Flow Of Shear-thinning Fluids Research Articles

Anomalies of solute transport in flow of shear-thinning fluids in heterogeneous porous media

Solute transport and mixing in heterogeneous porous media are important to many processes of practical applications. Most of the previous studies focused on solute transport in flow of Newtonian fluids, whereas there are many processes in which the phenomenon takes place in flow of a non-Newtonian fluid. In this paper, we develop a computational approach to evaluate and upscale dispersion of a solute in flow of a shear-thinning (ST) fluid in a heterogeneous porous medium. Our results indicate that the dispersivity is a non-monotonic function of the Péclet number and the shear rate, and this behavior is accentuated by the heterogeneity of the pore space and spatial correlations between the local permeabilities. As a result, solute transport in ST fluids deviates significantly from the same phenomenon in Newtonian fluids. Moreover, the shear-dependence of the dispersivity strongly influences the fate of solute transport in porous media at large length scales, including larger effluent concentration at the breakthrough point, which also occurs much faster than Newtonian fluids. To provide further evidence for the numerical findings, we compare dispersion in flow of a power-law fluid in a single tube with the same in a bundle of such tubes. Our results emphasize the shortcomings of the current theories of dispersion to account for the role of fluid rheology in solute mixing and spreading.

Density unstable fluid displacement in vertical annuli

We study displacement flows involving pairs of Newtonian and shear-thinning fluids in vertical annular geometries using experimental and computational methods. This investigation is motivated by the primary cementing of casing strings, which is part of the well construction operation. In displacement scenarios that involve density-unstable fluid pairs, it is well-known that buoyancy can increase the inter-mixing between fluids and hence contaminate cementing fluids due to gravity-driven instabilities. Our study seeks to investigate how the imposed flow rate, the degree of inner pipe centralization, and the viscosity of the fluids affect the displacement efficiency in such cases. The study complements our recent paper [R. Zhang et al., “Vertical cementing displacement flows of shear-thinning fluids,” Phys. Fluids 35, 113110 (2023)], which focused on density-stable configurations, and here we consider the more challenging, density-unstable displacement flows. Our experiments and three-dimensional computational results are in general agreement. The results show that displacements improve for viscosity-stable conditions, i.e., when the displacing fluid is the more viscous fluid. Characteristic fingering patterns occur in the interface region of the fluids for viscosity-unstable conditions. The eccentricity of the inner pipe is seen to promote the channeling of fluids, and viscosity-unstable conditions can exacerbate this effect further. A degree of stabilization of density unstable displacements can be achieved by increasing the imposed flow rate and the viscosity of the fluids while maintaining a stable viscosity ratio.

Scaling laws for optimized power-law fluid flow in self-similar tree-like branching networks

The power-law fluid flow in tree-like self-similar branching networks is prevalent throughout the natural world and also finds numerous applications in technology such as oil recovery and microfluidic devices. We investigate analysis of optimal power-law fluid flow conditions and the optimal structures within tree-like branching networks, focusing on maximizing flow conductance under the constraint of the network tube’s volume and the surface area. The study considered fully developed laminar power-law fluid flow regimes without considering any losses in the network system. A key observation was the sensitivity of the dimensionless effective flow conductance to the network’s geometrical parameters. We found that the maximum flow conductance occurs when a dimensionless radius ratio β∗ satisfies the equation β∗=N−1/3 and β∗=N−(n+1)/(3n+2) under constrained tube-volume and surface-area, respectively. Here, N represents the bifurcation number of branches splitting at each junction, and n is the fluid power-law index. We further find that this optimal condition occurs when pressure drops are equipartition across each branching level. We validated our results with various experimental results and theories under limiting conditions. Further, Hess–Murray’s law is justified and extended for the shear-thinning and shear-thickening fluid flows for an arbitrary number of branches N. Further, in this study, we also derive the relationships between the geometrical and flow characteristics of the parent and daughter tubes as well as the generalized scaling laws at the optimal conditions for the other essential parameters such as tube-wall stresses, length ratios, mean velocities, tube-volume, and surface-area of the tube distributing within the networks. We find that the fluid power-law index n does not influence the constrained tube-volume scaling at the optimal conditions; however, the scaling laws vary with n under the constrained tube’s surface area. These findings offer valuable design principles for developing efficient transport and flow systems.

