Flow Of Shear-thinning Fluids Research Articles

Numerical Investigation of the Apparent Viscosity Dependence on Darcy Velocity During the Flow of Shear-Thinning Fluids in Porous Media

The viscosity exhibited by shear-thinning fluids within the interstices of a porous medium differs depending on pore dimensions and injection velocity. Therefore, predicting the macroscopic value of viscosity required as input to Darcy’s law is challenging and needs accurate identification of the characteristic microscopic dimensions dominating global pressure losses. The most common approach consists of defining an apparent “in situ” shear rate which can be used in the bulk constitutive equation of the fluid to predict viscosity during flow through the porous medium. The dependence of this apparent shear rate on Darcy velocity has traditionally been assumed to be linear, which is appropriate in the case of Newtonian fluids and power-law fluids. However, yield stress and plateau viscosities that can potentially affect such dependence are not captured by power-law model, so the linear assumption may lead to inaccurate viscosity predictions. For this reason, a set of two-dimensional (2D) flow problems were considered and solved numerically to assess the effects of the shear rheology model, the pore size distribution and the microstructural complexity on the value of the apparent shear rate. In order to facilitate the analysis, the microscopic features of all the investigated porous media were well characterized through pore network modelling. The present results prove the inability of traditional approaches to predict the macroscopic viscous pressure losses generated during the creeping flow of widely used Herschel–Bulkley and Carreau fluids. In particular, the existence of a yield stress or a plateau viscosity induces significant deviations from linearity in the relationship between apparent shear rate and Darcy velocity. The importance of these deviations is, in turn, shown to be highly affected by the dispersion of the pore size distribution and the degree of shear thinning. Moreover, the reasons for such observations are discussed using an analytical approach.

Pulsatile flow and heat transfer of shear-thinning power-law fluids over a confined semi-circular cylinder

This work is an attempt to simulate the effects of pulsating flow upon the thermal and hydrodynamic behavior of shear-thinning non-Newtonian fluid (approximated as power-law fluid) while it flows past a semi-circular cylinder fixed in a symmetrically confining channel and deduces the optimum oscillating frequencies and amplitude for a particular power-law index (n) and Reynolds number (Re). The semi-circular cylinder studied has a fixed temperature while the wall confinement is insulating. The ranges of control parameters varied are ${\rm Re}=10$ -100 (based on object's diameter), the amplitude of oscillation (A) = 0-0.6, the Strouhal number (St) = 0-2 and the n ranging from 0.2 to 1. The Prandtl number has been kept fixed at $({\rm Pr})=50$ (which corresponds to several fluids of industrial importance like n-butanol, etc.). The isotherms and streamlines give a qualitative insight into the heat and flow transfer behavior as various parameters are varied, while the Nusselt number, overall drag and lift coefficients have been calculated to get a quantitative insight. Further, the augmentation in heat transfer and the decline in drag upon using a pulsating non-Newtonian fluid inlet as opposed to using a steady Newtonian flow have been established. Lastly, the temporal variations and the frequency of vortex shedding have been studied using a fast Fourier transform.

Direct numerical simulation of turbulent non-Newtonian flow using OpenFOAM

• OpenFOAM predictions for turbulent Newtonian fluids match very well with DNS references for mean turbulence statistics. • OpenFOAM predicts turbulent shear-thinning flow to be more transitional compared to a high-order spectral element DNS code. • Turbulence statistics predicted by OpenFOAM differ by at most 16% for shear-thinning fluids, and usually be less than 10%. • OpenFOAM scales well from 8 to 512 CPUs but has poor intranode scalability for less than 8CPUs. Understanding transition and turbulence in the flow of shear-thinning non-Newtonian fluids remains substantially unresolved and additional research is required to develop better computational methods for wall-bounded turbulent flows of these fluids. Previous DNS studies of shear-thinning fluids mainly use purpose-built codes and simple geometries such as pipes and channels. However in practical application, the geometry of mixing vessels, pumps and other process equipment is far more complex, and more flexible computational methods are required. In this paper a general-purpose DNS approach for shear-thinning fluids is undertaken using the OpenFOAM CFD library. DNS of turbulent Newtonian and non-Newtonian flow in a pipe flow are conducted and the accuracy and efficiency of OpenFOAM are assessed against a validated high-order spectral element-Fourier DNS code – Semtex . The results show that OpenFOAM predicts the flow of shear-thinning fluids to be a little more transitional than the predictions from Semtex , with lower radial and azimuthal turbulence intensities and higher axial intensity. Despite this, the first and second order turbulence statistics differ by at most 16%, and usually much less. An assessment of the parallel scaling of OpenFOAM indicates that OpenFOAM scales very well for the CPUs from 8 to 512, but the intranode scalability is poor for less than 8CPUs. The present work shows that OpenFOAM can be used for DNS of shear-thinning fluids in the simple case of pipe flow, and suggests that more complex flows, where flow separation is often important, are likely to be simulated with accuracies that are acceptably good for engineering application.

