Yield stress of structured fluids measured by squeeze flow

Various structured fluids were placed between the parallel circular plates of a squeeze-flow rheometer and squeezed by a force F until the fluid thickness h was stationary. Fluid thickness down to a few microns could be measured. Most fluids showed two kinds of dependence of f on h according to an experimentally-determined thickness h ^*. If h > h ^* then F varied in proportion to h ⁻¹ as predicted by Scott (1931) for a fluid with a shear yield stress τ₀. The magnitude of τ₀ from squeeze-flow data in this region was compared with the yield stress measured by the vane method. For some fluids τ₀ measured by squeeze flow was less than the vane yield stress, suggesting that the yield stress of fluid in contact with the plates was less than the bulk yield stress. If h < h ^* then F varied approximately as h ^−5/2 and the squeeze-flow data in this region analysed with Scott's relationship gave a yield stress which increased as the fluid thickness decreased. This previously unreported effect may result from unconnected regions of large yield stress in the fluid of size similar to h ^* which are not sensed by the vane and which become effective in squeeze flow only when h < h ^*. Received: 13 December 1999/Accepted: 4 January 2000     

Processing the Couette viscometry data using a Bingham approximation in shear rate calculation

This paper presents an approach to computing the shear flow curve from torque–rotational velocity data in a Couette rheometer. The approximation techniques in shear rate calculation are generally dictated by the radius ratio between coaxial cylinders and the rheological behaviour of fluid tested. Here, the approach consists in analysing the sheared material as a Bingham fluid and computing an average shear rate when the fluid in the cylindrical gap is partially and fully sheared. We focus in particular on the applicability of the Bingham approximation in shear rate calculation. First, the approach is assessed by examining synthetic data generated with Newtonian, non-Newtonian and yield stress materials with known properties, varying the gap radius ratio. The results, which are compared with commonly used techniques in shear rate calculation, prove the relevance of the proposed approach. Finally, its efficiency is examined by applying it to process Couette data of yield stress fluids taken from published works.     

Rheological characterization of complex fluids in electro-magnetic fields

The paper is focused on the experimental investigations and rheological characterisations in magnetic and electric fields of liquids based on water in crude oils emulsions, added with ferrofluids (two types of crude oils are used in experiments: asphaltic and paraffinic, respectively). The final samples disclose weakly effects in the presence of magnetic field (saturated magnetization: M_n < 300 [G]) and behave almost as isolators in electric field (conductivity: σ < 10⁻⁵ [S/m]). The main goal of the study is to explore to what extent rheometry of complex fluids in electric and magnetic fields is able to offer value information about the internal structure of the samples. The experimental results prove that anomalous rheological behaviour (thixotropy, non-monotonic flow curve or viscosity function) of a complex fluid (in our case, emulsions based on paraffinic oil) generate also thixotropic properties and non-monotonic answers in the presence ferrofluids, under low magnetic and/or electric fields intensity. Our prospective study suggests that novel experimental procedures based on interaction: electro-magnetic field–complex fluids can be developed, in order to determine indirectly some relevant rheological properties of the complex fluids with internal network structure.     

Rheo-PIV of a yield-stress fluid in a capillary with slip at the wall

An analysis of the yielding and flow behavior of a model yield-stress fluid, 0.2 wt% Carbopol gel, in a capillary with slip at the wall has been carried out in the present work. For this, a study of the flow kinematics in a capillary rheometer was performed with a two-dimensional particle image velocimetry (PIV) system. Besides, a stress-controlled rotational rheometer with a vane rotor was used as an independent way to measure the yield stress. The results in this work show that in the limit of resolution of the PIV technique, the flow behavior agrees with the existence of a yield stress, but there is a smooth solid?Cliquid transition in the capillary flow curve, which complicates the determination of the yield stress from rheometrical data. This complication, however, is overcome by using the solely velocity profiles and the measured wall shear stresses, from which the yield-stress value is reliably determined. The main details of the kinematics in the presence of slip were all captured during the experiments, namely, a purely plug flow before yielding, the solid?Cliquid transition, as well as the behavior under flow, respectively. Finally, it was found that the slip velocity increases in a power-law way with the shear stress.     

振荡剪切力作用下的电流变流体黏弹性研究

利用HAAKE RS600流变仪对电流变体进行了强制振荡实验研究,得到了流体在不同 剪切应力幅和振荡频率下,电流变体储能模量、损耗模量、损耗因子随剪切应力和 剪切频率的变化规律.     

