Flow Of Shear-thinning Fluids Research Articles

An Approximate Method for Predicting the Friction Factor of Viscoplastic Shear-Thinning Fluids in Non-Circular Channels of Regular Cross-Sections.

The objective of this study is to provide a straightforward generalized simple and quick method for the prediction of the friction factor for fully developed laminar flow of viscoplastic shear-thinning fluids in non-circular channels of regular cross-sections. The most frequently represented substances processed under these conditions are polymers in the processing and plastics industry. A generalized approximate method was proposed to express the relationship between the friction factor and the Reynolds number for the Herschel-Bulkley rheological model. This method uses the generalized Reynolds number for power-law fluids. Moreover, an additional simplified method for rapid engineering calculations was obtained as well. The suggested method was verified by comparing experimental data for concentric annulus found in the literature and results from simulations for concentric annulus, rectangular, square duct with a central cylindrical core and elliptical cross-sections. The results showed that the suggested methods enable us to estimate the friction factor with high accuracy for the investigated geometries.

Analysis of electroviscous effect and heat transfer for flow of non-Newtonian fluids in a microchannel with surface charge-dependent slip at high zeta potentials

In hydrophobic surfaces, pressure-driven flows induce electrokinetic flow retardation, where the slip length decreases due to the surface charge. In the current work, we investigate the thermal transport and fluid flow behavior of a pressure-driven flow of shear-thinning fluid with an electroviscous effect, accounting for the influence of surface charge on the slip. The electrical potential field induced in the electrical double layer (EDL), velocity, streaming potential, and temperature is obtained after solving the Poisson–Boltzmann equation, mass, momentum, and energy conservation equations without invoking the Debye–Hückel linearization. Results are presented for a broad range of dimensionless parameters, such as surface charge-independent slip length, Debye–Hückel parameter, zeta potential, heat flux, and flow consistency index (n). The flow velocity decreases after considering the effect of surface charge on slip, and such decrement is more for lower value of n, higher magnitude of zeta potential, and thicker EDL. Moreover, for lower value of n (1/3), the alteration of the Nusselt number with the surface charge is non-monotonic, whereas it increases with the surface charge magnitude for higher value of n (1/2). Further, for lower value of n, the Nusselt number enhances by the surface charge effect on the slip, whereas, for higher value of n, the trend is the opposite. Also, there is a strong interplay of the rheology of the fluid and EDL thickness in dictating the variation of the Nusselt number.

Numerical Investigations on Shear Thinning Fluid Flow Overhorizontal Stretching Sheet with Dissipation of Energy

Numerical Investigations on Shear Thinning Fluid Flow Overhorizontal Stretching Sheet with Dissipation of Energy

The Impact of Different Arrangements of Molecular Chains in Terms of Low and High Shear Rate's Viscosities on Heat and Mass Flow of Nonnewtonian Shear thinning Fluids.

Non-newtonian fluids, especially shear thinning fluids, have several applications in the polymer industry, food industry, and even everyday life. The viscosity of shear thinning fluids is decreased by two or three orders of magnitude due to the alignment of the molecules in order when the shear rate is increased, and it cannot be ignored in the case of polymer processing and lubrication problems. So, the effects of viscosities at the low and high shear rates on the heat and mass boundary layer flow of shear thinning fluid over moving belts are investigated in this study. For this purpose the generalized Carreau model of viscosity relate to shear rate is used in the momentum equation. The Carreau model contains the five parameters: low shear rate viscosity, high shear rate viscosity, viscosity curvature, consistency index, and flow behavior index. For the heat flow, the expression of the thermal conductivity model similar to the viscosity equation due to the non-Newtonian nature of the fluid is used in the energy equation. On the mathematical model of the problem, boundary layer approximations are applied and then simplified by applying the similarity transformations to get the solution. The solution of the simplified equations is obtained by numerical technique RK-shooting method. The results are compared with existing results for limited cases and found good agreement. The results in the form of velocity and temperature profiles under the impact of all the viscosity's parameters are obtained and displayed in graphical form. Moreover, the boundary layer parameters such as the thickness of the regions, momentum thickness, and displacement thickness are calculated to understand the structure of the boundary layer flow of fluid. The velocity and temperature of the fluid are decreased and increased respectively by all viscosity's parameters of the model. So, the results of the boundary layer fluid flow under rheological parameters will not only help engineers to design superior chemical equipment but also help improve the economy and efficiency of the overall process.

