Flow Of Yield Stress Fluid Research Articles

Coupled measurements of PIV and photoelasticimetry on a thixotropic yield stress fluid flow

To study the behavior of thixotropic yield stress fluids, information at the local scale is required in order to determine precisely the yield point value, and the shear rate and stresses can be obtained all over the flow. This study focuses on the flow in a large shear cell of a Laponite suspension. In order to be able to construct a local rheogram for this suspension, two different methods issued from fluid mechanics and solid mechanics are used. Local velocities are determined with a PIV technique, and local stresses are determined with the photoelasticimetry technique.

Efficient numerical computations of yield stress fluid flows using second-order cone programming

This work addresses the numerical computation of the two-dimensional flow of yield stress fluids (with Bingham and Herschel–Bulkley models) based on a variational approach and a finite element discretization. The main goal of this paper is to propose an alternative optimization method to existing procedures such as penalization and augmented Lagrangian techniques. It is shown that the minimum principle for Bingham and Herschel–Bulkley yield stress fluid steady flows can, indeed, be formulated as a second-order cone programming (SOCP) problem, for which very efficient primal–dual interior point solvers are available. In particular, the formulation does not require any regularization of the visco-plastic model as is usually the case for existing techniques, avoiding therefore the difficult choice of the regularization parameter. Besides, it is also unnecessary to adopt a mixed stress–velocity approach or discretize explicitly auxiliary variables as frequently proposed in existing methods. Finally, the performance of dedicated SOCP solvers, like the Mosek software package, enables us to solve large-scale problems on a personal computer within seconds only. The proposed method will be validated on classical benchmark examples and used to simulate the flow generated around a plate during its withdrawal from a bath of yield stress fluid.

Boundary layer (shear-band) in frustrated viscoplastic flows

We show that frustrated creep flows of yield stress fluids give rise to a boundary layer, which takes the form of a liquid region of uniform significant thickness separating two solid regions. In this boundary layer the shear rate is approximately constant for a given flow rate and the layer thickness varies extremely slowly with the flow rate.

Strong squeeze flows of yield-stress fluids: The effect of normal deviatoric stresses

This work aims to study squeeze flows when the lubrication approximation does not necessarily hold. Strong squeeze flows are defined as the cases in which a sample is compressed by a disk with the initial speed of 40 cm/s, whereas weak squeeze flows are realized when the disk is softly released manually to avoid any impact of the sample at the beginning of compression. Strong and weak squeeze flows of yield-stress materials are studied experimentally and theoretically. In the experiments, disk-like constant-volume samples of Carbopol solutions and bentonite dispersions are compressed between two approaching disks being subjected to constant forces. In addition, experiments with shear flows in parallel-plate and vane viscometers are conducted. Using visualization through the transparent wall of the squeezing apparatus, it is demonstrated that the no-slip conditions hold. It is also demonstrated that during the fast stage of strong squeeze flows, the material response can be explained by deviatoric normal stresses, which elucidates the link of strong squeeze flows to elongational flows. The analysis of the data in the framework of the Newtonian and Herschel–Bulkley models shows that in the present case the nonlinearity of the rheological response at the fast stage of strong squeeze flows is not very significant, and a strain-rate-independent viscosity can be used as a reasonable approximation. On the other hand, at the final stage of squeeze flows, when samples spread significantly under the action of a constant squeezing force, the compressive stresses become small enough, and the dominant role is played by the yield stress. No significant signs of thixotrophy were observed. It is shown that strong squeeze flow in the squeezing apparatus is a convenient tool useful for the measurement of viscosity and the yield stress of complex soft materials.

Measuring the surface tension of yield stress fluids

With the aim of studying the impact of capillary forces on the flow of yield stress fluids we investigate the properties of a film formed by withdrawing a blade from a bath of such a material. We show that before a progressive breakage of the film, the force amplitude reaches a maximum which is independent of the initial depth of penetration and the timing for blade lifting, but increases with the material yield stress and the blade thickness. This critical force is shown to reflect both capillary and viscous effects, even at vanishing blade velocity. We demonstrate that the ratio of this force to the blade perimeter provides the surface tension of the yield stress fluid in the limit of a low (≪1) capillary number (ratio of yield stress times the blade thickness to surface tension). Moreover we show that all our data for the force to perimeter ratio fall along a master curve which may be used to deduce the surface tension from measurements obtained at a capillary number up to 1, even if viscous effects are significant. Finally Carbopol gels appear to have almost the same value of surface tension whatever their yield stress, but this value is almost 10% smaller than that of pure water.

