A numerical study of the flow of Bingham-like fluids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics (SPH) based method

In this paper, a Lagrangian formulation of the Navier–Stokes equations, based on the smoothed particle hydrodynamics (SPH) approach, was applied to determine how well rheological parameters such as plastic viscosity can be determined from vane rheometer measurements. First, to validate this approach, a Bingham/Papanastasiou constitutive model was implemented into the SPH model and tests comparing simulation results to well established theoretical predictions were conducted. Numerical simulations for the flow of fluids in vane and coaxial cylinder rheometers were then performed. A comparison to experimental data was also made to verify the application of the SPH method in realistic flow geometries. Finally, results are presented from a parametric study of the flow of Bingham fluids with different yield stresses under various applied angular velocities of the outer cylindrical wall in the vane and coaxial cylinder rheometers. The stress, strain rate and velocity profiles, especially in the vicinity of the vane blades, were computed. By comparing the calculated stress and flow fields between the two rheometers, the validity of the assumption that the vane could be approximated as a cylinder for measuring the rheological properties of Bingham fluids at different shear rates was tested.     

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 simple shear cell for the direct visualization of step-stress deformation in soft materials

We introduce a custom-built stress-controlled shear cell coupled to a confocal microscope for direct visualization of constant-stress shear deformation in soft materials. The torque generator is a cylindrical Taylor–Couette system with a Newtonian fluid between a rotating inner bob and a free-to-move outer cup. A spindle/cone assembly is coaxially coupled to the cup and transfers the torque exerted by the fluid to the sample of interest in a cone-and-plate geometry. We demonstrate the performance of our device in both steady-state and transient experiments with different viscoelastic materials. Our apparatus can conduct unidirectional constant-stress experiments as accurately as most commercial rheometers, with the capability to directly visualize the flow field using tracer particles. Further, our step-stress experiments on viscoelastic materials are devoid of creep ringing, which is an advantageous aspect of our torque generation mechanism. We believe that the device presented here could serve as a powerful and cost-effective tool to investigate the microstructural determinants of nonlinear rheology in complex fluids.     

Development of a new mixing rheometer for studying rheological behaviour of concentrated energetic suspensions

The overall objective is to present a procedure based on a Couette analogy to quantitatively analyse torque/rotor speed data and extract viscosity/shear-rate curves using a non-conventional geometry. Diphasic flows of energetic concentrated suspensions of melt-cast insensitive explosives exhibit particular rheological properties. The characterization of these complex fluids may be a challenging task when conventional rheometers are used. Placing these dense suspensions in a classic cylindrical geometry may lead to a partial destruction of the internal fluid structure. To prevent that, a “RheoXF” a mixer-type rheometer has been developed: it consists of a mixing device with quite a complex geometry rotating in a cylindrical tank. To evaluate the rheological constants (virtual radius, virtual shear rate and stress constants) of thus mixing rheometer, we used five Newtonian fluids. After this calibration, the rheological characterizations were carried out on five formulations. The unique parameter which changes in these formulations is the batch's origin of a secondary explosive: the 3-nitro-1,2,4-triazole-5-one. These energetic particles differ by their morphology, maximum packing density and may be by their process synthesis. After having determined pseudoplastic parameters, a correlation has been made with the evolution of maximum packing density values calculated with De Larrard model.     