The combined effect of fluid rheology, inner pipe rotation and eccentricity on the flow of Newtonian and non-Newtonian fluid through the annuli

The accurate prediction of the fluid dynamics and hydraulics of the axial or helical flow of non-Newtonian drilling fluids in the annuli is essential for the determination and effective management of wellbore pressure during drilling operations. Previous studies have shown that the pressure losses and fluid velocity distributions in the annuli are highly influenced by the rheological properties of the fluid, inner pipe rotary speed and eccentricity. However, many studies in literature have developed or applied theoretical models that were either only valid for Newtonian annuli flows or have not considered the combined effect of the fluid rheological parameters with the inner pipe rotary speed and eccentricity when calculating the frictional annuli pressure losses for non-Newtonian shear thinning fluids. Furthermore, there have been inconsistencies in the description of the effect of inner pipe rotation on the pressure losses experienced for both Newtonian and non-Newtonian flows in concentric and eccentric annuli. In this study, an analytical and numerical approach were carried out to investigate and evaluate the hydrodynamic behaviour of the axial and helical isothermal flow of Newtonian and non-Newtonian fluids through the annuli. Techniques of computational fluid dynamics for fully developed steady-state fluid flow were applied to obtain detailed information of the flow field in the annuli. New analytical and numerical models were developed to obtain the fluid velocity and viscosity field distribution and determine the frictional pressure gradient for laminar and turbulent flows in the concentric and eccentric annuli with and without inner pipe rotation and were compared and validated favourably with models previously presented in literature. Results showed that for a fully developed flow of non-Newtonian shear thinning fluids, if the fluid flowrate is kept constant, an increase in inner pipe rotation leads to a decrease in the axial frictional pressure gradient when the pipe is rotating on its axis. For annuli flows of non-Newtonian fluids, the effect of inner pipe rotation on the axial pressure gradient is dependent on the fluid flowrate and at high fluid flowrates, the influence of the inner pipe rotation on the fluid hydraulics decreases. In general, for shear thinning non-Newtonian fluids, pipe rotation can improve the fluid flow in the region of lower flow in the eccentric annuli. Unlike the flow of Newtonian fluids through the annuli, the friction geometry parameter and thus the friction factor is highly influenced by the rheological parameters of the fluid, the fluid flowrate, inner pipe rotary speed and eccentricity.

An eddy-viscosity model for turbulent flows of Herschel–Bulkley fluids

This article presents a new turbulence closure based on the k-ω SST model for predicting turbulent flows of Herschel–Bulkley fluids, including Bingham and power-law fluids. The model has been calibrated with direct numerical simulations (DNS) data for fully-developed pipe flow of shear-thinning and viscoplastic fluids. The new model shows good agreement in the mean velocity, average viscosity, mean shear stress budget and friction factor. The latter compares well also against correlations from the literature for a wide range of Reynolds numbers. With the new model, improvements are also observed in the iterative convergence, which is often difficult for calculations with yield-stress fluids. Additionally, three eddy-viscosity models for Newtonian fluids, namely the k-ω SST, k-kL and Spalart–Allmaras model, have been tested on turbulent Herschel–Bulkley flows. Results show that (i) the new model produces the best prediction; (ii) the standard SST model may be considered for simulations of weakly shear-thinning/viscoplastic fluids at high Reynolds numbers; (iii) the k-kL and the Spalart–Allmaras models appear to be unsuitable for turbulent Herschel–Bulkley flows. The new model is simple and appealing for engineering applications concerned with turbulent wall-bounded flows and is presented in a formulation that can be easily adapted to other generalised Newtonian fluids.

The homotopy simulation of MHD time dependent three dimensional shear thinning fluid flow over a stretching plate

This article is devoted to investigate the analytic-numeric solutions of an unsteady 3-D MHD shear thinning fluid flow which is embedded in a permeable medium through a stretching sheet along with the attributes of heat transfer. The similarity transformation is adopted to convert the PDEs of current model into its dimensionless form. Then the model is solved by using an algorithm of a robusting technique named as method of Homotopy analysis (HAM). After that, solutions are compared by invoking Runge-Kutta based shooting method. All the symbolic calculations and vived construction of profiles are done by MATHEMATICA and MATLAB. To further discuss the HAM’s convergence and the results homology of the flow model; tabularization is used against multitudinous parameters.