On the existence of a simple yield stress fluid behavior

Materials such as foams, concentrated emulsions, dense suspensions or colloidal gels, are yield stress fluids. Their steady flow behavior, characterized by standard rheometric techniques, is usually modeled by a Herschel–Bulkley law. The emergence of techniques that allow the measurement of their local flow properties (velocity and volume fraction fields) has led to observe new complex behaviors. It was shown that many of these materials exhibit shear banding in a homogeneous shear stress field, which cannot be accounted for by the standard steady-state constitutive laws of simple yield stress fluids. In some cases, it was also observed that the velocity fields under various conditions cannot be modeled with a single constitutive law and that nonlocal models are needed to describe the flows. Doubt may then be cast on any macroscopic characterization of such systems, and one may wonder if any material behaves in some conditions as a Herschel–Bulkley material. In this paper, we address the question of the existence of a simple yield stress fluid behavior. We first review experimental results from the literature and we point out the main factors (physical properties, experimental procedure) at the origin of flow inhomogeneities and nonlocal effects. It leads us to propose a well-defined procedure to ensure that steady-state bulk properties of the materials are studied. We use this procedure to investigate yield stress fluid flows with MRI techniques. We focus on nonthixotropic dense suspensions of soft particles (foams, concentrated emulsions, Carbopol gels). We show that, as long as they are studied in a wide (as compared to the size of the material mesoscopic elements) gap geometry, these materials behave as ‘simple yield stress fluids’: they are homogeneous, they do not exhibit steady-state shear banding, and their steady flow behavior in simple shear can be modeled by a local continuous monotonic constitutive equation which accounts for flows in various conditions and matches the macroscopic response.

Startup flow of gelled crudes in pipelines

The startup flow of thixotropic yield stress fluids in tubes is studied numerically. In the situation of interest, the structured fluid is displaced by another fluid, under the application of a constant entrance pressure. The fluid is assumed to obey a recently proposed model for thixotropic yield-stress fluids that relies on a structure parameter. The momentum conservation principle is employed in a simplified form that arises by assuming quasi-steady flow, i.e. the shear stress radial distribution is assumed to be linear as it is in steady flow. Inertial effects are also included in the analysis. A numerical procedure was developed to integrate the differential equations that arise, and the average velocity as well as the radial distribution of the structure parameter are obtained for different combinations of the rheological and flow parameters, allowing the determination of the necessary conditions for a successful startup. Among other features, the approach is capable of predicting the “avalanche effect [5],” i.e. situations of no flow for long time periods and then the sudden onset of motion.

The consequences of yield stress on deployment of a non-Newtonian anti-HIV microbicide gel

A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when applied topically, significantly inhibits sexual HIV transmission to women [10]. However the gel for this drug, and anti-HIV microbicide gels in general, have not been designed using full understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model such spreading of microbicide gels, which are inherently non-Newtonian [13,15]. A yield stress is emerging as one of the important properties of microbicide gel vehicle deployment, as this may improve retention within the vaginal canal. On the other hand, a yield stress may decrease the initial extent of the coating flow. Here, we first explain a certain yield stress paradox observed generally in many lubrication flows. Four conditions are determined, via scaling analysis, which mitigate the inconsistency in the use of lubrication theory to analyze the specific problem of elastic wall squeezing flow of yield stress fluid. Parameters characterizing these conditions are obtained experimentally for a test gel. Using them, it is shown that the lubrication approximation may be applied to the elastic wall-squeezing problem for this gel.

An augmented Lagrangian approach to simulating yield stress fluid flows around a spherical gas bubble

SUMMARYWe simulated the flow of a yield stress fluid around a gas bubble using an augmented Lagrange approach. The piecewise linear equal‐order finite elements for both the velocity and the pressure approximations proposed and analyzed by Latché and Vola in 2004 were applied. A mesh adaptive strategy based on this element‐pair choice was also proposed to render the yield surfaces of desired resolution. The corresponding numerical scheme was formulated for general Herschel–Bulkley fluids. Numerical results on Bingham fluid flows around a slowly rising spherical gas bubble were provided to validate the proposed algorithm. Copyright © 2011 John Wiley & Sons, Ltd.

Numerical simulation of power law and yield stress fluid flows in double concentric cylinder with slotted rotor and vane geometries

In our previous report, we showed that a rheometer equipped with a double concentric cylinder geometry with slotted rotor could effectively reduce wall slip effects and thus it could be used as an alternative to a rheometer with a vane geometry in yield stress measurements. Here, we use three-dimensional CFD simulation to compare these two geometries for rheological measurements of power law and yield stress fluids. Our results indicate that the double concentric cylinder rheometer with slotted rotor (DCCR/SR) is able to accurately measure rheological properties of a wider spectrum of test fluids than a vane rheometer because of significant reduction of the end and secondary flow effects.

