Flow Of Yield Stress Fluid Research Articles

Application of lubrication theory to determine yield stress in slump tests

The slump test can determine the yield stress of slurries by measuring the slump height. The convex shape in the slumped slurry profile cannot be characterised by the Tresca criterion. Lubrication theory has been widely applied to analyse the slow flow of yield stress fluids. Thus, the present study incorporates lubrication theory and the Tresca criterion to establish a generalized model for reconstructing the slurry profile based on the yield stress. The convex profile in the lower zone can be well represented by the novel method. The predicted yield stresses by the slump tests are larger than those determined using the vane method. Slump height and spread are equally accurate for predicting yield stress via the proposed method. Overall, the combination of lubrication theory and Tresca criterion yields a good prediction of yield stress based on slump height.

On the efficient non-linear solver for hydraulic fracturing and well cementing simulations based on Anderson acceleration

The aim of this study is to create a fast and stable iterative technique for numerical solution of a quasi-linear elliptic pressure equation. We developed a modified version of the Anderson acceleration (AA) algorithm to fixed-point (FP) iteration method. It computes the approximation to the solutions at each iteration based on the history of vectors in extended space, which includes the vector of unknowns, the discrete form of the operator, and the equation's right-hand side. Several constraints are applied to AA algorithm, including a limitation of the time step variation during the iteration process, which allows switching to the base FP iterations to maintain convergence. Compared to the base FP algorithm, the improved version of the AA algorithm enables a reliable and rapid convergence of the iterative solution for the quasi-linear elliptic pressure equation describing the flow of particle-laden yield-stress fluids in a narrow channel during hydraulic fracturing, a key technology for stimulating hydrocarbon-bearing reservoirs. In particular, the proposed AA algorithm allows for faster computations and resolution of unyielding zones in hydraulic fractures that cannot be calculated using the FP algorithm. The quasi-linear elliptic pressure equation under consideration describes various physical processes, such as the displacement of fluids with viscoplastic rheology in a narrow cylindrical annulus during well cementing, the displacement of cross-linked gel in a proppant pack filling hydraulic fractures during the early stage of well production (fracture flowback), and multiphase filtration in a rock formation. We estimate computational complexity of the developed algorithm as compared to Jacobian-based algorithms and show that the performance of the former one is higher in modelling of flows of viscoplastic fluids. We believe that the developed algorithm is a useful numerical tool that can be implemented in commercial simulators to obtain fast and converged solutions to the non-linear problems described above.

Theoretical study on Poiseuille flow of thixotropic yield stress fluids: an exact solution

Theoretical study on Poiseuille flow of thixotropic yield stress fluids: an exact solution

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.

Variational linear comparison homogenization estimates for the flow of yield stress fluids through porous media

Variational linear comparison homogenization estimates for the flow of yield stress fluids through porous media

GPU computing of yield stress fluid flows in narrow gaps

GPU computing of yield stress fluid flows in narrow gaps

Heat transfer in the Jeffery-Hamel flow of a yield-stress fluid

Heat transfer in the Jeffery-Hamel flow of a yield-stress fluid that obeys the Bingham-Papanastasiou model is investigated in the present study. Among various rheological models proposed to formulate the flow of yield-stress fluids, the Bingham model is usually used to address the effect of yield-stress. A fluid that obeys the Bingham model does not show any shear-thinning or shear-thickening behaviors; this makes the interpretation of the results much easier. Addressing the unyielded regions (regions at which the yield-stress material behaves like a solid) in a yield-stress fluid flow is not a trivial task, and it could be impossible, especially in complex geometries. Unfortunately, the Bingham model itself cannot be used to formulate complex fluid flow problems due to the mathematical difficulties (i.e., addressing the unyielded regions); hence it is usually regularized to avoid these mathematical challenges. One of these regularized models is the Bingham-Papanastasiou model. Using an exponential term enables the Bingham-Papanastasiou model to address the unyielded regions. However, this exponential term results in highly non-linear equations, which are difficult to be handled mathematically. In the present study, the effect of the yield-stress (Bingham number) on the hydrodynamics and heat transfer in the Jeffery-Hamel flow is investigated by using the Bingham-Papanastasiou model. The momentum transfer in the Jeffery-Hamel flow of a Bingham-Papanastasiou fluid is governed by a highly non-linear ordinary differential equation (ODE) which is a boundary value problem. Assuming that the fluid's properties are independent of the temperature and pressure, this highly non-linear ODE is solved numerically. The heat transfer in the flow, with a constant wall temperature boundary condition, is investigated, assuming the flow to be an equilibrium viscous dissipation flow (the fluid's mixed mean temperature variation is negligible along the channel). The resultant linear energy equation is also solved numerically to obtain the temperature distribution across the channel. The results obtained in this work show that the yield-stress increases the wall shear stress, Nusselt number, and Stanton number. In fact, the effect of the yield-stress on the Nusselt number is comparable to the effects of Prandtl and Eckert numbers. It is also found that the yield-stress can prevent the flow separation in a divergent channel. Considering the advantages of using the yield-stress fluids as the working fluids in the Jeffery-Hamel flow, they can be considered as an alternative to nanoparticles which are usually used to enhance the fluid's thermal conductivity and also the Nusselt number.