The yield surface of viscoelastic and plastic fluids in a vane viscometer

Vane viscometers are often used to investigate the low shear rate properties of plastic fluids. The shear stress is determined by assuming that the material is held in the space between the vane blades so that it behaves like a rigid cylinder. Experimental evidence supports this assumption and the aim of the present study is to model numerically the yield process in a vane rheometer using viscoelastic and plastic fluids. The finite element method has been used to model the behavior of Herschel-Bulkley (Bingham), Casson and viscoelastic (Maxwell type) fluids. The penalty function approach for the pressure approximation and a rotating reference frame are used together with fine meshes containing more than 1300 elements. The results show that for Herschel-Bulkley (Bingham), and Casson fluids a rotating rigid cylinder of fluid is trapped inside the periphery of the vane, the shear stress is uniformly distributed over the surface of the cylinder. Finally a modified second order fluid is used to simulate the viscoelastic behaviour, anticipated to be an intermediate between the elastic deformation and the plastic flow, to provide a more realistic simulation of the yield process about a vane. In this case, contrast with the concentration of the elastic strain rate at the blade tips, a nearly uniform distribution of the plastic shear rate is still found. This implies that the plastic shear always distributes uniformly during the entire yielding process. Evidently the assumption of uniform shear on a rotating cylinder of material occluded in the blades of a vane is a valid and useful model for many types of fluid possessing a yield stress.     

Effect of viscoelasticity on the rotation of a sphere in shear flow

When particles are dispersed in viscoelastic rather than Newtonian media, the hydrodynamics will be changed entailing differences in suspension rheology. The disturbance velocity profiles and stress distributions around the particle will depend on the viscoelastic material functions. Even in inertialess flows, changes in particle rotation and migration will occur. The problem of the rotation of a single spherical particle in simple shear flow in viscoelastic fluids was recently studied to understand the effects of changes in the rheological properties with both numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346] and experiments [Snijkers et al., J. Rheol. 53 (2009) 459–480]. In the simulations, different constitutive models were used to demonstrate the effects of different rheological behavior. In the experiments, fluids with different constitutive properties were chosen. In both studies a slowing down of the rotation speed of the particles was found, when compared to the Newtonian case, as elasticity increases. Surprisingly, the extent of the slowing down of the rotation rate did not depend strongly on the details of the fluid rheology, but primarily on the Weissenberg number defined as the ratio between the first normal stress difference and the shear stress.In the present work, a quantitative comparison between the experimental measurements and novel simulation results is made by considering more realistic constitutive equations as compared to the model fluids used in previous numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346]. A multimode Giesekus model with Newtonian solvent as constitutive equation is fitted to the experimentally obtained linear and nonlinear fluid properties and used to simulate the rotation of a torque-free sphere in a range of Weissenberg numbers similar to those in the experiments. A good agreement between the experimental and numerical results is obtained. The local torque and pressure distributions on the particle surface calculated by simulations are shown.     

Studies on transport phenomena in polymer solutions and suspensions flowing through tubes of tortuous wall geometry

Attempts have been made to analyse the momentum and heat transfer characteristics in tortuous flow of non-Newtonian fluids such as suspensions and polymer solutions through tubes of diverging–converging geometry. The results of the study indicate that the transfer coefficients are significantly higher in such systems as compared to the conventional couette flow (through uniform cylindrical tubes). Moreover, the simultaneous increase in pressure drop due to the tortuous wall geometry has been observed to be relatively insignificant. Fluids with different rheological characteristics such as Bingham plastic fluids, pseudoplastic fluids, Ellis model fluids and fluids obeying Reiner–Philippoff rheology have been studied. The specific advantages of these geometries in providing enhanced performance efficiency have been effectively highlighted.     

A double wall-ring geometry for interfacial shear rheometry

The rheological properties of complex fluid interfaces are of prime importance in a number of technological and biological applications. Whereas several methods have been proposed to measure the surface rheological properties, it remains an intrinsically challenging problem due to the small forces and torques involved and due to the intricate coupling between interfacial and bulk flows. In the present work, a double wall-ring geometry to measure the viscoelastic properties of interfaces in shear flows is presented. The geometry can be used in combination with a modern rotational rheometer. A numerical analysis of the flow field as a function of the surface viscoelastic properties is presented to evaluate the non-linearities in the surface velocity profile at a low Boussinesq number. The sensitivity of the geometry, as well as its applicability, are demonstrated using some reference Newtonian and viscoelastic fluids. Oscillatory and steady shear measurements on these reference complex fluid interfaces demonstrate the intrinsic sensitivity, the accuracy, and the dynamic range of the geometry when used in combination with a sensitive rheometer.     