A numerical investigation of inertia flows of Bingham-Papanastasiou fluids by an extra stress-pressure-velocity galerkin least-squares method

This article is concerned with finite element approximations for yield stress fluid flows through a sudden planar expansion. The mechanical model is composed by mass and momentum balance equations, coupled with the Bingham viscoplastic model regularized by Papanastasiou (1987) equation. A multi-field Galerkin least-squares method in terms of stress, velocity and pressure is employed to approximate the flows. This method is built to circumvent compatibility conditions involving pressure-velocity and stress-velocity finite element subspaces. In addition, thanks to an appropriate design of its stability parameters, it is able to remain stable and accurate in high Bingham and Reynolds flows. Numerical simulations concerning the flow of a regularized Bingham fluid through a one-to-four sudden planar expansion are performed. For creeping flows, yield stress effects on the fluid dynamics of viscoplastic materials are investigated through the ranging of Bingham number from 0.2 to 100. In the sequence, inertia effects are accounted for ranging the Reynolds number from 0 to 50. The numerical results are able to characterize accurately the morphology of yield surfaces in high Bingham flows subjected to inertia.

Modelling the Flow of Yield-Stress Fluids in Porous Media

Yield-stress is a problematic and controversial non-Newtonian flow phenomenon. In this article, we investigate the flow of yield-stress substances through porous media within the framework of pore-scale network modelling. We also investigate the validity of the Minimum Threshold Path (MTP) algorithms to predict the pressure yield point of a network depicting random or regular porous media. Percolation theory as a basis for predicting the yield point of a network is briefly presented and assessed. In the course of this study, a yield-stress flow simulation model alongside several numerical algorithms related to yield-stress in porous media were developed, implemented and assessed. The general conclusion is that modelling the flow of yield-stress fluids in porous media is too difficult and problematic. More fundamental modelling strategies are required to tackle this problem in the future.

Development Length Requirements for Fully Developed Laminar Pipe Flow of Yield Stress Fluids

In this technical brief, we report the results of a systematic numerical investigation of developing laminar pipe flow of yield stress fluids, obeying models of the Bingham-type. We are able to show that using a suitable choice of the Reynolds number allows, for high Reynolds number values at least, the development length to collapse to the Newtonian correlation. On the other hand, the development length remains a weak, nonmonotonic, function of the Bingham number at small values of the Reynolds number (Re≤40).

Stability of Water Lubricated Flow of Yield Stress Fluid in Sloping Pipe

To facilitate the transport of viscous crudes in a pipe, an immiscible lubricating liquid, usually water, is added. In such configuration, the water migrates into the regions of high shear at the pipe wall where it lubricates the flow. The pumping pressures being balanced by wall shear stresses in the water, the flow therefore requires pressures comparable to pumping water alone, at the same total throughput (1). So significant savings in pumping power can be derived from this process provided that it is well monitored. Indeed, instabilities usually take place at the oil/water interface and they constitute an important source of energy dissipation. Precisely, a core annular flow is known to undergo a long-wave instability of capillary type, modified by shear occuring at low Reynolds. Above a given critical Reynolds number, the flow is unstable to shorter waves which leads to an emulsification system of water droplets in oil. In present work, an experimental study of the stability of sloping plane Poiseuille flow of well characterized viscoplastic mineral oils lubricated by water was performed. The investigation was carried out by means of image analysis based on spatiotemporal diagrams (STD). Notably indicated are the effects of bed slope, flow rates ratio and oil rheology on flow stability.

The Dean instability in power-law and Bingham fluids in a curved rectangular duct

The laminar flow of power-law and yield-stress fluids in 180° curved channels of rectangular cross section was studied experimentally and numerically in order to understand the effect of rheological fluid behavior on the Dean instability that appears beyond a critical condition in the flow. This leads to the apparition of Dean vortices that differ from the two corner vortices created by the channel wall curvature. Flow visualizations showed that the Dean vortices develop first in the near-wall zone on the concave (outer) wall, where the shear rate is higher and the viscosity weaker; then they penetrate into the centre of the channel cross section where power-law fluids have high viscosity and Bingham fluids are unyielded in laminar flow. Based on the complete formation on the concave wall of the new pairs of counter-rotating vortices (Dean vortices), the critical value of the Dean number decreases as the power-law index increases for the power-law fluids, and the Bingham number decreases for the Bingham fluids. For power-law fluids, a diagram of critical Dean numbers, based on the number of Dean vortices formed, was established for different axial positions. For the same flow conditions, the critical Dean number obtained using the axial velocity gradient criterion was smaller then that obtained with the visualization technique.

