Considère reconsidered: Necking of polymeric liquids

We review the Considère construction and discuss its applicability to the prediction of the inception of necking in extensional flow. The behaviour of simple fluid models is used to illustrate the importance of fully specifying the flow conditions. Even for a Newtonian liquid there is a marked difference in the prediction of necking under the application of a constant force and the imposition of a constant rate of strain.     

Fluidization with viscoelastic polymer solutions in the transition flow region

Fluidization of spherical and non-spherical particle beds with shear thinning viscoelastic polymer solutions was investigated experimentally in the transition flow region. It was observed that the influence of elasticity on the anomalous expansion course weakens with the increasing value of Reynolds number. After exceeding a critical value of Reynolds number, which depends on the measure of liquid elasticity, the effect of elasticity vanishes and the expansion curves have the same linear shape as for fluidization with Newtonian (or purely viscous non-Newtonian) fluids. Semi-empirical equations based on the Carreau viscosity model were proposed for predicting the critical value of Reynolds number and the bed expansion in the region of diminishing elasticity effects.     

Synergistic Influence of pH and Temperature on Rheological Behavior of Adhesive Emulsions Stabilized with Micelle Dispersion of an Anionic Surfactant

The influence of emulsion pH and temperature on the rheological behavior of adhesive oil-in-water (o/w) emulsions stabilized with an anionic surfactant (sodium dodecyl benzene sulfonate, SDBS) was studied. The flow properties of emulsions as a complex fluid were investigated using steady and dynamic rheometry for characterization of non-Newtonian behavior. Emulsion pH was varied from 2 to 12 and temperature was varied from 20 to 50 °C, respectively. The influences of the above-mentioned variables on the rheology of o/w emulsion were studied using steady-shear and dynamic oscillatory experiments. Various viscosity models (2, 3, and 4 parameter rheological model) were used to predict the rheological parameters. An increase in the pH of the emulsion led to an increase in the emulsion stability, viscosity, and viscoelastic properties ( G′ , G″ , η* , and tan δ ), and a decrease in the mean droplet size of the emulsion. A decrease in the temperature yields higher values of steady-shear viscosity and viscoelastic properties upon a decrease in droplet size. Emulsions were characterized as flocculated structured liquid exhibiting a characteristic crossover frequency ( ω* ) within the range of angular frequency studied in oscillatory measurements. Overall, emulsions exhibited non-Newtonian shear-thinning behavior and the synergy of pH and temperature significantly influences the emulsion rheology.     

In‐Situ Formation of Viscoelastic Wormlike Micelles in Mixtures of Non‐Surface‐Active Compounds

Viscoelastic fluids based on surfactant self‐assembled wormlike micelles have been in focus over the past decade. In this work, we report wormlike micellar solutions formed in situ by simply mixing two non‐surface‐active compounds, N‐(3‐(dimethylamino)propyl)palmitamide (C16AMPM) and salicylic acid (HSal), without specialized organic synthesis of a surfactant. In the absence of HSal, C16AMPM is poorly soluble in pure water; after introducing HSal, C16AMPM is protonated into quaternary ammonium, behaving like a cationic surfactant with a low critical micellar concentration (0.25 mM) and a small area per molecule, which favors the formation of long cylindrical wormlike micelles. Above the overlapping concentration (~28 mM), the wormlike micelles formed entangle each other into viscoelastic networks, enhancing the viscosity by several orders of magnitude. In contrast to the worms formed by a single ultra‐long‐chain surfactant, the current system shows the advantages of a smaller flow activation energy and end‐cap energy, simpler formulation and lower cost, which make it more suitable for practical use.     