Experiments and numerical modelling of secondary flows of blood and shear-thinning blood analogue fluids in rotating domains

The transition from concentric primary flow to non-tangential secondary flow of blood was investigated using experimental steady shear rheometry and numerical modelling. The aims were to: assess the difference in secondary flow in a Newtonian versus shear-thinning blood analogue; and measure the secondary flow in the blood. Both experiments and numerical modelling showed that the transition from primary to secondary flow was the same in a Newtonian fluid and a shear-thinning blood analogue. Experiments showed whole blood transitioned to secondary flow at lower modified Reynolds numbers than the Newtonian fluid; and transition was haematocrit dependent with higher RBC concentrations transitioning at lower modified Reynolds numbers. These results indicate that modelling blood as a purely shear-thinning fluid does not predict the correct secondary flow fields in whole blood; non-Newtonian effects beyond shear-thinning behaviour are influential, and incorporating effects such as multiphase contributions and viscoelasticity, yield stress and thixotropy is necessary.

Elasto-inertial instability in torsional flows of shear-thinning viscoelastic fluids

It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate or the flow in a Taylor–Couette geometry, can become unstable to a three-dimensional time-dependent instability at conditions exceeding a critical Weissenberg ( $Wi$ ) number. However, the combined effects of fluid elasticity, shear thinning and finite inertia (as quantified by the Reynolds number $Re$ ) on the onset of elasto-inertial instabilities are not fully understood. Using a set of cone–plate geometries, we experimentally explore the entire $Wi$ – $Re$ phase space for a series of nonlinear viscoelastic fluids (with the dependence on shear rate $\dot{\gamma}$ quantified using a shear-thinning parameter $\beta _P(\dot {\gamma })$ ). We tune $\beta _P(\dot {\gamma })$ by varying the dissolved polymer concentration in solution. This progressively reduces shear thinning but leads to finite inertial effects before the onset of elastic instability, and thus naturally results in elasto-inertial coupling. Time-resolved rheometric measurements and flow visualization experiments allow us to investigate the effects of flow geometry, and document the combined effects of varying $Wi, Re$ and $\beta _P(\dot {\gamma })$ on the emergence of secondary motions at the onset of instability. The resulting critical state diagram quantitatively depicts the competition between the stabilizing effects of shear thinning and the destabilizing effects of inertia. We extend the curved streamline instability criterion of Pakdel & McKinley (Phys. Rev. Lett., vol. 77, no. 12, 1996, p. 2459) for the onset of purely elastic instability in curvilinear geometries by using scaling arguments to incorporate shear thinning and finite inertial effects. The augmented condition facilitates predictions of the onset of instability over a broader range of flow conditions, and thus bridges the gap between purely elastic and elasto-inertial curved streamline instabilities.

Regularity results for 3D shear-thinning fluid flows in terms of the gradient of one velocity component

Regularity results for 3D shear-thinning fluid flows in terms of the gradient of one velocity component

The statistical characteristics and auto-regeneration of backflow in non-Newtonian turbulent pipe flow

The backflow phenomenon in shear-thinning and shear-thickening fluids is investigated in pipe flows at friction Reynolds number Reτ=180 via direct numerical simulations. Conditional average results show that the extreme fluctuation of wall shear stress around the backflow regions is more abrupt under the shear-thinning effect. The statistical characteristics of the backflow at different flow indices from 0.5 to 1.5 show remarkable differences. The probability of the backflow events at the wall increases in both the shear-thinning and the shear-thickening fluids under different mechanisms. The backflow occurs more frequently and exists further away from the wall in the shear-thinning fluids owing to the suppressed near-wall turbulent structures and the laminarization at low flow indices. The increase in the probability of the backflow events in the shear-thickening fluids is caused by increased Q2 and Q4 events in the near-wall region. The variation in the size and the lifespan of the backflow regions with the flow index is very prominent which both increase with the shear-thinning effect and decrease as the flow becomes dilatant. In the weakly turbulent flow of shear-thinning fluid, large backflow regions appear near the leading edge of the turbulent spots where the off-axial turbulent fluctuations are significantly lowered. Observations show the linked evolution between the hairpin vortices and the backflow regions induced underneath the strong spanwise rotations. The backflow follows the auto-regeneration process of the hairpin vortices in a packet which results in coherent streamwise-aligned backflow regions under the hairpin packets confined closer to the wall.