3D Microscale Flow Simulation of Shear-Thinning Fluids in a Rough Fracture

The shear-thinning fluid flow in rough fractures is of wide interest in subsurface engineering. Inertial effects due to flow regime, fracture aperture variations as well as fluid rheology affect the macroscopic flow parameters in an interrelated way. We present a 3D microscale flow simulation for both Newtonian and Cross power-law shear-thinning fluids through a rough fracture over a range of flow regimes, thus evaluating the critical Reynolds number above which the linear Darcy’s law is no longer applicable. The flow domain is extracted from a computed microtomography image of a fractured Berea sandstone. The fracture aperture is much more variable than any of the previous numerical or experimental work involving shear-thinning fluids, and simulations are 3D for the first time. We quantify the simulated velocity fields and propose a new correlation for shift factor (parameter relating in situ porous medium viscosity with bulk viscosity). The correlation incorporates tortuosity (parameter calculated either based only on fracture image or on detailed velocity field, if available) as well as a fluid-dependent parameter obtained from the analytical/semi-analytical solutions of the same shear-thinning fluids flow in a smooth slit. Our results show that the shift factor is dependent on both the fracture aperture distribution (not only the hydraulic/equivalent aperture) and fluid rheology properties. However, both the inertial coefficient and critical Reynolds number are functions of the fracture geometry only, which is consistent with a recent experimental study.

Concentric cylinder viscometer flows of Herschel-Bulkley fluids

AbstractDrilling fluids and well cements are example non-Newtonian fluids that are used for geothermal and petroleum well construction. Measurement of the non-Newtonian fluid viscosities are normally performed using a concentric cylinder Couette geometry, where one of the cylinders rotates at a controlled speed or under a controlled torque.In this paper we address Couette flow of yield stress shear thinning fluids in concentric cylinder geometries.We focus on typical oilfield viscometers and discuss effects of yield stress and shear thinning on fluid yielding at low viscometer rotational speeds and errors caused by the Newtonian shear rate assumption. We relate these errors to possible implications for typical wellbore flows.

Vortex shedding from a circular cylinder in shear-thinning Carreau fluids

Results from numerical simulations of two-dimensional, shear-thinning Carreau fluid flow over an unconfined circular cylinder are presented in this paper. Parametric sweeps are performed over the various Carreau model parameters, and trends of the time-averaged force coefficients and vortex characteristics are reported. In general, increased shear-thinning results in lower viscous forces on the body but greater pressure forces, resulting in a complex non-monotonic drag response. Lift forces generally increased with shear-thinning due to the dominant pressure contribution. The decrease in fluid viscosity also led to shorter vortex formation lengths and the consequent rise in the Strouhal frequency of vortex shedding. It is expected that these results will be useful for verification of computational models of unsteady non-Newtonian flows.

Power-law fluid flow in a T-shaped channel with slip boundary conditions on the solid walls

Planar flow of shear-thinning fluid in a T-shaped channel is investigated assuming slip occurs along the wall. Motion of the fluid is caused by pressure difference between inlet/outlet boundaries. On the solid walls, two models of fluid interaction with solid walls are employed: no slip boundary condition and Navier slip boundary condition relating the wall shear stress to the slip velocity. The problem is solved numerically using a finite difference method based on the SIMPLE procedure. The parametric studies of the flow pattern depending on the main parameters of the problem have been performed. Dependences describing kinematic and dynamic characteristics of the flow have been shown.