A macroscopic model for shear-thinning flow in packed beds based on network modeling

The flow of non-Newtonian fluids in packed beds and other porous media is important in several applications such as polymer processing, filtration, and enhanced oil recovery. Expressions for flowrate versus pressure gradient are desirable for a-priori prediction and for substitution into continuum models. In this work, physically representative network models are used to model the flow of shear-thinning fluids, including power-law and Ellis fluids. The networks are used to investigate the effects of fluid rheology and bed morphology on flow.A simple macroscopic model is developed for the flow of power-law and Ellis fluids in packed beds using results from the network model. The model has the same general functionality as those developed using the popular bundle-of-tubes approach. The constant β, which appears in these models, is often directly derived from the tortuosity and a simple representation of the porous media. It is shown here that this can lead to incorrect and ambiguous values of the constant. Furthermore, the constant is a weak function of the shear-thinning index, indicating that no single bundle-of-tubes could ever properly model flow for a wide variety of shear-thinning fluids.The macroscopic model is compared to experimental data for shear-thinning fluids available in the literature. The model fits the data well when β is treated as an experimental parameter. The best-fit values of β vary, which is expected because even the constant C in the Blake-Kozeny equation varies depending on the source consulted. Additionally, physical effects, such as adsorption and filtration, as well as rheological effects such as viscoelasticity may affect the value of β. We believe that in the absence of these effects, β equals approximately 1.46 for packed beds of uniform spheres at relatively moderate values of the shear-thinning index (>0.3).     

The effects of fluid viscoelasticity on the settling behaviour of horizontally aligned spheres

A study on the interaction of particles settling in non-Newtonian fluids of shear-thinning, thixotropic and viscoelastic characteristics has been conducted. Key aspects of the rheological characteristics of the fluids that influence the interaction of the particles were examined by analysing the trajectories of two particles that are initially placed side-by-side in the fluid medium.The interaction of the particles was found to be highly dependent on the separation distance that is initially set between them. If the initial distance is smaller than a critical value, the spheres would tend to attract and converge. In cases where the initial distance is greater than this critical value, the two spheres would tend to diverge, resulting in a slight (∼20%) increase in their separation distance over their course of settling. This tendency to diverge was found to diminish as the initial distance is increased further from the critical value.The magnitude of the critical separation distance was found to be primarily dependent on the normal stresses of the fluids. A correlation was thus proposed based on this observation. In cases where the two spheres do attract and converge, it was found that the spheres tend to follow a non-symmetrical trajectory, where one of the spheres possesses a slightly lower settling velocity than the other. As a result, the spheres appear to re-arrange themselves into a vertically aligned configuration. Once aligned, the shear-thinning and thixotropic characteristics of the fluid causes the lagging sphere to accelerate and collide with the leading sphere.     

Numerical simulation of viscoelastic two-phase flows using openFOAM

In this work a new solver is developed for the OpenFOAM^® CFD toolbox, which handles viscoelastic two-phase flows. A derivative of the volume-of-fluid (VoF) methodology is used to describe the interface. Established constitutive equations derived from kinetic theory, such as Oldroyd-B, Giesekus, FENE-P and FENE-CR, from network theory of concentrated solutions and melts, such as linear and exponential Phan-Thien–Tanner (PTT), and from reptation theory, such as Pom–Pom and XPP models, as well as multi-mode formulations are implemented in OpenFOAM. Validation of the numerical technique is performed by comparing detailed simulation predictions to data from several experimental studies, numerical studies and analytical models found in the literature. Two well-known viscoelastic free-surface effects, namely the Weissenberg and the Die Swell effect, are simulated. Furthermore, transient and steady-state droplet flow in shear and elongational flows is examined.     

Modeling the melt blowing of viscoelastic materials

Several outstanding issues concerning modeling of melt blowing of viscoelastic materials are addressed in this work. Using a slender-jet model for the melt-blown fiber, we probe the effects of rheology by considering Newtonian, upper-convected Maxwell, Phan-Thien and Tanner (PTT), and Giesekus constitutive equations. The effects of a non-uniform shear stress along the fiber length and heat transfer are also addressed. Our results suggest that by combining the slender-jet approach with a Giesekus (or PTT) constitutive equation, useful engineering predictions can be made concerning the final fiber diameter, even when assuming a constant shear stress and neglecting heat transfer. Finally, questions related to linear stability, nonlinear dynamics, and sensitivity are explored. Steady-state fiber profiles are found to be linearly stable, and numerical simulations indicate that the predictions from linear theory can be carried over into the nonlinear regime. Sensitivity analysis reveals that disturbances are likely to become especially amplified at particular frequencies, with elasticity reducing the magnitude of the amplification but broadening the spectrum of frequencies susceptible to large amplification. This suggests an explanation for the narrower fiber diameter distributions that are observed experimentally.     

Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square–square contractions

In this work we investigate the laminar flow through square–square sudden contractions with various contraction ratios (CR=2.4, 4, 8 and 12), using a Newtonian fluid and a shear-thinning viscoelastic fluid. Visualizations of the flow patterns were carried out using streak line photography and detailed velocity field measurements were performed using particle image velocimetry. The experimental results are compared with numerical predictions obtained using a finite-volume method. For the Newtonian fluid, a corner vortex is found upstream of the contraction and increasing flow inertia leads to a reduction of the vortex size. Good agreement is observed between experiments and numerical simulations. For the shear-thinning fluid flow a corner vortex is also observed upstream of the contraction independently of the contraction ratio. Increasing the elasticity of the flow, while still maintaining low inertia flow conditions, leads to a strong increase of the vortex size, until an elastic instability sets in and the flow becomes time-dependent at De≈200, 300, 70 and 450 for CR=2.4, 4, 8 and 12, respectively. At low contraction ratios, viscoelasticity brings out an anomalous divergent flow upstream of the contraction. For both fluids studied the flow presents a complex three-dimensional helical vortex structure which is well predicted by numerical simulations. However, for the viscoelastic fluid flow the maximum Deborah number achieved in the numerical simulations is about one order of magnitude lower than the critical Deborah number for the onset of the elastic instability found in the experiments.     

Estimation of rheological parameters using velocity measurements

In the present investigation, we develop a method for estimating rheological parameters of viscoelastic fluids using velocity measurement in a square straight channel. It is believed that a somewhat complicated patterns of secondary flows due to the non-zero second normal stress difference are more useful than the simple viscometric flows traditionally adopted in the determination of rheological parameters. The inverse problem of determining the rheological parameters from a set of velocity measurements is solved using a conjugate gradient method. When applied to a general constitutive equation encompassing the UCM model, the Oldroyd-B model and the PTT model, the present method is found to yield a reasonably accurate estimation of five rheological parameters simultaneously even with noisy velocity measurements.     

The strength of paraffin gels formed under static and flow conditions

When the temperature of a solution of paraffins in oil is dropped below the ‘cloud point’ temperature, the high molecular weight n-paraffin molecules precipitate out of solution, crystallize and form a gel. The gelation and concomitant deposition of these paraffin gels in crude oil pipelines poses a major transportation problem by reducing the flow efficiency. Implementation of mechanical methods of remediation of paraffin deposition requires knowledge of the gel strength. Rheometric studies were performed on a model system to study the yield strength of paraffin-oil gels formed under various shear and thermal histories. It was observed that when the gel was formed under quiescent (shut-in) conditions, the yield stress of the gel decreased with an increasing cooling rate. However, when a shear stress was exerted on the gel during cooling (as would be experienced in a flow line), the trend of the yield stress vs. cooling rate curve was strongly influenced by the magnitude of this shear stress. Additionally, experimentation over a range of applied shear stresses revealed that the yield stress of the gel reaches a maximum at a moderate value of the applied shear. These rheometric results are explained with the help of 3-D polarized light microscopy observations of the paraffin crystal structure formed under various shear and cooling conditions using static and flow cell systems. The effects of crystal size on the gel properties are enunciated.     

