Flow Of Shear-thinning Fluids Research Articles

Two dimensional unsteady flow past a square cylinder: Influence of proximal plane wall and power-law index

A numerical analysis using Ansys Fluent has been done to investigate the flow physics involved in both Newtonian and Power-law (shear-thinning) fluid flow over a square cylinder, placed near a wall with altered gap-to-side (G/a) ratios (where G represents the gap between the cylinder and the plane wall and a represents side of the square cylinder). At a constant Reynolds number, Re = 150, numerical calculations for unsteady, incompressible Navier-Stroke (N-S) equation with varying viscosity is carried out by using second-order upwind momentum and least square cell based pressure solver. It is found that for small G/a ratio shear-thinning fluid exhibits vortex shedding which was absent for Newtonian fluid. G/a ratio and power-law index have a strong influence on the coefficient of lift and coefficient of drag (CL and CD respectively). With the increase in gap-ratio, CD decreases and CL increases at a constant value of power-law (n) index. Also, CL increases and CD reduces with a decrease in n at a constant value of G/a. Detailed observation of instantaneous and mean vorticity and streamlines, coefficient of lift and drag, mean pressure distribution over the cylinder and the plane wall and recirculation length have been presented.

Predicting the co-extrusion flow of non-Newtonian fluids through rectangular ducts – A hybrid modeling approach

Co-extrusion has become the state-of-the-art process technology in nearly all application areas of polymer processing. By combining different types of polymeric materials within multilayer structures, products with a broad range of property profiles can be obtained for advanced applications. Design of co-extrusion dies and feedblock systems requires extensive knowledge of process and material behavior. To accurately describe the shear-thinning behavior of polymer melts in co-extrusion processes and to predict characteristic process quantities, numerical methods are essential. We present a hybrid approach to modeling stratified co-extrusion flows of two power-law fluids through rectangular ducts. By applying the theory of similarity and transforming the problem into dimensionless representation, we identified four independent influencing parameters that fully describe the flow situation: (i) the power-law index of the first fluid, (ii) the power-law index of the second fluid, (iii) the dimensionless position of the interface, and (iv) the ratio of dimensionless pressure gradients. We varied these input parameters within ranges that cover almost all combinations of industrial relevance, creating in the process a set of more than 44,000 design points. By means of the shooting method, numerical solutions were obtained for (i) pressure-throughput behavior, (ii) interfacial shear stress, (iii) interfacial velocity, and (iv) individual volume flow rates. Finally, we used symbolic regression based on genetic programming to model these target quantities as functions of their influencing parameters and obtain algebraic relationships between them. Our mathematical models thus enable accurate prediction of several characteristic process quantities in two-layer co-extrusion flows of shear-thinning fluids through rectangular ducts. The models are not restricted to the field of polymer processing, but can be used in all industrial applications that involve such co-extrusion flows.

A Rational Friction Factor Correlation for Laminar Fully Developed Pipe Flows of Shear-Thinning Non-Newtonian Fluids

Abstract A friction factor correlation for laminar, hydrodynamically fully developed pipe flows of shear-thinning non-Newtonian fluids is derived through analysis and asymptotic considerations. The specific non-Newtonian fluid model used is the extended modified power law model, which is functionally equivalent to the Cross model, and spans the entire shear rate range from the low to the high shear rate Newtonian regions, including the intermediate power law region. The friction factor correlation is a function of three dimensionless parameters and has an explicit form, making it well-suited to design calculations. The overall accuracy of the correlation is 6.6%, though it is much better than this in most cases. Graphical results for the correlation, and deviations with respect to high-accuracy numerical calculations are presented and discussed.