Processing the capillary viscometry data of fluids with yield stress

The capillary viscometer is used to measure the shear stress-shear rate relationship of a wide range of purely viscous fluids. It is however not considered as an appropriate instrument for obtaining the yield stress and the post-yield behaviour of fluids that have a yield stress. This is partly because conventional methods of processing the capillary viscometry data of purely viscous fluids cannot be applied to similar data of fluids with yield stress. The unavoidable experimental noise in the capillary data, particularly at low shear rates, also makes it difficult to obtain a reliable estimate of the yield stress from capillary data. In this investigation the problem of converting the capillary viscometry data of yield stress fluids into a shear stress-shear rate curve and a yield stress is formulated as a Volterra integral equation of the first kind. This is an ill-posed problem i.e. noise in the data will be amplified by inappropriate methods of data processing. A method, based on Tikhonov regularisation that takes into account the ill-posed nature of the problem, is then developed to solve this problem for fluids with yield stress. The performance of this method is assessed by applying it to a set of “synthetic” capillary viscometry data with added random noise and to a set of experimental data for a concentrated suspension of TiO₂ taken from the literature. In both cases Tikhonov regularisation was able to extract the complete shear properties of these fluids from capillary viscometry data alone. Received: 22 November 1999/Accepted: 17 December 1999     

Squeeze flow between plane and spherical surfaces

Experiments are described in which a constant force F squeezed a fluid, either between two parallel circular plates, or between a plate and convex spherical lens. Newtonian fluids obeyed the relation of Stefan (1874) for plates, and the relation of Adams et al. (1994) for plate and lens. The non-Newtonian yield stress fluids Brylcreem, Laponite and Sephadex were squeezed between plates of various diameter D to attain a stationary separation h. Only for separations greater than h ^* (which depended on the fluid) did Brylcreem and Laponite obey the relation F/D ³ ∝ h ⁻¹ of Scott (1931) and give a yield stress in agreement with the vane method. For Sephadex the dependence of F/D ³ on h disagreed with Scott's relation, but varied as h ^−5/2 for h > 0.6 mm and h ^−3/2 for h < 0.6 mm. On rotating one plate in its plane the yield stress fluids at a fixed F suffered a marked decrease of h. This, and the existence of h ^*, are discussed in terms of the soft glassy material model of Sollich et al. (1997) and Sollich (1998). Brylcreem and Laponite were squeezed between a plate and lenses of various curvature and their yield stress obtained using the relation of Adams et al. (1994) was compared with measurements by plate-plate squeeze-flow and vane methods. Received: 12 April 2000 Accepted: 26 October 2000     

Load and rheometric unit for the test of magnetorheological fluid

The article describes the original design of a slit flow rheometer. The behavioral problems of MR fluids and the main deviation from the commonly introduced Bingham model, which describes the MR fluid, are explained at the beginning of this article. Furthermore, the usual operating parameters of the MR fluids and devices are defined, such as: shear rate, viscosity in the off-state, yield stress, their dependence on temperature and the expected life of the filling. In the absence of a suitable rheometer a new design of rheometer was proposed, which allows long-term testing of MR fluids under real loading conditions. This article describes the important details of the construction. Particular attention is devoted to temperature measurement, calibration of the rheometer and data analysis, including mathematical tools and statistical evaluation of a set of measured points.     

Measuring static yield stress of electrorheological fluids using the slotted plate device

An electrorheological (ER) response is defined as the dramatic change in rheological properties of a suspension of small particles due to the application of a large electric field transverse to the direction of flow. ER fluids are typically composed of nonconducting or semiconducting particles dispersed in a nonconducting continuous phase. A sufficiently large electric field will cause ER fluids to solidify, giving rising to a yield stress. Many applications in torque and stress transfer devices were proposed employing the reversible yielding behavior of ER fluids. Successful applications depend on a large yield stress of ER fluids and therefore accurate measurements of the yield stress of ER fluids are required. Reported experimental yield stresses of ER fluids have been dynamic yield stresses obtained by extrapolating the shear stress–shear rate data to zero-shear rate. It would be very helpful to the understanding of ER behaviors and the applications of ER fluids to be able to measure the static yield stress of ER fluids accurately. The slotted plate technique has been shown to be a successful method to determine the static yield stress of suspensions. The values obtained via the slotted plate method are static yield stress as the platform is designed for extremely low-speed motion. In this study, we modified the slotted plate device for the application of large electric fields and measured the static yield stress of TiO₂ ER fluids under various electric fields. The measured static yield stress values are also compared with the static yield stress values from a commercial rheometer.     