Effect of disorder in the pore-scale structure on the flow of shear-thinning fluids through porous media

Modeling the flow of fluids with shear-dependent viscosity through porous media is a challenging fundamental and engineering problem. At continuum-scale, such flows are usually described using modified versions of Darcy’s law, which are obtained by considering either an apparent viscosity or an apparent permeability. In the two cases, Darcy’s law becomes nonlinear as the apparent viscosity or permeability both depend on the velocity or pressure gradient. The main difference between these two approaches is the impact of non-Newtonian effects on the flow direction. With the apparent viscosity, the flow direction is determined by the standard permeability tensor and unaltered by non-Newtonian effects. On the other hand, with the apparent permeability, the flow direction may be modified by non-Newtonian effects contained in the second-order tensor. Here, we ask the question of whether it is necessary to use a general tensorial correction including changes of flow direction or if the (scalar) apparent viscosity approach is sufficient. To study this, we solve numerically the non-Newtonian flow problem in a variety of isotropic porous structures for a model fluid where the viscosity depends on the shear rate following a power law with a Newtonian cut-off in the limit of low shear rates. We find that the structure of the porous medium plays a fundamental role and that there is a competition between the nonlinearity of the flow, induced by the non-Newtonian rheology, and the disorder of the porous structure. Our main result is that an apparent viscosity is sufficient in cases of sufficiently disordered porous media, as is the case of some sandstones found in petroleum engineering. Fundamentally, this suggests that the disorder in the geometry of the porous structure is mitigating part of the nonlinear effects due to the rheology.

Electroosmotic flow of power-law fluids in curved rectangular microchannel with high zeta potentials

In this article, electroosmotic flow of non-Newtonian fluids through a curved rectangular microchannel is studied numerically. The power-law model is used to simulate the rheological behavior of fluid. Moreover, the flow is assumed to be hydrodynamically fully developed and the walls carry high zeta potentials. To do so, the Poisson–Boltzmann equation without imposing the Debye–Hückel linear approximation is solved by applying the central difference scheme. Furthermore, the continuity and Cauchy momentum equations in the cylindrical coordinate system are solved using SIMPLE finite-volume method. Consequently, the effects of governing parameters such as flow behavior index, electrokinetic separation distance, curvature, zeta potential, and channel aspect ratio on the flow field and hydrodynamic characteristics are studied in details. The results show that the secondary flows which are created in shear-thinning fluid flows are stronger in comparison to that of shear-thickening and Newtonian fluid flows. Also, the variation of electrokinetic separation distance changes the secondary flow patterns in shear-thinning fluid flows, and it does not have a monotonic effect on the strength of secondary flows. Moreover, the obtained results for shear-thinning and Newtonian fluid flows indicate that the increasing of curvature, in addition to increasing the circulation strength considerably, also causes the volumetric flow rate to slightly increase. Furthermore, it is found that the increasing of zeta potential can be employed in shear-thinning fluid flows in order to significantly increase the volumetric flow rate and the performance of mixing. Additionally, it is observed that the increasing of channel aspect ratio leads to an increase in the circulation strength of shear-thinning fluid flow.

Heat transfer enhancement in suddenly expanding annular shear-thinning flows

Heat transfer enhancement in suddenly expanding annular pipe flows of Newtonian and shear-thinning non-Newtonian fluids is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported over the following range of parameters: Re = {50, 100, 150}, k = {0, 0.5, 0.7}; n = {1, 0.8, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers greater than the downstream fully developed value, Nu/Nufd > 1, is only observed for Pr = 10 and 100. In general, higher Prandtl numbers, power-law index values, and annular-diameter-ratios, result in more significant heat transfer enhancement downstream of the expansion plane. Heat transfer augmentation, for Pr = 10 and 100, increases with the annular-diameter-ratio. For a given annular-diameter-ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr = 100, always results in higher peak Nu values, Numax, for both Newtonian and shear-thinning flows. All Numax values are located downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e., κ = 0. However, for suddenly expanding annular pipe flows, i.e., κ = 0.5 and 0.7, Numax values appear upstream the flow reattachment point. For Pr = 10 and 100, shear-thinning flows display two local peak Nu/Nufd values, in comparison with one peak value in the case of Newtonian flows. The highest heat transfer enhancement, Numax/Nufd ≈ 5, is observed at κ = 0.7, n = 0.6, and Pr = 100.