Transient finite element analysis of generalized Newtonian coextrusion flows in complex geometries

A two-dimensional transient finite element model capable of simulating problems related to two-layer polymer flows has been developed. This technique represents an effective tool which can be used to study the possibility of the onset of interfacial instability in coextrusion flows, considering melt rheology as well as the fluid–geometry interaction. A code has been developed to solve the transient problem of the flow of bi-component systems of Newtonian and generalized Newtonian fluids through parallel plates and complex geometries, such as: 2:1 abrupt expansion, 2:1 (30°) expansion, 4:1 abrupt contraction and 4:1 tapered (30°) contraction. Solutions are compared with experimental data from the literature and results provided by linear stability analysis (LSA) for the case of parallel plate flows. Numerical results are in agreement with LSA results for the parallel plate geometry cases studied. The expansion geometries tend to stabilize flows in the parallel plate section downstream of the expansion. Contractions may give rise to break-up of the interface depending on the flow conditions. © 1998 John Wiley & Sons, Ltd.     

Obtaining the steady shear rheological properties and apparent wall slip velocity data of a water-in-oil emulsion from gap-dependent parallel plate viscometry data

A two-stage Tikhonov regularisation procedure has been used to obtain rheological properties for a high internal phase emulsion from gap-dependent steady-state parallel plate shear data. This method is beneficial in that it can convert the steady shear data into rheological property functions. The built-in regularisation parameters of the method are able to keep noise amplification under control. The two-stage method is able to obtain not only the shear stress–shear rate function but also the apparent slip velocity as a function of wall shear stress. The method is such that it obtains the rheological functions over the maximum range of shear rate covered by the data. The results obtained using the new method are compared to those obtained using the vane geometry with good agreement being observed.     

Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.     

A study on the limitations of a vane rheometer for mineral suspensions using image processing

This study presents the results from the rheological measurement of clay suspensions using vane geometry in a wide gap configuration. It focuses on how measurement of viscosity cannot be effective for two reasons: the limits of the vane geometry itself and the limits of the material depending on its content of solid particles. Image analysis of the flow while shearing the material is carried out to relate the flow behavior. Several approaches to compute the shear flow curve from torque-rotational velocity data are used. The results demonstrate that the applied setpoint while applying a logarithmic shear rate ramp can be very different from the calculated shear rate from existing theories. Depending on the solid volume fraction of the particles in the mixture, we relate the macroscopic behavior using image analysis and the shear flow curves to the rheophysical regime of the flow of the suspensions. Therefore, this paper has two simultaneous goals: the first one is to describe the physical phenomena which control macroscopic behavior and the second one is to highlight the limits of the vane geometry for viscosity measurement of mineral suspensions like kaolinite pastes.     

A two-phase solver for complex fluids: Studies of the Weissenberg effect

In this work a new two-phase solver is presented and described, with a particular interest in the solution of highly elastic flows of viscoelastic fluids. The proposed code is based on a combination of classical Volume-of-Fluid and Continuum Surface Force methods, along with a generic kernel-conformation tensor transformation to represent the rheological characteristics of the (multi)-fluid phases. Benchmark test problems are solved in order to assess the numerical accuracy of distinct levels of physical complexities, such as the interface representation, the influence of advection schemes, the influence of surface tension and the role of fluid rheology. In order to demonstrate the new features and capabilities of the solver in simulating of complex fluids in transient regime, we have performed a set of simulations for the problem of a rotating rod inserted into a container with a viscoelastic fluid, known as the Weissenberg or Rod-Climbing effect. Firstly, our results are compared with numerical and experimental data from the literature for low angular velocities. Secondly, we have presented results obtained for high angular velocities (high elasticity) using the Oldroyd-B model which displayed very elevated climbing heights. Furthermore, above a critical value for the angular velocity, it was observed the onset of elastic instabilities driven by the combination of elastic stresses, interfacial curvature and secondary flows, that to the authors best knowledge, were not yet reported in the literature.     