Numerical and experimental prediction of free surface flow of shear-thinning fluids

Within this study, a prediction of free surface flow during the gravity casting of shear-thinning fluids is of interest. An experimental test setup which enables analysis of the casting flow by means of optical measurements is designed and an in-house computational fluid dynamics solver based on the lattice Boltzmann method is implemented. The model of isothermal free surface flow of non-Newtonian incompressible fluid is considered. In particular, the study focuses on liquids which rheological properties can be idealised by the power-law model and its modifications. Parameters of the non-Newtonian models are identified based on the rheological measurements of the applied fluid samples. The gravity casting flow is examined both experimentally and numerically, while the experiments provide a reference set of data for validation of the implemented lattice Boltzmann algorithm. The computational results indicate that the algorithm is capable of resolving well the studied flow for computational grids with low spatial resolution.

Weak solutions to stationary motions of shear thinning fluids with nonhomogeneous Dirichlet boundary conditions

We consider steady flows of shear thinning fluids in bounded domains under the action of external forces and Dirichlet boundary conditions. For a power-law index q∈(2d∕(d+2),3d∕(d+2)], we construct weak solutions to the nonhomogeneous boundary value problem assuming that the boundary data is small enough. Moreover, under the restriction q∈((2d−1)∕d,2), d=2,3, and extra regularity for the boundary data, we construct weak solutions by extending the tangential part of the velocity at the boundary in such a way that it is possible to partially control the inertial term. This imposes restrictions only on the size of the normal component of the boundary data.

Generation and Dynamics of Janus Droplets in Shear-Thinning Fluid Flow in a Double Y-Type Microchannel.

Droplets composed of two different materials, or Janus droplets, have diverse applications, including microfluidic digital laboratory systems, DNA chips, and self-assembly systems. A three-dimensional computational study of Janus droplet formation in a double Y-type microfluidic device filled with a shear-thinning fluid is performed by using the multiphaseInterDyMFoam solver of the OpenFOAM, based on a finite-volume method. The bi-phase volume-of-fluid method is adopted to track the interface with an adaptive dynamic mesh refinement for moving interfaces. The formation of Janus droplets in the shear-thinning fluid is characterized in five different states of tubbing, jetting, intermediate, dripping and unstable dripping in a multiphase microsystem under various flow conditions. The formation mechanism of Janus droplets is understood by analyzing the influencing factors, including the flow rates of the continuous phase and of the dispersed phase, surface tension, and non-Newtonian rheological parameters. Studies have found that the formation of the Janus droplets and their sizes are related to the flow rate at the inlet under low capillary numbers. The rheological parameters of shear-thinning fluid have a significant impact on the size of Janus droplets and their formation mechanism. As the apparent viscosity increases, the frequency of Janus droplet formation increases, while the droplet volume decreases. Compared with Newtonian fluid, the Janus droplet is more readily generated in shear-thinning fluid due to the interlay of diminishing viscous force, surface tension, and pressure drop.

A pore network modelling approach to investigate the interplay between local and Darcy viscosities during the flow of shear-thinning fluids in porous media

During the flow of non-Newtonian fluids in porous media, the relationships between macroscopic quantities are governed by extremely complex microscopic fluid dynamics resulting from solid-fluid interactions. Consequently, the Darcy-scale viscosity exhibited by a shear-thinning fluid depends on the injection velocity, contrarily to the case of Newtonian fluids. In the present work, pore network modelling is used to investigate the relationships between local and macroscopic viscosities during the flow of shear-thinning fluids in 3D porous media. Special efforts are devoted to 1) identifying the influence of the viscosity exhibited by the fluid within the constrictions of the preferential flow paths on the value of Darcy-scale viscosity and 2) proposing an analytical expression to upscale viscosity from the local viscosity values. To go further, the reduction in average hydraulic tortuosity stemming from the directional nature of shear-thinning behavior in 3D porous media will also be quantified. The results of the present study show that Darcy-scale viscosity can be accurately calculated as the flow-rate weighted average of local viscosities in the investigated media. Moreover, the velocity maps provided by the proposed pore network flow simulations are suitable to assess hydraulic tortuosity reduction as compared to the flow of a Newtonian fluid.