Modeling of Shear Flows over Superhydrophobic Surfaces: From Newtonian to Non-Newtonian Fluids.

The design and use of superhydrophobic surfaces have gained special attentions due to their superior performances and advantages in many flow systems, e.g., in achieving specific goals including drag reduction and flow/droplet handling and manipulation. In this work, we conduct a brief review of shear flows over superhydrophobic surfaces, covering the classic and recent studies/trends for both Newtonian and non-Newtonian fluids. The aim is to mainly review the relevant mathematical and numerical modeling approaches developed during the past 20 years. Considering the wide ranges of applications of superhydrophobic surfaces in Newtonian fluid flows, we attempt to show how the developed studies for the Newtonian shear flows over superhydrophobic surfaces have been evolved, through highlighting the major breakthroughs. Despite the fact that, in many practical applications, flows over superhydrophobic surfaces may show complex non-Newtonian rheology, interactions between the non-Newtonian rheology and superhydrophobicity have not yet been well understood. Therefore, in this Review, we also highlight emerging recent studies addressing the shear flows of shear-thinning and yield stress fluids in superhydrophobic channels. We focus on reviewing the models developed to handle the intricate interaction between the formed liquid/air interface on superhydrophobic surfaces and the overlying flow. Such an intricate interaction will be more complex when the overlying flow shows nonlinear non-Newtonian rheology. We conclude that, although our understanding on the Newtonian shear flows over superhydrophobic surfaces has been well expanded via analyzing various aspects of such flows, the non-Newtonian counterpart is in its early stages. This could be associated with either the early applications mainly concerning Newtonian fluids or new complexities added to an already complex problem by the nonlinear non-Newtonian rheology. Finally, we discuss the possible directions for development of models that can address complex non-Newtonian shear flows over superhydrophobic surfaces.

Numerical Investigation on the Conical Flow of Viscoelastic Fluids

The conical problem represents one of the important problems in the various fields of industrial as the automotive industry and the aerospace industry, due to their great role in controlling the flow of liquids and gases. This article covers a computational investigation of incompressible the Phan–Thien/Tanner shear-thinning viscoelastic fluid flow through a conical converging channel. Here, we select hybrid finite element/finite volume algorithm as a first time to treat such problem. This method consists of the combination of a Taylor-Galerkin/pressure correction finite element method (TGPC-FEM) and a cell-vertex finite volume approach (CV-FEA) to solve the system of partial differential equations that govern the fluid flow. The TGPC-FEM is employed to the momentum and mass conservation models, while the stress constitutive models are treated by finite volume implementation. The findings of current study are concerned with stress response, deformation rate, and pressure drop under variations in Weissenberg number and EPTT parameters. The effect of shear-thinning behaviour with the EPTT representation is also considered.

Motion of a circular particle in the power-law lid-driven cavity flow

In this paper, the motion of a circular particle in a lid-driven square cavity with the power-law fluids is studied by the diffuse interface lattice Boltzmann method, and the effects of the initial position of particle, power-law index, Reynolds number and particle size are mainly considered. The numerical results show that the circular particle is first in a centrifugal motion under the effect of inertia, but finally, it moves steadily on the limit cycle. Furthermore, it is also found that the initial position of the particle has no influence on the limit cycle.For shear-thinning fluid flows, the limit cycle moves towards the bottom right corner of the square cavity. Moreover, the particle velocity is small, and the period of the particle motion is long. On the other hand, for shear-thickening fluid flows, the limit cycle moves towards the top left corner of the cavity. In addition, the particle velocity is large, and the period of the particle motion is short.With the increase of Reynolds number, the limit cycle moves towards the bottom right corner of the square cavity, which is caused by a strong fluid flow field. Meanwhile, the particle velocity becomes larger, and the period of the particle motion is shorter. With the increase of particle size, the effect of confinement of the cavity boundary becomes significant, and the circular particle is pushed toward the center of the cavity. In this case the limit cycle shrinks toward the center of the cavity. The circular particle squeezes the secondary vortices, especially when the circular particle is located in the left bottom, right bottom and left upper corners. Additionally, The appearance of the circular particle has a significant influence on the position of the primary vortex, which changes periodically around the position of the primary vortex without the particle. It is also found that the effect of the circular particle is more significant with the increase of the particle size and the decrease of the power-law index.