Effect of shear thinning on superhydrophobic slip: Perturbative corrections to the effective slip length

We find expressions for the change in hydrodynamic slip length when a weakly shear-thinning fluid flows longitudinally, or transversely, over a periodic array of flat, unidirectional no-shear slots from a modified reciprocal theorem of Stokes flow and exact solutions for a Newtonian fluid.

Effects of shear-thinning nature and opposing buoyancy from a square geometry in a confined framework

ABSTRACTNumerical computations were brought up to study the effect of opposing buoyancy mixed convection (Ri = 0 to − 1) flow of power law shear-thinning fluids past a confined cooled square bluff body at Prandtl numbers (Pr) = 1, 50 and Reynolds numbers (Re) = 1–40. Irrespective of the n, Ri, Pr, and Re, the flow separation is delayed with increasing confinement (β). The vortex shedding and flow separation start earlier for shear-thinning fluids than Newtonian fluid. For opposing buoyancy (Ri < 0), the vortex shedding starts earlier on increasing Pr (except for n = 0.2, Ri = −1). Also, the periodic unsteady transition appears at some higher value of Re on increasing Ri for fixed Pr. The drag coefficient (CD) value reduces with the decrease in n, whereas the maximum CD is noted for Newtonian fluids. The maximum augmentation in the heat transfer was reached about 9 and 36% on comparing with Newtonian fluids and forced convection case, respectively, and also the corresponding maximum compression in heat transfer was found about 15 and 5%, respectively. The numerical results have also been correlated for CD and the Colburn jh factor values for various Re, Pr, Ri, and n. In surplus, the effects of wall confinement ranging from β = 25 to 50% on flow separation and engineering output parameters were studied in a steady regime.

Effects of Pore and Grain Size on Water and Polymer Flooding in Micromodels

We have conducted a comprehensive series of experiments to evaluate the effects of pore size distribution of porous media on the dynamics of shear-thinning fluid flow and oil displacement efficiency. To do so, we have conducted microfluidic experiments, using micromodels fabricated from X-ray computed tomography images of sand-packs with varying grain sizes to create a realistic pore network. Three micromodels with well-defined particle size distribution were fabricated and used in our experiments. The use of micromodels to assess the effectiveness of polymer flooding is often superior to methods such as core flooding because of the detailed pore-scale information obtained during the experiments. The micromodels were initially saturated by oil, and the displacing fluids were prepared as aqueous solutions with dissolved xanthan gum. The dynamics and patterns of the interface displacement as well as the size distribution of the trapped oil ganglia were visualized using an optical microscope. The main findin...

Experimental evidence of a helical, supercritical instability in pipe flow of shear thinning fluids

When a viscoelastic, shear-thinning fluid is extruded through a large aspect ratio capillary, it exhibits an inertia free, bulk flow instability resulting in helical undulations of the extrudate. This instability is shown to be supercritical, at odds with that occurring in non-shear-thinning fluids.

Apparent slip of shear thinning fluid in a microchannel with a superhydrophobic wall.

The peculiarities of simple shear flow of shear thinning fluids over a superhydrophobic wall consisting of a set of parallel gas-filled grooves and solid stripes (domains with slip and stick boundary conditions) are studied numerically. The Carreau-Yasuda model is used to provide further insight into the problem of the slip behavior of non-Newtonian fluids having a decreasing viscosity with a shear rate increase. This feature is demonstrated to cause a nonlinear velocity profile leading to the apparent slip. The corresponding transverse and longitudinal apparent slip lengths of a striped texture are found to be noticeably larger than the respective effective slip lengths of Newtonian liquids in microchannels of various thicknesses and surface fractions of the slip domains. The viscosity distribution of the shear thinning fluid over the superhydrophobic wall is carefully investigated to describe the mechanism of the apparent slip. Nonmonotonic behavior of the apparent slip length as a function of the applied shear rate is revealed. This important property of shear thinning fluids is considered to be sensitive to the steepness of the viscosity flow curve, thus providing a way to decrease considerably the flow resistance in microchannels.