A Graphics Process Unit-Based Multiple-Relaxation-Time Lattice Boltzmann Simulation of Non-Newtonian Fluid Flows in a Backward Facing Step

A modified power-law (MPL) viscosity model of non-Newtonian fluid flow has been used for the multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) and then validated with the benchmark problems using the graphics process unit (GPU) parallel computing via Compute Unified Device Architecture (CUDA) C platform. The MPL model for characterizing the non-Newtonian behavior is an empirical correlation that considers the Newtonian behavior of a non-Newtonian fluid at a very low and high shear rate. A new time unit parameter (λ) governing the flow has been identified, and this parameter is the consequence of the induced length scale introduced by the power law. The MPL model is free from any singularities due to the very low or even zero shear-rate. The proposed MPL model was first validated for the benchmark study of the lid-driven cavity and channel flows. The model was then applied for shear-thinning and shear-thickening fluid flows through a backward-facing step with relatively low Reynolds numbers, Re = 100–400. In the case of shear-thinning fluids (n=0.5), laminar to transitional flow arises while Re≥300, and the large vortex breaks into several small vortices. The numerical results are presented regarding the velocity distribution, streamlines, and the lengths of the reattachment points.

Flow and hydrodynamic shear stress inside a printing needle during biofabrication.

We present a simple but accurate algorithm to calculate the flow and shear rate profile of shear thinning fluids, as typically used in biofabrication applications, with an arbitrary viscosity-shear rate relationship in a cylindrical nozzle. By interpolating the viscosity with a set of power-law functions, we obtain a mathematically exact piecewise solution to the incompressible Navier-Stokes equation. The algorithm is validated with known solutions for a simplified Carreau-Yasuda fluid, full numerical simulations for a realistic chitosan hydrogel as well as experimental velocity profiles of alginate and chitosan solutions in a microfluidic channel. We implement the algorithm in an easy-to-use Python tool, included as Supplementary Material, to calculate the velocity and shear rate profile during the printing process, depending on the shear thinning behavior of the bioink and printing parameters such as pressure and nozzle size. We confirm that the shear stress varies in an exactly linear fashion, starting from zero at the nozzle center to the maximum shear stress at the wall, independent of the shear thinning properties of the bioink. Finally, we demonstrate how our method can be inverted to obtain rheological bioink parameters in-situ directly before or even during printing from experimentally measured flow rate versus pressure data.

Flow of shear-thinning fluids through porous media

Pseudo-plastic fluids exhibit a non-linear stress-strain relationship which can provoke large, localized viscosity gradients. For the flow of such fluids in porous media the consequence is a strong variability of the effective permeability with porosity, angle of the macroscopic pressure gradient, and rheological parameters of the fluid. Such a variability is investigated on the basis of adjoint homogenization theory for a Carreau fluid in an idealized porous medium geometry, highlighting differences with respect to the Newtonian case. It is shown in particular that the more we depart from Newtonian conditions, the more the (often used) hypothesis of an effective viscosity in Darcy’s law is a poor approximation, for the effective permeability tensor becomes strongly anisotropic.

Friction factor of shear thinning fluids in non-circular ducts—a simplified approach for rapid engineering calculation

This work reports on an investigation of the relationship between the Reynolds number and the friction factor of the fully developed laminar flow of power-law fluids through non-circular cross-sections (elliptical, concentric annuli, symmetrical L-shape, isosceles triangle, eccentric annuli, and square duct with a central cylindrical core), with the aim of providing a simple method for rapid and simplified engineering calculations. The friction factor—Reynolds number relation has been derived for non-circular ducts on the basis of the modified Reynolds number proposed by Metzner and Reed. It has been shown that the proposed correlation enables a prediction of the friction factor for the fully developed laminar flow of shear thinning fluids in non-circular cross-sections by using a calculation method similar to the method used for laminar flow of a Newtonian fluid. The correlation that is provided has been validated by analytical and numerical methods. It has been found that the proposed method can be used to determine the friction factor with high accuracy. This method yields a friction factor with a deviation of less than 5% in comparison with the conventional method.