Darcy's law of yield stress fluids on a treelike network.

Understanding the flow of yield stress fluids in porous media is a major challenge. In particular, experiments and extensive numerical simulations report a nonlinear Darcy law as a function of the pressure gradient. In this letter we consider a treelike porous structure for which the problem of the flow can be resolved exactly due to a mapping with the directed polymer (DP) with disordered bond energies on the Cayley tree. Our results confirm the nonlinear behavior of the flow and expresses its full pressure dependence via the density of low-energy paths of DP restricted to vanishing overlap. These universal predictions are confirmed by extensive numerical simulations.

Yield stress fluid flows in superhydrophobic channels: From creeping to inertial regime

In this work, inertial flows of a yield stress fluid in a channel equipped with a superhydrophobic groovy wall are studied through numerical computations. Assuming an ideal Cassie state, the superhydrophobic wall is modeled via arrays of slip, quantified using the Navier slip law, and arrays of stick, corresponding to the no-slip boundary condition. The viscoplastic rheology is modeled using the Bingham constitutive model, implemented via the Papanastasiou regularization technique. The focus is on inertial flows in the thin channel limit, where the groove period is much larger than the half-channel height. The effects of the flow parameters are quantified on the flow variables of interest, including the slip and axial velocity profiles, unyielded plug zones, regime classifications, flow asymmetry indices, effective slip lengths, and friction factors. In particular, an increase in the flow inertia quantified via the Reynolds number affects the flow in several ways, such as reducing the dimensionless slip velocity and effective slip length, increasing the friction factor, inducing an asymmetry in the velocity profile, and showing a non-monotonic effect on the yielding of the center plug. The present work addresses the complex interplay between the yield stress fluid rheology, the wall superhydrophobicity, and the flow inertia, and it can find applications in macro-/micro-transports of non-Newtonian fluids, from oil and gas to health-related industries.

On the channel flow of yield stress fluids with an internal microstructure

Thin films consisting of polymer solutions are typically produced through a combination of extrusion and shearing processes, where the anisotropic, non-Newtonian solution is deformed and subjected to thermal treatment. This paper investigates the shearing of polymeric thin films by studying the channel flow rheology of polymer solutions that experience yield stress. The material rheology is described by the transversely isotropic fluid (TIF) model, which contains a yield behavior term related to microstructure distortion. Our results show that this distortional stress is able to resist the pressure gradient, and non-trivial stress distributions can exist in the absence of a flow. This represents a significant improvement over existing viscosity-based yield stress models (e.g., the Heschel–Bulkley model). The unyielded state is achieved as the end result of a transient process, where a pressure gradient produces a short-lived flow that ceases when opposing stresses from microstructure distortion are produced. Predictions of the TIF model are compared with the phenomenological Saramito model. Both models are found to predict yielding when a threshold stress is exceeded. In both cases, the velocity profile is Newtonian near the wall, while plug flows are encountered close to the centerline.

Stability of yield stress fluid flows, Part 1

<h2>Abstract</h2> Yield stress fluids are idealized simple models (e.g., Bingham, Casson, Herschel-Bulkley), describing fluids for which there is no deformation wherever the deviatoric stress lies below the yield stress. This simple rheological change results in hydrodynamic stability features that are quite different from those of purely viscous fluids. We can classify the flows into those that have a non-zero base flow <b>U</b>, and those for which <b>U</b> = 0. Unlike purely viscous fluids, flows with <b>U</b> = 0 have meaningful applications beyond hydrostatics. It is these flows that we explore here, focusing on general features of stability, control and determining the critical limits.

Dynamics and friction losses of the flow of yield-stress fluids through 90° pipe bends

We characterise the dynamics and the pressure losses of yield-stress fluid flow through 90° pipe bends using Computational Fluid Dynamics. We show that the bend can influence the flow far upstream and downstream depending on the Bingham number – the ratio of the yield-stress to viscous stresses – even under conditions where fluid inertia can be considered negligible. Moreover, non-Newtonian viscous effects counteract centrifugal forces and suppress secondary motion. We also show that the Darcy–Weisbach equation with a generalised version of the Reynolds number can accurately predict pressure losses. This applies to a wide range of bend curvatures and rheological parameters, and elastoviscoplastic fluids with Saramito-type rheology and elastic moduli as small as 500 Pa. Our model holds for multiple adjacent bends, with minimal impact from interactions between bends. Deviations from this model occur when inertial effects in the flow become significant and are smaller for yield stress fluids than Newtonian fluids.