Enhanced thermal fingering in a shear-thinning fluid flow through porous media: Dynamic pore network modeling

Thermal-viscous fingering instability in porous media is a common phenomenon in nature as well as in many scientific problems and industrial applications. Despite the importance, however, thermal transport in flow of a non-Newtonian fluid in porous media and the resulting fingering has not been studied extensively, especially if the pore space is heterogeneous. In this paper, we propose a pore network model with full graphics processing unit-parallelized acceleration to simulate thermal transport in flow through three-dimensional unstructured pore networks at centimeter scale, containing millions of pores. A thermal Meter equation is proposed to model temperature- and shear stress-dependent rheology of the non-Newtonian fluids. After comparing the simulation results with an analytical solution for the location of the thermal front in a spatially uncorrelated pore network, thermal transport in flow of both Newtonian and non-Newtonian fluids is studied in the spatially uncorrelated and correlated pore networks over a range of injection flow rates. The simulations indicate that the injection flow rate, the shear-thinning rheology, and the morphological heterogeneity of the pore space all enhance thermal-viscous fingering instability in porous media, but with distinct patterns. In spatially correlated networks, the average temperature and apparent viscosity at the breakthrough point in flow of a shear-thinning fluid exhibit non-monotonic dependence on the injection flow rate. An analysis of the fractal dimension of thermal patterns at the breakthrough point supports the conclusion. The results highlight the importance of designing optimal flow conditions for application purposes.

Characterization of vortical structures in a stirred tank

Data obtained from large eddy simulations of single-phase, turbulent flow of Newtonian and shear-thinning fluids in a baffled stirred tank reactor are considered to identify and characterize vortical structures. The identification proceeds through an objectivized Eulerian method, accounting for the inhomogeneities in the flow, which palliates some shortcomings of previous implementations. The characterization focuses on turbulent vortices larger than the dissipative scales and, to a lesser extent, on trailing and macro-instability vortices. The characterization performed through different statistical analyses includes aspects such as size, number density, shape, distribution and organization in space, and correlation with the kinetic energy due to turbulence and the periodic passage of the blades. To the authors' knowledge, some of these representative aspects have been rarely investigated or have not been addressed at all for the turbulent flow in a stirred vessel. The influence of changing the rotational speed of the tank and the rheology of the working fluid are explored as well. Finally, considering one-way coupling, some potential and practical implications for liquid–liquid and gas–liquid dispersed systems are briefly discussed.

Analysis of the Shear-Thinning Viscosity Behavior of the Johnson–Segalman Viscoelastic Fluids

This paper presents a numerical comparison of viscoelastic shear-thinning fluid flow using a generalized Oldroyd-B model and Johnson–Segalman model under various settings. Results for the standard shear-thinning generalization of Oldroyd-B model are used as a reference for comparison with those obtained for the same flow cases using Johnson–Segalman model that has specific adjustment of convected derivative to assure shear-thinning behavior. The modeling strategy is first briefly described, pointing out the main differences between the generalized Oldroyd-B model (using the Cross model for shear-thinning viscosity) and the Johnson–Segalman model operating in shear-thinning regime. Then, both models are used for blood flow simulation in an idealized stenosed axisymmetric vessel under different flow rates for various model parameters. The simulations are performed using an in-house numerical code based on finite-volume discretization. The obtained results are mutually compared and discussed in detail, focusing on the qualitative assessment of the most distinct flow field differences. It is shown that despite all models sharing the same asymptotic viscosities, the behavior of the Johnson–Segalman model can be (depending on flow regime) quite different from the predictions of the generalized Oldroyd-B model.

Stratified Shear-Thinning Fluid Flow Past Tandem Cylinders in the Presence of Mixed Convection Heat Transfer With a Channel-Confined Configuration