Dynamics of spheroids in pressure-driven flows of shear thinning fluids

Dynamics of spheroids in pressure-driven flows of shear thinning fluids

Molecular dynamics simulation of the flow mechanism of shear-thinning fluids in a microchannel

Shear-thinning fluids have been widely used in microfluidic systems, but their internal flow mechanism is still unclear. Therefore, in this paper, molecular dynamics simulations are used to study the laminar flow of shear-thinning fluid in a microchannel. We validated the feasibility of our simulation method by evaluating the mean square displacement and Reynolds number of the solution layers. The results show that the change rule of the fluid system’s velocity profile and interaction energy can reflect the shear-thinning characteristics of the fluids. The velocity profile resembles a top-hat shape, intensifying as the fluid’s power law index decreases. The interaction energy between the wall and the fluid decreases gradually with increasing velocity, and a high concentration of non-Newtonian fluid reaches a plateau sooner. Moreover, the velocity profile of the fluid is related to the molecule number density distribution and their values are inversely proportional. By analyzing the radial distribution function, we found that the hydrogen bonds between solute and water molecules weaken with the increase in velocity. This observation offers an explanation for the shear-thinning phenomenon of the non-Newtonian flow from a micro perspective.

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.

Electro-Osmotic Blood Flow of Shear-Thinning Fluid with Hall Current and Wall Flexibility

The presented article aims to present the flow of blood in microchannels such as veins and arteries via peristaltic flow. The magnetic field is imposed to regulate the flow as laminar. Also, its impacts in terms of Hall current have been considered. The rate of heat transfer is further based on Joule heating and viscous dissipation aspects. Mathematical analysis has been conducted given long wavelength and small Reynolds number. Such preferences are relatable to the medical domain where the magnetic field regulates the flow stream and aids in the melting of blood clots in patients with various heart diseases. The solution for electric potential is calculated analytically while the velocity, temperature, and heat transfer rate are executed directly via the built-in command of Mathematica software. Since the magnetic field acts as an opposing force. Results show that the velocity and temperature are decreasing functions of the magnetic field. However, the temperature is increasing for Weissenberg number.

Evolution of Entropy Generation on Mixing Process Using a Novel Chaotic Micromixer

This study aims to compare numerically the laminar steady flow of shear-thinning non Newtonian fluids in novel chaotic micromixer. The process is verified for non-Newtonian flow in a complex geometry that is heated with a constant flux. The selected geometry produce secondary flow structures that greatly improve fluid dynamic performance. To measure this performance, the Poincaré map method is used for various cases of fluid power-law index in different geometries. In addition, thermal mixing behavior is studied for shear-thinning fluids in the chosen geometry with two different inlet temperatures.In different cases of fluid power-law indexes, the novel geometry resulted in an 82% increase in thermal mixing degree relative to the thermal mixing degree observed in the C-shaped and serpentine channels. The second law of thermodynamics is examined in terms of entropy generation caused by thermal and hydrodynamic processes, as a function of low rates of generalized Reynolds number and power-law index, while taking into consideration the effects of chaotic advection. As a result, the new configuration showed a significant improvement in the degree of mixing compared to other geometries considered, while also minimizing friction and thermal irreversibilities.

Predicting Shear-Thinning Fluid Flows in Porous Media Using Pore Network Modeling: Simulations and Experimental Validation

Predicting Shear-Thinning Fluid Flows in Porous Media Using Pore Network Modeling: Simulations and Experimental Validation

Oblique Flow of Shear Thinning Fluid through an Absorptive Radiative Medium with Hall Effect

The assumption of Hall current and ion slip is extremely crucial in several industrial and manufacturing processes, such as MHD (magneto hydrodynamics) accelerators, preservation coils, transmission lines, electric converters, and heating elements. Keeping this in view, the main aim of this article is to present a computational analysis of MHD ion Hall current with nonlinear thermal radiation on the sloping flow of shear thinning fluid through a porous medium on a stretching sheet that allows fluid suction and injection. The major mathematical modelling of governed problems is converted into a system of nonlinear ODEs (ordinary differential equations) by means of appropriate similarity relations. The influence of all relative physical parameters on velocity and temperature is studied through graphs and discussed in a detailed physical manner. Some beneficial mathematical quantities from the practical engineering and industrial point of view, such as skin friction factor and heat transfer rate at the porous surface, are calculated numerically and presented through graphs. It has been observed that flow may become unstable when M is small and the existence of a magnetic field and a porous ground contributes to a highly rough flow over the stretching surface. Suction is actually a resistive force which results in higher skin friction that is beneficial in controlling flow separation. Temperature of the fluid rises with stronger magnetic field and higher thermal radiation effects. The local heat flux decreases as the magnetic field strength and permeability parameter increase.