Acoustophoretic Liquefaction for 3D Printing Ultrahigh-Viscosity Nanoparticle Suspensions.

An acoustic liquefaction approach to enhance the flow of yield stress fluids during Digital Light Processing (DLP)-based 3D printing is reported. This enhanced flow enables processing of ultrahigh-viscosity resins (μapp > 3700 Pa s at shear rates = 0.01 s-1 ) based on silica particles in a silicone photopolymer. Numerical simulations of the acousto-mechanical coupling in the DLP resin feed system at different agitation frequencies predict local resin flow velocities exceeding 100 mm s-1 at acoustic transduction frequencies of 110 s-1 . Under these conditions, highly loaded particle suspensions (weight fractions, ϕ= 0.23) can be printed successfully in complex geometries. Such mechanically reinforced composites possess a tensile toughness 2000% greater than the neat photopolymer. Beyond an increase in processible viscosities, acoustophoretic liquefaction DLP (AL-DLP) creates a transient reduction in apparent viscosity that promotes resin recirculation and decreases viscous adhesion. As a result, acoustophoretic liquefaction Digital Light Processing (AL-DLP) improves the printed feature resolution by more than 25%, increases printable object sizes by over 50 times, and can build parts >3 × faster when compared to conventional methodologies.

Flow of a yield-stress fluid past a topographical feature

Free-surface flows of yield-stress fluids down inclined planes are modelled under the assumptions that they are shallow and sustained by a uniform oncoming stream to determine the steady state that emerges as the flow passes topographic features. In general, the flow may surmount the topography and be deflected around it depending on the thickness of the oncoming flow, the lateral extent and elevation of the mound, the inclination of the plane, and the magnitude of the yield stress relative to the gravitational stress of the flowing layer. Flows deepen upstream of mounds, with amplitude increasing with increasing yield stress. In the absence of a yield stress, flows around isolated mounds exhibit a maximum thickness at a location that is displaced laterally and downstream of the mound due to flow diversion. However, the location of the maximum thickness differs for yield-stress fluids: with increasing yield stress, the flow thickens immediately upstream of the mound and the deflected flux is diminished, leading to a sharp transition in the location of the maximum. Larger amplitude mounds may not be surmounted at all, leading to ‘dry zones’ downstream into which no fluid flows. It is shown that the steady shape of the dry zone is dependent on the initial condition, because the transient evolution towards it depends upon the plug at its margin, which is not unique. The results are computed by numerical integration of the governing equations and through their asymptotic analysis in various flow regimes to draw out the interplay of the dynamical processes. • Models of free-surface flow of yield-stress fluid around a topographic feature. • Flows deepen upstream of mounds, with amplitude increasing with yield stress. • The diversion of the flow by the mound is reduced at higher yield stresses. • For larger mounds, a ‘dry zone’ forms with non-unique shape due to the plugged edge.

Effect of Sinusoidally Varying Flow of Yield Stress Fluid on Heat Transfer From a Cylinder

Abstract The effect of pulsating laminar flow of a Bingham plastic fluid on heat transfer from a constant temperature cylinder is studied numerically over wide ranges of conditions as Reynolds number (0.1 ≤ Re ≤ 40) and Bingham number (0.01 ≤ Bn ≤ 50) based on the mean velocity, Prandtl number (10 ≤ Pr ≤ 100), pulsation frequency (0 ≤ ω* ≤ π), and amplitude (0 ≤ A ≤ 0.8). Results are visualized in terms of instantaneous streamlines, isotherms, and apparent yield surfaces at different instants of time during a pulsation cycle. The overall behavior is discussed in terms of the instantaneous and time-averaged values of the drag coefficient and Nusselt number. The size of the yielded zone is nearly in phase with the pulsating velocity, whereas the phase shift has been observed in both drag coefficient and Nusselt number. The maximum augmentation (∼30%) in Nusselt number occurs at Bn = 1, Re = 40, Pr = 100, ω* = π, and A = 0.8 with respect to that for uniform flow. However, the increasing yield stress tends to suppress the potential for heat transfer enhancement. Conversely, this technique of process intensification is best suited for Newtonian fluids in the limit of Bn → 0. Finally, a simple expression consolidates the numerical values of the time-averaged Nusselt number as a function of the pertinent dimensionless parameters, which is consistent with the widely accepted scaling of the Nusselt number with ∼Pe1/3 under these conditions.