Transient response of slot coating flows of shear-thinning fluids to periodic disturbances

Slot coating is a popular coating method, in which the film thickness is precisely controlled by adjusting the flow rate and production speed. When the coating flow undergoes small-scale disturbances generated by rotating elements such as motors, pumps, or uneven rolls, the downstream meniscus fluctuates, which causes film thickness variation in the flow direction. Although most coating liquids including polymeric and particulate solutions exhibit a shear-thinning rheological property, their effect on transient coating flow behaviors is not deeply understood. Here, the effect of shear-thinning property on film thickness variation under different disturbances is investigated using a computer-aided analysis of transient slot coating flow. In this study, the Carreau model is used to describe the shear-thinning property, and four different disturbances are considered.

Hölder continuity of velocity gradients for shear-thinning fluids under perfect slip boundary conditions

This paper is concerned with non-stationary flows of shear-thinning fluids in a bounded two-dimensional \(\mathcal {C}^{2,1}\) domain. Assuming perfect slip boundary conditions, we provide a proof of the existence of a solution with the Hölder continuous velocity gradients and pressure under condition that a stress tensor satisfies power-law with growth \(p\in [5/3;2]\).

Two-dimensional Flow of Power-law Fluids over a Pair of Cylinders in a Side-by-Side Arrangement in the Laminar Regime

Abstract This manuscript presents the effect of Reynolds number (Re) and proximity of the bodies on the hydrodynamics of flow of shear-thinning, Newtonian and shear-thickening fluids over a pair of cylinders kept in side-by-side arrangement. Results obtained from the numerical simulations carried out with a combination of different parameters in the range of 0.2 ≤ power law index (n) ≤ 1.8, 0.1 ≤ Re ≤ 100 and 1.2 ≤ G (gap between the cylinders/diameter) ≤ 4 have been discussed in details. Analysis of the results gives a clear insight into the complex influence of Re on streamline patterns, surface pressure profiles, drag and lift coefficients for various fluids when the gap between two cylinder is changed.

Jetting of a shear banding fluid in rectangular ducts.

Non-Newtonian fluids are susceptible to flow instabilities such as shear banding, in which the fluid may exhibit a markedly discontinuous viscosity at a critical stress. Here we report the characteristics and causes of a jetting flow instability of shear banding wormlike micelle solutions in microfluidic channels with rectangular cross sections over an intermediate volumetric flow regime. Particle-tracking methods are used to measure the three-dimensional flow field in channels of differing aspect ratios, sizes, and wall materials. When jetting occurs, it is self-contained within a portion of the channel where the flow velocity is greater than the surroundings. We observe that the instability forms in channels with aspect ratio greater than 5, and that the location of the high-velocity jet appears to be sensitive to stress localizations. Jetting is not observed in a lower concentration solution without shear banding. Simulations using the Johnson-Segalman viscoelastic model show a qualitatively similar behavior to the experimental observations and indicate that compressive normal stresses in the cross-stream directions support the development of the jetting flow. Our results show that nonuniform flow of shear thinning fluids can develop across the wide dimension in rectangular microfluidic channels, with implications for microfluidic rheometry.

Experimental evidence of symmetry-breaking supercritical transition in pipe flow of shear-thinning fluids

Experimental results reveal that the asymmetric flow of shear-thinning fluid through a cylindrical pipe, which was previously associated with the laminar-turbulent transition process, appears to have the characteristics of a nonhysteretic, supercritical instability of the laminar base state. Contrary to what was previously believed, classical transition is found to be responsible for returning symmetry to the flow. An absence of evidence of the instability in simulations (either linear or nonlinear) suggests that an element of physics is lacking in the commonly used rheological model for inelastic shear-thinning fluids. These unexpected discoveries raise new questions regarding the stability of these practically important fluids and how they can be successfully modeled.