Abstract The article examines the consequence of thermal buoyancy-driven cross-flow and heat transfer for shear-thinning power-law fluids on the tandem orientation of two cylinders. Finite volume methodology is used to investigate the effect of the gap ratio (2.5 ≤ S/D ≤ 5.5), power-law index (0.2 ≤ n ≤ 1), and Richardson number (0 ≤ Ri ≤ 1) on flow and thermal output parameters at Reynolds number Re = 100 and Prandtl number Pr = 50 in a confined channel. An unprecedented jump has been witnessed in the flow/thermal parameters at the critical gap ratio (critical spacing). At forced convection (Ri = 0), this critical spacing keeps on increasing with shear-thinning character, from S/D = 3.9 (at n = 1) to 4.9 (at n = 0.2). On the contrary, an increase in shear-thinning characteristic leads to a decrease in critical spacing from S/D = 3.9 (at n = 1) to 2.8 (at n = 0.4) for Ri = 1 (mixed convection). The heat transfer rate increases with shear-thinning behavior, with a maximum heat transfer, noted at n = 0.2. A higher unprecedented increment for flow/thermal parameters is seen at critical spacing for the downstream cylinder than the upstream cylinder. At the highest gap ratio, the output parameters for the upstream cylinder approximate that of an isolated cylinder. The time-variant fluctuations in lift coefficients for a shear-thinning flow in a tandem arrangement provide a new understanding of coshedding and extended body flow regimes.

Secondary instabilities in Taylor–Couette flow of shear-thinning fluids

The stability of the Taylor vortex flow in Newtonian and shear-thinning fluids is investigated in the case of a wide gap Taylor–Couette system. The considered radius ratio is$\eta = R_1/R_2=0.4$. The aspect ratio (length over the gap width) of experimental configuration is 32. Flow visualization and measurements of two-dimensional flow fields with particle image velocimetry are performed in a glycerol aqueous solution (Newtonian fluid) and in xanthan gum aqueous solutions (shear-thinning fluids). The experiments are accompanied by axisymmetric numerical simulations of Taylor–Couette flow in the same gap of a Newtonian and a purely viscous shear-thinning fluid described by the Carreau model. The experimentally observed critical Reynolds and wavenumbers at the onset of Taylor vortices are in very good agreement with that obtained from a linear theory assuming a purely viscous shear-thinning fluid and infinitely long cylinders. They are not affected by the viscoelasticity of the used fluids. For the Newtonian fluid, the Taylor vortex flow (TVF) regime is found to bifurcate into a wavy vortex flow with a high frequency and low amplitude of axial oscillations of the vortices at${Re} = 5.28 \, {Re}_c$. At${Re} = 6.9 \, {Re}_c$, the frequency of oscillations decreases and the amplitude increases abruptly. For the shear-thinning fluids the secondary instability conserves axisymmetry. The latter is characterized by an instability of the array of vortices leading to a continuous sequence of creation and merging of vortex pairs. Axisymmetric numerical simulations reproduce qualitatively very well the experimentally observed flow behaviour.

Channel flows of shear-thinning fluids that mimic the mechanical response of a Bingham fluid

The linear stability of channel flows driven by pressure drops is carried out for fluids that exhibit a yield stress, the mechanical response of which is prescribed by the Bingham constitutive relation or two of its regularizations: the model due to Allouche and co-workers that is usually referred to as the “simple model”, and Papanastasiou model. Despite the fact that these two regularized models provide a good approximation of the steady Poiseuille flow of a Bingham fluid, they fail to predict the stability characteristics of the exact Bingham model. The critical thresholds for the onset of turbulence predicted by using the simple and Papanastasiou models are essentially the same, but they differ significantly from that of the exact Bingham model. This discrepancy is shown to be due to the absence of energy dissipation in the rigid core of a Bingham fluid.

Numerical study of the effect of blockage ratio in forced convection confined flows of shear-thinning fluids

In this work, the fluid dynamics and heat transfer of time-dependent flows with shear-thinning behaviour over two confined square cylinders in tandem arrangement are studied numerically. The case studies include two- and three-dimensional flows under a wide range of power-law indices, $0.25\leq n \leq 1.0$ , and blockage ratios, $\beta =0.50$ , 0.66 and 0.80, for a fixed Reynolds number of $Re=100$ and Prandtl number of $Pr=10$ . The fluid dynamic analysis includes detailed qualitative and quantitative comparisons between the different fluids and blockage ratios, where streamlines, viscosity fields, and lift and drag coefficients are presented. Moreover, a detailed study of the route from laminar time-dependent to chaotic flows is included. It was determined that the flow exhibits a transition from laminar to chaotic by decreasing the power-law index ( $n$ ) and increasing the blockage ratio ( $\beta$ ). With respect to the thermal analysis, isotherms and Nusselt numbers are compared between the different case studies. This analysis demonstrates that the average Nusselt numbers increased in chaotic flows. The three-dimensional cases confirmed the results proposed for the two-dimensional case.

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.