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.     

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number (Wi > 1).     

The oscillatory squeeze flow rheometer: comprehensive theory and a new experimental facility

In this paper, we give detailed attention to a relatively recent method for the determination of the linear dynamic properties of viscoelastic systems, namely, the so-called oscillatory squeeze flow (OSF) technique. We provide a comprehensive theory for the OSF rheometer, which includes a full discussion of the influence of fluid inertia. In the process, it is argued that, fortuitously perhaps, fluid inertia is more easily accommodated in the OSF rheometer than in the corresponding torsional-flow techniques. A new version of the OSF rheometer is described and experimental results on a set of viscoelastic systems are used to demonstrate the versatility of the technique. In the process, the potential use of the instrument within an industrial quality control environment is stressed.     

一种平板式磁流变体静态屈服应力测试方法

针对目前国内外磁流变体（MR流体）屈服应力测试设备较为缺乏这种状况,本文设计加工了一套平板式磁流变体静态屈服应力测试设备,并用该设备对本文实验制作的两种MR流体进行了屈服应力测试,同时探讨了磁感应强度、分散相体积浓度、分散相粒度对这两种MR流体静态屈服应力的影响。     

Axial annular flow of plastic fluids: dead zones and plug-free flow

In axial annular flow, the shear stress decreases from its value τ(κR) at the inner cylinder to 0 at r = λR and increases from then on to τ(R) at the outer cylinder. For plastic fluids with a yield stress τ _c, λ will be such that flow commences when τ(κR) = τ(R) = τ _c. For fluids with position-dependent yield stresses (electro- and magnetorheological fluids are examples), the situation is more complex. While it is possible that yielding and flow occur everywhere, it is also possible that flow occurs only in parts of the fluid-filled space, and a dead zone (region in which the fluid is at rest) close to one of the walls exists. In that case, the fluid will flow no matter how small the applied pressure difference is. If P is large enough, the dead zone ceases to exist and flow without any plug is possible. The fluid flows as if no yield stress exists.

Rheological aspects of dense lignite–water suspensions; structure development on consecutive flow loops

Aspects of dense lignite–water slurries (LWS) rheology were investigated using controlled stress and controlled strain rheometers with parallel disks and Couette geometries. During the preparation of the slurries, the achieved solids volume fractions were up to 0.425 and the particle size distributions were polydispersed with sizes up to 300 μm. In the ascending parts of consecutive flow loops, a slope transition of the flow curve was observed and studied in relation to the solids volume fraction. The obtained results with the different geometries and rheometers were qualitatively the same. By following the model proposed by Cheng (Rheol Acta 42:372–382, 2003) for thixotropic fluids, and taking into account the yield stress appearance, a suitable correlation for LWS is proposed, which is consistent with the experimental flow curves.     

Experimental validation of steady shear and dynamic viscosity relation for yield stress fluids

A common problem when studying yield stress fluids under steady shear in rotating rheometry is that of sample fracture. It is therefore preferable to work with oscillating shear, where fracture is limited. Doraiswamy et al. (1991) proposed a model for yield stress fluids that predicts the relation: ^*( _m ) = (y) between the viscosity in steady shear and the complex viscosity in dynamic shear. The present study validates this relation experimentally with both controlled stress and controlled strain, and demonstrates its limitations. Three yield stress fluids were used: a lubricating grease with lithium based soap, a thixotropic dispersion of colloidal silica in a polymer solution and a non-thixotropic aqueous gel.     

Rheometry on magnetorheological (MR) fluids

Test fixtures of a commercial concentric cylinder rheometer (Physica Rheolab MC 20) were modified to enable measurements under magnetic inductions up to 0.5 Tesla in a shear rate range of 0.1 up to 1000 s ^–1 and temperatures 0° to 150°C. In the 2 x90°-cups only two 90° sectors of the stationary part of the double concentric cylinder arrangement are submitted to the magnetic field which is created outside the test tools by an electromagnet. A prototype of a 360°-cup contains the electromagnet within the cup and avoids the correction necessary for the sector geometry. Measurements are shown for a carbonyl iron MR fluid and two nano MR fluids. An encouraging comparison of the viscosity function and MR effect (shear stress changes due to the field) measured by using the various cups is presented. The detailed investigation of the magnetic field distribution in the tools yields a distinct radial field gradient and also stray fields that make the quantification of the effective field in the gap difficult. The change of the field when the gap is filled with MR fluid is addressed. MR effects up to 13 000 Pa have been found, the limited torque range of the rheometer making it necessary to use relatively small gap dimensions which introduce errors due to edge effects. Shear rates up to 40000 s^–1 as typical for the application in dampers were investigated by a piston-driven capillary rheometer making use of a thermostated rectangular slit with superimposed magnetic field. A satisfactory agreement of the magnetorheological data with the concentric cylinder results is found in the overlapping shear rate range.     