Flow around individual Taylor bubbles rising in stagnant CMC solutions: PIV measurements

The flow around single Taylor bubbles rising in non-Newtonian solutions of Carboxymethylcellulose (CMC) polymer was studied using simultaneously particle image velocimetry (PIV) and shadowgraphy. This technique made it possible to determine the correct position of the bubble interface. Solutions of polymer with weight percentage varying from 0.1 to 1.0 wt% were used to cover a wide range of flow regimes. The rheological fluid properties and pipe dimension yielded Reynolds numbers between 4 and 714 and Deborah numbers for the higher concentration solutions between 0.001 and 0.236. The shape of the bubbles rising in the different solutions was compared. The flow around the nose of the bubbles was found to be similar in all the studied conditions. Velocity profiles in the liquid film around the bubble were measured and different wake structures were found. With increasing solution viscosity, the wake flow pattern varied from turbulent to laminar, and a negative wake was observed for the higher polymer concentration solutions.     

羧酸盐型表面活性剂对功能化Gemini表面活性剂流变性质的影响

利用稳态和动态剪切实验考察了功能化Gemini表面活性剂1,3双-(二羟乙基十二烷基溴化铵)-丙烷[简写为12(2OH)-3-12(2OH)·2Br]与传统阴离子表面活性剂(十二酸钠、十四酸钠和十六酸钠)混合体系在25℃下的流变性质。12(2OH)-3-12(2OH)·2Br的浓度为50 mmol/L时,十二酸钠、十四酸钠和十六酸钠均可以增强溶液的黏弹性。十二酸钠与12(2OH)-3-12(2OH)·2Br的混合摩尔比β为0.3时,溶液的零剪切黏度η0出现最大值,为12.35 Pa·s,平台模量G'∞为31.88 Pa;β=0.4时,G'∞值为14.67 Pa。混合体系的黏弹性顺序为:十二酸钠/12(2OH)-3-12(2OH)·2Br十四酸钠/12(2OH)-3-12(2OH)·2Br十六酸钠/12(2OH)-3-12(2OH)·2Br。改变12(2OH)-3-12(2OH)·2Br的浓度到60 mmol/L且十二酸钠/12(2OH)-3-12(2OH)·2Br的混合摩尔比β为0.3时,零剪切黏度η0和平台模量G'∞均增大,分别为33.92 Pa·s和46.41 Pa。     

Effect of flow on solutions of rod-coil block co-polymers

An elongational flow field is imposed on a solution of block copolymers consisting of semirigid macromolecules with rigid, rodlike sequences of units in combination with random coil (flexible) units. The problem is formulated according to the lattice treatment of Matheson and Flory. In this formulation, the system consists of rigid blocks whose lengths and locations are fixed by the structure within each macromolecule. These blocks are separated by random coiled units. An excess free energy other than the equilibrium Gibbs free energy of the quiescent solution has to be considered due to the flow field that tends to align the rods. This excess free energy is calculated from the potential energy of rods when a steady-state, homogeneous and irrotational flow field is applied to the solution. The effects of composition, polymer-solvent interaction, size of the co-polymer and flow rates are investigated. Depending on the size and number of rods, some of the chains studied exhibit a biphasic region at equilibrium that shifts to lower concentrations with increasing flow. Longer chains with shorter rods that are isotropic at equilibrium, exhibit a biphasic region at finite values of flow. The degree of orientation increases sharply when the system is biphasic. For larger flows, the orientation function is very close to unity which is perfect orientation.     

Determination of shear viscosity and shear rate from pressure drop and flow rate relationship in a rectangular channel

In this study, we present a unique approach to calculate the shear viscosity and shear rate with the pressure drop and flow rate data from a channel having a rectangular cross-section with a height-to-width ratio (H/W) of close to one. The derived equation was verified with experimental data from rectangular dies whose height-to-width ratio (H/W) ranges from 0.1 to 1. It was confirmed that the proposed approach is reliable for the calculation of the shear viscosity and shear rate from the flow data in a rectangular channel.     