Shear-Thinning Fluid Flow in Variable-Aperture Channels

Non-Newtonian fluid flow in a single fracture is a 3-D nonlinear phenomenon that is often averaged across the fracture aperture and described as 2-D. To capture the key interactions between fluid rheology and spatial heterogeneity, we adopt a simplified geometric model to describe the aperture variability, consisting of adjacent one-dimensional channels with constant aperture, each drawn from an assigned aperture distribution. The flow rate is then derived under the lubrication approximation for the two limiting cases of an external pressure gradient that is parallel/perpendicular to the channels; these two arrangements provide upper and lower bounds to the fracture conductance. The fluid rheology is described by the Prandtl–Eyring shear-thinning model. Novel closed-form results for the flow rate and hydraulic aperture are derived and discussed; different combinations of the parameters that describe the fluid rheology and the variability of the aperture field are considered. The flow rate values are very sensitive to the applied pressure gradient and to the shape of the distribution; in particular, more skewed distribution entails larger values of a dimensionless flow rate. Results for practical applications are compared with those valid for a power-law fluid and show the effects on the fracture flow rate of a shear stress plateau.

Numerical investigation of unsteady pulsatile Newtonian/non-Newtonian blood flow through curved stenosed arteries.

A numerical investigation of Newtonian/non-Newtonian unsteady pulsatile entry blood flow inside a 3D curved stenosed artery is presented. For considering the non-Newtonian effect (shear thinning or shear thickening behavior), the blood viscosity is characterized by the power-law model (Ostwald de Waele Equation). At the inlet of the artery, a realistic pulsatile waveform is utilized according to the experimental data reported by other researchers. This study belongs to the analysis of the curvature ratios, percentage and length ratio of stenosis, and blood thickening on hemodynamic characteristics of the flow. The results emphasize that the maximum wall shear stress happens near the stenosis neck and as expected, by decreasing the stenosis length, the maximum value of wall shear stress increases. In addition, the results indicate that the shear thickening fluid shows a more stable velocity profile rather than the shear thinning fluid flow.

CFD simulation of two-phase gas/non-Newtonian shear-thinning fluid flow in pipes

The multiphase flow has always been a major concern since it is encountered in many industrial processes that are crucial. Gas/non-Newtonian two-phase flow is found in the upstream of the petroleum industry, where slug flow is the most common flow pattern. This flow pattern has complex hydrodynamics which is crucial to study and evaluate. This study assessed the two-phase gas/non-Newtonian fluid flow in different configurations of pipes. The model was developed using computational fluid dynamics with an orthogonal mesh to evaluate the behavior of the slug dynamics in the different configurations. The model volume of fluid was used to estimate and predict the most important parameters: pressure drop, slug frequency, and length. First, the model was validated with experimental data found in literature in a horizontal 9-m long glass pipe, with an inner diameter of 22.8 mm. The validation was made with carboxymethyl cellulose CMC–water solutions as test fluids. Two concentrations (w/w) of CMC were used: 1% and 6%. The overall average relative error of the model, taking into account the three parameters, was 24.9%. With this result, it was proceeded to evaluate the model and the effect in the slug flow in three different pipe trajectories: toe-down well, one undulation with a hump well and one undulation with a sump well. The comparison was made between results of a gas/Newtonian fluid flow and the gas/non-Newtonian fluid flow. It was found that the slug frequency and length vary in great form. The slug frequency increased in almost all the cases, and the slug length decreased.