Sliding flows of yield-stress fluids

Abstract

Empirical Flow Rate/Pressure Drop Relationships for Capillaries of Triangular and Rectangular Cross-Sections to be Used in Yield Stress Fluid Porosimetry

The aim of the present work is to investigate the flow rate/pressure gradient relationship for the flow of yield stress fluids through rectilinear capillaries of non-circular cross-sections. These capillaries very often serve as basic elements in the modeling of porous media as bundles of capillaries or pore-network models. Based on the notions of shape coefficient and critical Bingham number, empirical flow rate/pressure gradient relationships have been proposed for both Bingham and Herschel–Bulkley fluids. The reliability of these relationships has been assessed by performing numerical simulations with the open-source Computational Fluid Dynamics (CFD) package OpenFOAM. For the considered cross-sectional shapes (equilateral triangle and square), and for a wide range of Bingham numbers, the predictions of the proposed empirical relationships have shown to be in very good agreement with the results of the current numerical simulations, as well as with previous results from the literature. An interesting feature of the proposed empirical relationships is the possibility to easily predict the total flow rate under a given imposed pressure gradient in a bundle of non-circular capillaries having any random distribution of inscribed circle radii. Furthermore, in the context of the yield stress fluid porosimetry method (YSM), experimental data may now be processed based upon bundles of capillaries with non-circular cross-sections.

Flow and Yield Characteristics of Yield Stress Fluids Using Hysteresis Loop Test Below Slip Yield Point

Abstract The flow characteristics of angel O/W emulsion, which is a yield stress fluid, was investigated. The hysteresis loop test was conducted for the strain below the slip yield point, and the single relaxation Maxwell model was used to fit the experimental data. Using these methods, the shear-rate dependence, stress dependence, and time dependence of the viscoelastic properties of the sample were evaluated in the region below the slip yield point. The shear-rate dependence induced by the stress-ramp rate and the stress dependence from the maximum applied stress influence the viscoelastic characteristics below the slip yield point in terms of the flow history. However, the time dependence of the viscoelastic characteristics could not be confirmed for any creep time. The yield stress measured in the stress-ramp test increases with the stress-ramp rate owing to the contribution of the viscous strain from the flow history.

Use of Concentric Hele-Shaw Cell for the Study of Displacement Flow and Interface Tracking in Primary Cementing

We present our new designed concentric Hele-Shaw cell geometry with dynamic similarity to a real field wellbore annulus during primary cementing, and then, the results of displacement flow of Newtonian and yield-stress non-Newtonian fluids in it are described. The displacement stability and efficiency, the effect of back, front, and side boundaries on displacement, bypassing pockets of displaced yield-stress fluid in displacing fluid, and the behavior of pressure gradients in the cell are investigated. Applications of intermediate buoyant particles with different sizes and densities intermediate between those of successively pumped fluids for tracking the interface between the two displaced and displacing fluids are examined. The main idea is to upgrade this concentric Hele-Shaw cell geometry later to an eccentric one and check the possibility of tracking the interface between successive fluids pumped in the cell. Successful results help us track the interface between drilling fluid and spacer/cement during primary cementing in wells penetrating a CO2 storage reservoir and decreasing the risk of CO2 leakage from them.

Determination of the aperture distribution of rough-walled rock fractures with the non-toxic Yield Stress fluids porosimetry method

Fractures in geological formations constitute high-conductivity conduits which potentially act as preferential paths during fluid injection in soil remediation and reservoir engineering operations. Recently, the measurement of the pressure drop under different flow rates during the flow of yield stress fluids in porous media has been proposed as the basis for an environmentally friendly method to characterize the Pore Size Distribution. However, the Yield Stress fluids porosimetry Method (YSM) has still not been extended to the characterization of the hydraulic aperture distribution of rough-walled rock fractures. The potential interest of such an extension is intense, considering that the distinct characteristics of rock fractures vs the matrix represent a burden to other traditional porosimetry techniques. In the particular case of X-ray microtomography, time-consuming calibration is often needed, and serious difficulties arise due to beam hardening and reconstruction artifacts. The specific objective of the present investigation is to adapt YSM to the characterization of rough-walled rock fractures. For this purpose, the results of laboratory experiments in which a yield stress fluid was injected through two natural rock fractures were exploited, and the YSM model and algorithm was adapted to the particular topological and geometrical features of flows in fractures. Moreover, numerical experiments were performed at the scale of a single 2D channel with variable aperture to identify the dimension characterized by YSM and decipher the yielding behaviour of the fluids. The present findings show that YSM can be successfully used to characterize the distribution of hydraulic apertures of the flow channels in rough-walled rock fractures. Furthermore, the numerical results revealed that the plug of stagnant fluid is located in the central part of these flow channels and breaks close to the constrictions, forming islands of unyielded fluid.