study of irreversibility analysis on pulsatile flow of blood through a ω-shaped stenotic artery

The mathematical modeling of blood flow in a stenotic blood vessel is very important for understanding the effects of various geometric and rheological parameters on the normal flow of blood. The present study is concerned with the heat and mass transfer in the blood flow of a non-Newtonian fluid through a ω-shaped stenotic arterial segment. The non-Newtonian behavior of blood is described mathematically by employing the constitutive equation of the Herschel-Bulkley fluid. The wall of the artery is considered to be rigid having ω-shaped constriction in its lumen. The mild stenosis assumption is used to simplify the fully coupled momentum, energy, and concentration equations as well as the constitutive equation of the Herschel-Bulkley fluid. Numerical solutions for fluid velocity, temperature, mass concentration, and entropy generation are evaluated by using the explicit finite difference scheme. The effects of various emerging parameters on the velocity, wall shear stress, flow rate, temperature, concentration, and entropy distributions have been analyzed in detail. A comparison between different fluid models has also been presented. It is found that the temperature in the Herschel-Bulkley fluid is marginally lower than that of the Newtonian, Power law, and Bingham fluids whereas an opposite trend is noticed in the case of mass concentration.

Knee synovial fluid flow and heat transfer, a power law model

For the purpose of understanding, the governing system of partial differential equations for synovial fluid flow velocity and temperature distribution in the knee joint has been successfully solved for the first time. Therefore, such an article is shedding light on the convective diffusion of the viscous flow along the articular surfaces of the joints through the introduction of power-law fluids with different features of permeability, and stagnation point flow along a magnetic field. Henceforth, the frictional energy causes the knee joint’s temperature to increase. By way of filtration, heated synovial fluid reaches the articular cartilage and provides heat to the bone and cartilage. The lubricant in the joint cavity is properly mixed with this cooled fluid. A rectangular region flow and diffusion model is used to define the issue, thermal diffusion and flow inside the intra-articular gap, as well as flow and thermal diffusion within the porous matrix covering the approaching bones at the joint. Using the similarity solution approach, the linked mixed boundary value problem is addressed. The fluid has been shown to resist moving into or out of the cartilage in certain sick and/or aging synovial joints, causing the temperature to increase. By changing the values of the parameters from their usual levels, it is observed that the temperature did increase in aged and sick joints which impact cartilage and/or synovial fluid degradation.

Effect Of Power-Law Fluids Flow Structures On Germicides Disinfection Through Taylor-Couette Configuration

Abstract Fluid disinfection involving ultraviolet rays (UV) is a promising method due to its easy implementation and low cost compared to other methods. In the present work, fluid disinfection in a Taylor-Couette configuration operating with power-law fluids with different absorbance coefficients,and fluence rates were simulated using the Lattice Boltzmann Method. The effects of operating parameters such as Taylor and axial Reynolds numbers, power-law index behavior, and fluence rate were analyzed. Results show that the required UV dose decreases for an increase in absorbance coefficient, while it grows for increasing power-law indexes. For T a = 120 and Re = 3, the disinfection reaches 82.3% for pseudo-plastic fluids and is complete for dilatant fluids. Considering different absorbance coefficients, it was observed that a = 0.4 leads to complete disinfection regardless of the fluid. For a = 0.5, fluid disinfection is complete for the dilatant fluid only. A value of 0.6 leads to partial disinfection (~90%) for all fluids.