Experimental and Numerical Analysis of the Effect of Rheological Models on Measurements of Shear-Thinning Fluid Flow in Smooth Pipes

The aim of this research is to investigate the effects of rheological models of shear-thinning fluids and their estimated parameters on the predictions of laminar, transitional, and turbulent flow. The investigation was carried out through experimental and computational fluid dynamics (CFD) studies in horizontal pipes (diameters of 19.1 mm and 76.2 mm). Six turbulent models using Reynolds averaged Navier–Stokes equations in CFD_ANSYS Fluent 19.0 were examined in a 3D simulation followed by comparison studies between numerical and experimental results. Regarding results of laminar regions in power-law rheology models, Metzner and Reed presented the best fit for the pressure loss and transitional velocity. For the turbulent region, correlations observed by Wilson and Thomas as well as Dodge and Matzner had good agreement with the experimental results. For Herschel–Bulkley fluids, pressure losses and transitional regions based on a yielded region were examined and compared to the experimental results and the modified Slatter Reynolds number, where the results provided good estimation. For both pipe diameters, the Slatter model was the best fit for pressure losses of Herschel–Bulkley fluids in the turbulent regime. Furthermore, when comparing k-omega and k-epsilon turbulence models to the power-law behaviour, numerical studies delivered the most accurate results with fluids that have a higher behaviour index. However, the error percentage significantly increased at a higher shear rate in the Herschel–Bulkley fluids with a greater yield stress effect. Moreover, the modified Herschel–Bulkley viscosity function by Papanastasiou was implemented in the current CFD study. This function was numerically stabilized, devoid of discontinuity at a low strain rate, and more effective in transitional regions.

Slug flows of gas and shear-thinning fluids in horizontal pipes

Experiments on slug flow are carried out with air and three solutions of carboxymethylcellulose (CMC)(0.05, 0.1 and 0.2% w/w) in a 44.2 mm ID horizontal pipe. The lengths, velocities and frequency of passage of the large bubbles are obtained through a high-speed digital camera. The gas fraction and length of liquid slugs are also estimated. Pressure changes along the pipe are measured with a differential pressure transducer. Particle Image Velocimetry is used to obtain the mean velocity of the continuous liquid field in the film and slug regions. The combination of tested gas and liquid superficial velocities and of distinct fluid rheology results in 48 different experimental conditions. The flow behavior is found to be strongly dependent on the rheological properties of the continuous phase. In particular, the gas volume fraction within the liquid slug (α=1−Rs), the passage frequency of the large bubbles (νt) and the pressure changes are increased. New expressions are proposed for α and νt to account for the rheology of the liquid phase. Predictions of the flow parameters obtained through two modified mechanistic models are compared with the experimental data. The friction coefficient expression proposed by Anbarlooei et al. (Phys. Rev. E, 92(6), 5–9, 2015) is also tested. The impact of the proposed modifications on the calculated properties of slug flow is assessed; typical RMS-errors of less than 15% are obtained for parameter predictions.

Horizontal cementing displacement flows of shear-thinning fluids, with and without casing rotation

Results from a laboratory experimental study of displacement flows in an eccentric horizontal annulus are presented. The fluids are shear-thinning or Newtonian, with density differences. The scenario represents a typical horizontal well cementing setup. In general terms, we find that having a viscosity stable configuration (more stable fluid displacing less stable fluid) produces better displacements. However, now the effective viscosity ratio between fluids can vary at different locations around the annulus and with the imposed flow rate. Thus for example, we demonstrate how a flow rate increase can improve displacement by shear-thinning the displaced fluid. Casing rotation (i.e. rotating the inner cylinder), has been found to be effective at improving the displacement, but in the case of adverse viscosity ratios, displacement from the annulus walls remains poor. Moreover, the displacement efficiency follows a non-linear trend with increasing the casing rotational speed. Lastly, it is noted that these reported effects of fluid rheology are mostly secondary to the dominant competition between eccentricity and buoyancy.