Wicking with a yield stress fluid

This work presents an experimental investigation of the flow of a model yield stress fluid(yield stresses between 5 and 21 Pa) driven by capillarity in horizontal glass tubes withdiameters ranging from 0.46 to 1.5 mm. It is shown that the liquid penetration stops aftertypically a few centimeters. The results disagree with a simple model based on the balancebetween capillary and frictional forces, suggesting that the yield stress fluid constitutiveequation may not be valid in the immediate vicinity of the wall. Scaling is proposed withrespect to a dimensionless number comparing the yield stress with the capillarypressure.

Transition from supercritical to subcritical regime in free surface flow of yield stress fluids

Characteristics of the transition from supercritical to subcritical regime (hydraulic jump) in laminar flow of a Herschel‐Bulkley fluid on an horizontal plane are examined. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid. The determination of the flow conditions downstream, given those upstream, involves solution of a nonlinear algebraic system in three unknowns; an approximate analytical formula for conjugate depths is derived since no exact solution can be obtained in closed form. The relative error thus introduced is then evaluated numerically; its maximum value is shown to be less than a few percent. The behavior of flow depth, bottom shear stress and critical depth are established and illustrated as function of the flow behavior index; the critical depth and the ratio of conjugate depths increase with the behavior index and until the bottom shear stress exceeds a certain value, and then decrease afterwards.

Pore-scale network modeling of Ellis and Herschel–Bulkley fluids

Network modeling is used to study the flow in porous media of Ellis and Herschel–Bulkley fluids, which model a large group of time-independent non-Newtonian fluids. Previous work is extended to include yield-stress and shear-thickening phenomena. We use two topologically-disordered networks representing a sand pack and Berea sandstone. Analytical expressions for the volumetric flow rate in a single tube are derived and implemented in each pore and throat to simulate single-phase flow in the pore space. An iterative technique is used to compute the relationship between flow rate and pressure gradient across the whole network. The single tube behavior is compared to that of the network. Experimental data in the literature are compared to the network simulation results to validate the model and investigate its predictive capabilities. Good agreement is obtained in many cases. The flow of yield-stress fluids in porous media is analyzed. Two algorithms to predict the network threshold yield pressure are implemented and compared to the numerically computed threshold yield pressure of the network.

An experimental study of electrorheological fluid flow through a packed bed of glass beads

This paper shows that pressure drop-flow rate performance of an electrorheological (ER) fluid flowing through a packed bed of glass beads is consistent with a modified Ergun equation for yield stress flow through a packed bed. ER fluids are of scientific and engineering interest due to the sensitivity of their rheological properties on the applied electric field. As far as we know ER fluids have not been studied for flows through porous media. In this work a silica particle–silicone oil suspension is pumped through a rectangular packed bed of glass beads with applied electric fields. The silica particles are observed to form fibrous structures parallel to the electric field that stretch between the beads and extend between the electrodes. The pressure drop-flow rate performance agrees well with the expected performance calculated from a modified Ergun equation for a yield stress fluid flow through the packed bed with the viscosity and yield stress as functions of the applied electric field.

Flow of a yield stress fluid over a rotating surface

We study the flow of yield stress fluids over a rotating surface when both the viscoelastic solid behavior below a critical deformation (γ c) and liquid properties beyond γ c can play a significant role. We review the detailed characteristics of the flow in the solid regime in the specific case of a pure elongational strain (large height to radius ratio). We, in particular, show that there exists a critical rotation velocity (ω c) associated with the transition from the solid to the liquid regime. We then consider the specific case of lubricational regime (small height to radius ratio) in the liquid regime. In that case we describe the different possible evolutions of the equilibrium shape of the material as a function of the rotation velocity (ω), from which we extrapolate the transient shape evolutions as ω increases. We show that for a sufficiently large rotation velocity the sample separates into two parts, one remaining at rest around the rotation axis, the other going on moving radially. These predictions are then compared with systematic spin-coating tests under increasing rotation velocity ramps followed by a plateau at ω f with typical yield stress fluids. It appears that there exists a critical velocity below which the material undergoes a limited elongation and beyond which it starts to spread significantly over the solid surface. For a larger ω f value the sample forms a thick peripheral roll, leaving behind it a thin layer of fluid at rest relatively to the disc. These characteristics are in qualitative agreement with the theoretical predictions. Beyond a sufficiently large ω f value this roll eventually spreads radially in the form of thin fingers. Moreover, in agreement with the theory in the lubricational regime, the different curves of deformation vs ω fall along a master curve when the rotation velocity is scaled by ω c for different accelerations, different sample radii, or different material yield stress. The final thickness of the deposit seems to be mainly governed by the displacement of the roll, the characteristics of which take their origin in the initial stage of the spreading, including the solid–liquid transition.