Influence of flowing fluid property through an elastic tube on various deformations along the tube length

The study of fluid flow characteristics in collapsible elastic tubes is useful to understand biofluid mechanics encountered in the human body. The research work presented here is aimed at thoroughly investigating the influence of both Newtonian and/or non-Newtonian fluids (low and high shear thinning) during steady flow through an elastic tube on various tube deformations, which enables understanding of the interaction between wall motion, fluid flow, and intestinal transmembrane mass transfer as a crucial contribution to a mechanistic understanding of bioaccessibility/bioavailability. It is observed that for a given steady volume flow rate, the tube is buckled from an elliptical shape to a line or area contacted two lobes as the critical external pressure is increased. The downstream transmural pressure is found to get more negative than that at the upstream as the outlet pressure decreased due to stronger tube collapse resulting in a reduced cross-sectional area. The experimental results depict that the tube cross-sectional area decreased by only about a factor of one for PEG (polyethylene glycol) and about a factor of six for both CMC (carboxymethyl cellulose) and PAA (polyacrylamide) from the undeformed one under an applied external pressure of 105 mbar. The corresponding maximum velocity increased by a factor of two during steady flow of shear-thinning fluids. The shear-thinning behavior of both CMC and PAA solutions is clearly observed at a constant flow rate of 17 ml/s as the tube cross-sectional area decreased due to an increase in compressive transmural pressure. In addition, the viscosity of PAA is drastically decreased due to its high shear-thinning behavior than that of the CMC under the same applied external pressure.

Taylor-vortex flow in shear-thinning fluids.

This paper deals with the Taylor-Couette flow of shear-thinning fluids. It focuses on the first principles understanding of the influence of the viscosity stratification and the nonlinear variation of the effective viscosity μ with the shear rate γ[over ̇] on the flow structure in the Taylor-vortex flow regime. A wide gap configuration (η=0.4) is mainly considered. A weakly nonlinear analysis, using the amplitude expansion method at high order, is adopted as a first approach to study nonlinear effects. For the numerical computation, the shear-thinning behavior is described by the Carreau model. The rheological parameters are varied in a wide range. The results indicate that the flow field undergoes a significant change as shear-thinning effects increase. First, vortices are squeezed against the inner wall and the center of the patterns is shifted axially toward the radial outflow boundaries (z=0,z/λ_{z}=1). This axial shift leads to increasing concentration of vorticity at these positions. The outflow becomes stronger than the inflow and the extent of the inflow zone where the vorticity is low increases acoordingly. Nevertheless, the strength of the vortices relative to the velocity of the inner cylinder is weaker. Second, the pseudo-Nusselt number, ratio of the torque to that obtained in the laminar flow, decreases. Third, higher harmonics become more relevant and grow faster with Reynolds number. Finally, the modification of the viscosity field is described.

Natural Convection Flow of Power-Law Fluids over a Heated Horizontal Plate Surface

Abstract The current work attempts to investigate the existence of similarity solution for the natural convection boundary layer flow of a power-law fluid over a heated horizontal semi-infinite plate surface. Three types of surface temperature variation are considered, namely (i) constant surface temperature (CST), (ii) power-law variation of surface temperature (PST) and (iii) power-law variation of surface heat flux (PHF). A reduction of the governing partial differential equations is achieved by using a suitable similarity transformation. But, a careful mathematical verification confirms that the similarity solution does not exist in the CST case and for the PST case it exists only under a particular value of the wall temperature parameter r = 1/3. It also ensured the existence of similarity solution for the PHF case and this will happen only when the plate surface is held at a constant heat flux situation. A new fundamental parameter S arises from the dimensionless analysis which is reduced to the reciprocal of the usual Prandtl number Pr for Newtonian fluids. A novel result of this analysis is that the salient features of the Grashof number Gr which differentiates the thermal responses of the shear-thinning fluid (0 < n < 1) flows from the shear-thickening fluid (n > 1) flows while the Newtonian fluid (n = 1) flows remain unaffected by this parameter no matter what be the value of S.