A novel geometry for rheological characterization of viscoelastic materials

A novel geometry for generating a viscometric flow presents advantages of both cone and plate and parallel plate geometries, regarding uniform shear field and adjustable range of measurement. Kinematics and dynamics of the generated flow have been described mathematically utilizing an orthogonal curvilinear coordinate system based on the shapes of the shearing surfaces which are similar to the surface that generates the flow. Simple equations that allow the calculation of quantities of experimental interest in the rheological characterization of liquid materials, namely, shear rate, shear stress and two normal stress differences, have also been derived.The geometry, called pseudosphere, was tested with two types of fluids (Newtonian and pseudoplastic). Results show that the geometry can be used with low viscosity liquids (Newtonian liquids) by only adjusting the gapH. The behavior of pseudoplastic fluids for both low and moderately high viscosity could also be studied with this geometry. Very reproducible results were obtained when compared with those obtained with cone and plate geometry. Regions of lower shear rate could be studied using only the pseudosphere geometry.     

活性流体流变行为的布朗动力学模拟研究

活性流体在用于开发新材料方面具有巨大潜力, 满足这一需求就要定量掌握活性流体所表现的特殊力学行为, 特别是流变行为. 扩展布朗运动方程, 建立自驱动活性粒子的运动模型, 基于反向非平衡法确定活性流体的黏度, 考察活性粒子体积分数、直行速度和转向扩散系数对活性流体流变行为的影响规律, 确定活性流体特殊流变行为的形成机理. 结果表明, 活性流体的流变曲线可被划分为黏度下降区、过渡区和牛顿区; 活性粒子体积分数越高, 活性流体的非牛顿特性越显著, 活性粒子的直行运动引起活性流体在低剪切速率区域黏度下降, 直行运动和转向运动的耦合作用导致中剪切速率区域流变曲线非单调变化, 活性粒子频繁发生转向运动会导致活性流体非牛顿特性受到抑制; 活性流体的宏观流变学特性和粒子的涨落直接相关, 活性粒子体积分数越高、直行速度越快和转向扩散系数越小, 活性流体中活性粒子越容易产生显著的涨落; 低剪切速率区域内活性粒子涨落明显, 随着剪切速率增大, 活性粒子的涨落逐渐被削弱, 粒子的聚集结构不断被破坏, 最终体系的流变行为类似一般被动流体.      

Determination of thermal conductivity of liquids and polymers from batch mixer data

The paper proposes a new technique allowing the determination of thermal conductivity of liquids and polymer melts with unknown rheological behavior from batch mixer data; the mixing elements can have simple or complex geometries. The simple mixer is represented by an equivalent simple Couette with a cup and a bob having an effective hydrodynamic (or thermal) radius, and the true batch mixer is represented by two adjacent concentric cylinder viscometer. Using the universal internal effective radius, the thermal conductivity for four polymers was estimated from the batch mixer temperature?Crotor speed and torque data. A good agreement was found with the values measured by transient line source method and those of the literature. Melt activation energy was calculated from torque?Ctemperature batch mixer data, and the obtained values were found to be consistent with the values extracted from low-amplitude oscillatory shear experiments as well as with the available published data.     

A generalized equation for rheology of emulsions and suspensions of deformable particles subjected to simple shear at low Reynolds number