Simultaneous determination of shear and extensional viscosities and wall slip by on-line rheometry with parameter fitting: an application to EPDM rubber

Shear and extensional viscosities and wall slip are determined simultaneously under extrusion processing conditions using an on-line rheometer. Because it is not possible to independently control flow rate and temperature, classical methods for interpretation of capillary data cannot be used with on-line rheometry. This limitation is overcome using computational optimization to fit parameters in a flow model. This consists of three parts, representing shear viscosity, extensional viscosity, and wall slip. Three-parameter, power law forms, based on local instantaneous deformation rates and including temperature dependence, are used for each, and analytic solutions applied for entry flow and flow in the capillary. For entry flow, the Cogswell–Binding approach is used, and for developed flow in the capillary a solution incorporating wall slip is derived. The rheometer, with interchangeable capillaries, is mounted in place of the die on a rubber profile extrusion line. Pressure drops and temperatures for extrusion of an EPDM rubber through 2 mm diameter capillaries of length 0, 2, 3, 4, and 5 mm are logged and flow rates determined for a range of extruder speeds (5 to 20 rpm). Pressures ranged from 60 to 75 bar and temperatures from 86 to 116 °C. Mean flow velocity in the capillaries was between 5 × 10⁻³ and 5 × 10⁻¹ m s⁻¹. The nine material parameters are optimized for best fit of the analytic pressure drops to experimental data, using about 100 data points, with the Levenberg–Marquardt method. It is concluded that flow is dominated by extension and wall slip. Shear flow appears to play little part. The slip model indicates that slip velocity increases much more rapidly than the wall shear stress (in the range 0.5–1 MPa) and decreases with temperature for a given stress level. Results for the (uniaxial) extensional viscosity represent an engineering approximation to this complex phenomenon at the high strains (approximately 200) and high extension rates (up to 800 s⁻¹) applying in the extrusion. Results indicate a slight extension hardening and a decrease with temperature. Results are put into the context of the available studies in the literature, which, particularly with regard to wall-slip and extensional flow, consider conditions far removed from those applying in industrial extrusion. The present methods provide a powerful means for flow characterization under processing conditions, providing data suitable for use in computer simulations of extrusion and optimization of die design.     

The end correction for power-law fluids in the capillary rheometer

The finite element scheme developed by Nickell, Tanner and Caswell is used to compute the entry and exit losses for creeping flow of power-law fluids in a capillary rheometer. The predicted entry losses for a Newtonian fluid agree well with available experimental and theoretical results. The entry losses for inelastic power-law fluids increased with decreasing flow behaviour index and show an increasing deviation from available upper bound results as the flow behaviour index in the power-law decreases.The exit losses are found to be finite for inelastic power-law fluids and increase as the flow behaviour index decreases. The predicted die swell for Newtonian fluids agrees well with the available experimental data while the influence of shear thinning is to reduce the die swell.The end correction which is the sum of the entry and exit losses relative to twice the viscometric wall shear stress varies from 0.834 for n = 1 to 2.917 for n = 1/6. This figure reaches a very high value as n tends to zero. The experimental variation in the Couette correction factor in capillary rheometry is explained in terms of the shear thinning characteristics of the fluid. It is concluded that the exit flow is not viscometric, contrary to a common assumption.     

Transient and steady-state drag in foam

The steady-state force exerted on a sphere moving at constant speed through an aqueous foam is studied experimentally. The dependence of the force on container size indicates that the moving sphere is surrounded by a fluidised region that extends approximately one sphere radius into the foam. The force increases with the speed of the sphere, but with a finite zero-speed intercept which is a measure of the yield stress of the foam. The steady-state force as a function of pulling speed yields a flow curve which can be described by a Herschel-Bulkley constitutive relation. The transient build-up of the force when motion starts, and its relaxation when motion stops, are also studied. While the initial build-up has a single time constant inversely proportional to the imposed shear rate, the relaxation involves three distinct processes which we relate to events on the scale of the individual bubbles making up the foam.