Effect of Silica Nanoparticles on Wormlike Micelles with Different Entanglement Degrees

Enhancing the viscoelastic properties of wormlike micelles by adding nanoparticles has been widely reported. Various mechanisms have been proposed to explain how nanoparticles strengthen the network formed by wormlike micelles. It remains unclear whether nanoparticles produce the same effect on systems with different entanglement degrees. To clarify this issue, the concentration of potassium chloride was used to control the entanglement degree of wormlike micelles. The rheological behavior of different nanoparticle-enhanced wormlike micellar systems (NEWMS) was investigated using rheology. Three critical parameters including zero-shear viscosity (η₀), relaxation time (τ_R), and contour length (L) were calculated to analyze the effect of nanoparticles on the different wormlike micellar systems. An appropriate mechanism describing the interaction between nanoparticles and wormlike micelles with different structures was proposed.     

The numerical simulation of some contraction flows of highly elastic liquids and their impact on the relevance of the Couette correction in extensional rheology

Existing experimental data on planar and axisymmetric contraction flows of constant-viscosity and shear-thinning elastic liquids have presented rheologists with some provocative challenges, some of which we hope to discuss in this paper by carrying out numerical simulations for various constitutive models. Amongst the questions we hope to address are the following:

1.

Why do existing numerical simulations for the Oldroyd B model fail to predict the significant increases observed in the Couette correction for Boger fluids?

2.

What are the roles of ‘normal stress differences’ and ‘extensional viscosity’ in determining the Couette correction?

3.

What is the future for contraction-flow experiments in providing a measure of ‘resistance to stretch’?

In order to make headway, we shall concentrate on the axisymmetric contraction-expansion 4:1:4 geometry with rounded corners, which from a numerical standpoint is easier to handle than the more popular 4:1 contraction geometry with sharp corners. (There is sufficient evidence in the experimental literature to indicate that the contraction-expansion geometry shows many of the features found in the 4:1 contraction geometry.)     

Effects of viscosity and relaxation time on the hydrodynamics of gas–liquid systems

Effects of liquid properties on the hydrodynamics of gas–liquid systems were investigated in lab-scale bubble column (BC) and internal loop airlift (ILA). Alginate solutions, a glycerol solution and a Boger fluid were adopted to separately address the effects of viscosity and of surface tension for Newtonian fluids, and the effects of relaxation time for non-Newtonian fluid characterized by approximately constant viscosity (low shear thinning). Hydrodynamic regimes were characterized in terms of overall gas holdup, gas–liquid mass transfer coefficient, drift-flux and liquid circulation velocity. The superficial gas velocities at the transition between hydrodynamic regimes (homogenous regime–vortical-spiral regime–heterogeneous regime) as a function the liquid viscosity was characterized by a maximum. The same behavior was observed for the maximum stable gas holdup and gas–liquid mass transfer coefficient in BC. Viscosity enhances homogeneous regime stability for μ<4.25 mPa s, in BC, and μ<7.68 mPa s, in ILA. For non-Newtonian fluids the transition velocity increases with liquid elasticity. The stabilization mechanism related to the relaxation time of Boger fluids has been discussed.     

聚合物熔体延伸粘度的研究方法

聚合物熔体的延伸粘度是影响聚合物熔体流动特性和成型制品性能的重要因素。本文较为系统地介绍了聚合物熔体延伸粘度的理论和实验研究方法,着重介绍了Cogswell、Gibson、Binding和Berstered等人的理论研究工作,为进一步研究熔体的延伸粘度提供思路。     

Predicting laminar-turbulent transition in Poiseuille pipe flow for non-Newtonian fluids

We present a new phenomenological approach for quantifying laminar-turbulent transition in pipe flow. This criterion is based on averaging a local Reynolds number to give Re_G. Our localised parameter shows strong radial variations that are maximal at approximately the radial positions where puffs first appear during the first stages of turbulent transition. We present comparative data for experiments conducted with Glycerin, Xanthan and Carbopol solutions, each of which serves to demonstrate the validity of our approach.