Flow Of Shear-thinning Fluids Research Articles

Flow enhancement produced by a pulsatile flow of shear-thinning fluids in circular and concentric annular tubes

Although the analysis of the flow enhancement of non-Newtonian fluids produced by pulsatile flows through tubes is common in the literature, the case of Carreau fluid has not been analyzed, which is the aim of this work. This study determines the flow enhancement caused by the pulsatile fluid flow through (a) a circular tube and (b) a concentric annular tube. We show that the flow rate enhancement of the shear-thinning fluid is controlled by the Carreau number Cu, the Womersley number Wo, the fluid power-law index n, the ratio between the outer and inner radii κ, a parameter β that represents the ratio between the infinite and zero-shear viscosities, and the amplitude of the oscillatory signal ɛ. In both cases (a) and (b), a numerical solution of the start-up of the hydrodynamic is evaluated. With the aid of the velocity solution, the volumetric flow rate is determined under periodic conditions after the initial transient has vanished. Then, the fractional increase in the mean flow rate I due to the pulsatile pressure gradient is calculated. Furthermore, an asymptotic solution for small, intermediate, and very large values of the Carreau number is performed to provide physical insight into flow enhancement.

Inertial migration of rigid particles in shear-thinning fluids under asymmetric wall slip conditions

The determination of flow-induced equilibrium positions in pressure-driven flows in microchannels is of great practical importance in particle manipulation. In the computational analysis presented in this paper, the inertial ordering of neutrally buoyant rigid spheres in shear-thinning fluid flow through a hydrophobic microchannel is investigated. The combined effect of the viscosity index n of a power-law fluid and fluid slippage at the wall on the lateral focusing of microspheres is examined in detail. Using the finite element method, the Eulerian flow field between partially slipping parallel walls is simulated, and the Lagrangian movement of particles is continuously tracked. The Navier slip model is used to ensure a finite fluid velocity at the wall, and it is tuned by modifying the slip-length. It is observed that inertial particles concentrate at a standard equilibrium position of 0.6 times the channel half-width H, irrespective of fluid slip due to the symmetry of the flow field. However, this equilibrium position shifts closer to the walls as the viscosity index increases; for instance, when n = 0.5, particles stabilize at 0.75H. As a consequence of asymmetry in hydrodynamic behavior due to different fluid slippages at the upper and lower walls, the particle migration path is altered. In a channel with a no-slip upper wall and a partially slipping lower wall (β/H = 0.4), particles settle closer to the lower wall at 0.8H. Most importantly, the lateral movement of a particle released at a given vertical position can be altered by tailoring the wall hydrophobicity and viscosity index, thus enabling multiple equilibrium locations to be achieved.

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.

Viscosity-model-independent generalized Reynolds number for laminar pipe flow of shear-thinning and viscoplastic fluids

Understanding the flow dynamics of non-Newtonian fluids is crucial in various engineering, industrial, and biomedical applications. However, the existing generalized Reynolds number formulations for non-Newtonian fluids have limited applicability due to their dependencies on their specific viscosity models. In this study, we propose a new viscosity-model-independent generalized Reynolds number formulation for laminar pipe flow. The proposed method is based on the direct adaptation of the measurement principles of rotational viscometers for wall shear rate estimation. We assess the accuracy of this proposed formulation for power-law and Carreau-Yasuda viscosity models through robust friction factor experiments. The experimental results demonstrate the applicability and effectiveness of the proposed viscosity-model-independent Reynolds number, as the measured friction factor data align closely with our Reynolds number predictions. Furthermore, we compare the accuracy of our Reynolds number formulation against established generalized Reynolds formulations for pure shear-thinning (Carreau-Yasuda) and viscoplastic (Herschel-Bulkley-extended) models. The results of the comparative analysis confirm the reliability and robustness of this generalized Reynolds number in characterizing and interpreting flow behavior in systems with visco-inelastic non-Newtonian fluids. This unified generalized Reynolds number formulation presents new and significant opportunities for precise pipe flow characterization and interpretation as it is applicable to any visco-inelastic (time-independent) viscosity model without requiring additional derivations.

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 fluid is studied by using the diffuse interface lattice Boltzmann method, and the study mainly considers the effects of the particle's initial position, the power-law index, the Reynolds number, and the particle size. The numerical results show that the circular particle is first in a centrifugal motion under the effect of inertia, and it finally 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 a shear-thinning fluid flow, 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, in the case of shear-thickening fluid flow, 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 towards the center of the cavity. In this case, the limit cycle shrinks towards the center of the cavity. The circular particle squeezes the secondary vortices, especially when the circular particle is located in the bottom left, bottom right and top left corners. Additionally, the appearance of the circular particle has a significant influence on the position of the primary vortex, which changes periodically near the position of the primary vortex without the particle. It is also observed that the influence of the circular particle becomes more significant as its size increases and the power-law index decreases.

Study of Rheological Characteristics of a Water-Based Drilling Fluid in Presence of Biopolymers, Synthetic Polymer, and Modified Natural Polymer

The major contemplation in the recent decades is to minimize the operational difficulties during any drilling activity by improving the characteristics of water-based drilling fluids (WBDF). Such problem as a poor hole-cleaning because of settling of drill cutting and debris are extremely common. This problem will eventually convert into a serious non-productive time event in the form of pipe sticking. The most common additives added in the mud system to improve its rheological properties and tackle sedimentation issues are polymeric materials. During this study, four different polymers including sodium alginate and pure-bore as biopolymers, PHPA as a synthetic polymer, and the L-grade polyanionic cellulose (PAC-L) as a modified natural polymer have been used to improve rheological characteristics of WBDF. Laboratory measurements have indicated no considerable changes in the mud weight in the case of addition of these polymers. Moreover, these results reveal that all the systems behave as shear thinning fluid (flow index 1). A decrease in the dynamic viscosity with an increase in the shear rate has been observed for all samples. The disentangling of polymeric chains occurring at high shear rate eventually reduces the viscosity of these systems. In addition, samples that comprised of pure-bore and sodium alginate exhibit the desired operating magnitude of rheology (PV, YP, GS, AV, and YP/PV). These results show such particles minimize operational problems arising because of a poor hole-cleaning. In contrast, a system with PHPA and PAC-L has shown detrimental rheological characteristics. The high molecular weight of PHPA and the hydration of PAC-L in the presence of potassium chloride decrease their performance.

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