Accurate Approximate Methods for the Fully Developed Flow of Shear-Thinning Fluids in Ducts of Noncircular Cross Section

The fully developed laminar flow of Non-Newtonian fluids in ducts has broad application in engineering. The power-law viscosity model is utilized most often in the engineering literature, but it is deficient for many fluids as it does not admit limiting Newtonian viscosities at low and high shear rates. The goal of this work is to demonstrate two approximate but accurate and efficient methods for computing the pressure gradient in ducts of noncircular cross section for shear-thinning fluids following a general viscosity curve. Both methods predict the pressure gradient to better than 1% as established by full numerical solutions for ten cross-sectional shapes, a result representing an order-of-magnitude improvement over previous approximate methods. In the first method, an approach recently proposed and demonstrated to be accurate for a circular duct is shown to be equally applicable to noncircular ducts. In the second method, a widely used approach for noncircular ducts based on a generalization of the Rabinowitsch–Mooney equation is improved through an alternate evaluation of its parameters. Both methods require one-time numerical solutions of the power-law viscosity model for a duct shape of interest, and the necessary results are tabulated for the ten cross-sectional shapes analyzed. It is additionally demonstrated that the pressure-gradient error of the second method is approximately halved by simply replacing the hydraulic diameter with a viscous diameter obtained from the Hagen–Poiseuille equation.

Taylor-Couette flow of shear-thinning fluids

The flow between two concentric cylinders, one of which is rotating (Taylor-Couette flow), has been the focus of extensive research, due to the number of flow instabilities that may occur and its use in various industrial applications. We examine Taylor-Couette flow of Newtonian and shear-thinning fluids (solutions of xanthan gum in water/glycerol) using a combination of particle-image velocimetry and flow visualization for a wide range of Reynolds number, spanning the circular Couette flow, Taylor vortex flow, and wavy vortex flow regimes. Shear thinning is associated with an increase in the axial wavelength and has a nonmonotonic effect on the critical Reynolds number for transition to Taylor vortex flow and wavy vortex flow. The magnitude of vorticity and the strength of the radial jets transporting fluid away from the inner cylinder (“outward jets”) are both reduced in shear-thinning fluids relative to the Newtonian case; the vorticity in the shear-thinning fluids also tends to concentrate at the edges of vortices, rather than in the cores. In the wavy vortex flow regime for Newtonian fluids, the amplitudes of the waves at the “inward jets” (moving toward the inner cylinder) are low compared to those at the outward jets. However, for the shear-thinning fluids, the amplitudes of the waves at both the inward and outward jets tend to be significantly larger. Finally, shear thinning is associated with greater variations in time and space: we observe slow drifts in the axial positions of vortices and spatial variations in the amplitudes of the wavy instability, which are absent in Newtonian fluids.

Analysis of finishing forces and surface finish during magnetorheological abrasive flow finishing of asymmetric workpieces

Magnetorheological abrasive flow finishing (MRAFF) is an advanced hybrid process for producing ultrafine finished surfaces. Such surfaces reduce frictional forces and thereby minimize wear and tear to increase functional lifetime of the components. In the present research work, a model has been developed for simulating the results of MRAFF process. First, magnetic field is simulated and then a detailed study on the rheology of the magnetorheological polishing (MRP) fluid is conducted to develop a viscosity model for the flow of non-Newtonian shear thinning fluid. To calculate the forces acting in the process of material removal, the flow of MRP fluid around an asymmetric workpiece (knee joint) in a spatially varying magnetic field is simulated. Finishing forces exerted by the abrasive particles on the workpiece surface are analysed to develop a model for predicting surface roughness. A methodology has been proposed to evolve a variable correction factor to determine active abrasive particles at different locations on the workpiece surface for accurate simulation of surface finish operation. It is found that the magnetic field greatly influences the process performance by governing the viscosity of the MRP fluid and the distribution of the abrasive particles in the medium. During finishing of an asymmetric workpiece, the surface finish obtained at different locations on the workpiece surface is different. The developed model is capable to predict final surface finish within the acceptable accuracy when compared with the experimental results.