We present analyses to provide a generalized rheological equation for suspensions and emulsions of non-Brownian particles. These multiparticle systems are subjected to a steady straining flow at low Reynolds number. We first consider the effect of a single deformable fluid particle on the ambient velocity and stress fields to constrain the rheological behavior of dilute mixtures. In the homogenization process, we introduce a first volume correction by considering a finite domain for the incompressible matrix. We then extend the solution for the rheology of concentrated system using an incremental differential method operating in a fixed and finite volume, where we account for the effective volume of particles through a crowding factor. This approach provides a self-consistent method to approximate hydrodynamic interactions between bubbles, droplets, or solid particles in concentrated systems. The resultant non-linear model predicts the relative viscosity over particle volume fractions ranging from dilute to the the random close packing in the limit of small deformation (capillary or Weissenberg numbers) for any viscosity ratio between the dispersed and continuous phases. The predictions from our model are tested against published datasets and other constitutive equations over different ranges of viscosity ratio, volume fraction, and shear rate. These comparisons show that our model, is in excellent agreement with published datasets. Moreover, comparisons with experimental data show that the model performs very well when extrapolated to high capillary numbers (C a?1). We also predict the existence of two dimensionless numbers; a critical viscosity ratio and critical capillary numbers that characterize transitions in the macroscopic rheological behavior of emulsions. Finally, we present a regime diagram in terms of the viscosity ratio and capillary number that constrains conditions where emulsions behave like Newtonian or Non-Newtonian fluids.     

A model for the thermorheological behavior of viscoelastic fluids

Using a power-law ansatz for the temperature dependence of the shear modulus on the level of internal variables, the thermorheological behavior is modeled for viscoelastic fluids of a special group of rheological constitutive equations (rate-type models). The model parameter introduced characterizes thermoelastic contributions. The relation between the model parameter and the physical quantities appearing in deformation processes is discussed. Based on the chosen temperature dependence of the shear modulus, thermodynamically consistent equations like the nonlinear rheological constitutive equation and the temperature equation are derived. The special cases of entirely entropy and energy elastic fluids are also considered. The thermorheological behavior (exo-, - or endothermal processes) of a viscoelastic fluid in a stress-growth experiment followed by relaxation is analyzed with respect to the model parameter.     

Rheology of wormlike micelles from non-equilibrium molecular dynamics

In this work, the rheology of complex fluids, i.e., surfactants of varying concentration in a Lennard–Jones fluid, is analyzed with non-equilibrium molecular dynamics simulations. The molecular model considers that the surfactant molecule is composed of a hydrophilic head, affine to solvent, and a hydrophobic tail made of four monomers. The solvent is modeled by a Lennard–Jones fluid, which shows mostly a Newtonian behavior, but at relatively high shear rates, a slight shear-thinning followed by a slight shear thickening are exhibited. The intermolecular potential produces an equilibrium configuration, in which the surfactant molecules self-assemble in a wormlike micelle. With the aim to analyze the system behavior with various stress fields, two flows are simulated under non-equilibrium conditions: (1) simple shear and (2) Poiseuille's flow. In simple shear, by keeping the velocity of the upper plate of the flow cell constant, a monotonic flow curve is predicted within a range of shear rates. At low shear rates, a concentration-dependent Newtonian region of viscosity η₀ corresponds to an isotropic condition in which the wormlike micelle preserves its equilibrium conformation. At intermediate shear rates, the solution exhibits a slight shear thinning, generating bands placed normal to the gradient direction (gradient banding). At high shear rates the solution exhibits shear-thickening, with bands now generated normal to the vorticity direction. These predictions by molecular models explain, to our knowledge for the first time, experiments in shear-thickening wormlike micellar solutions, where shear-thickening appears simultaneously with bands generated perpendicular to the vorticity axis. In Poiseuille's flow, we also find agreement between predictions of the model with theoretical developments and experiments performed by other authors.     

Rheological characterization of a solder paste for surface mount applications

Solder pastes used in surface mount soldering techniques (SMT) are very complex suspensions containing high volumes of metallic powder in a carrier fluid. The rheological complexity results largely from the carrier fluid itself, which is a suspension of colloidal particles. In this work, we have characterized the rheological properties of a typical carrier fluid and its solder paste containing 64 vol.% metallic powder. A six-blade vane geometry was used to avoid wall slip and sample fracture. All measurements were carried out following pre-shearing and rest time in order to obtain reproducible results. Steady shear experiments showed that the solder paste was highly shear-thinning and thixotropic. In oscillatory shear, the linear viscoelastic domain was found to be very narrow for both the suspending fluid and the paste. Frequency sweep tests in the linear domain revealed a gel-like structure with a nearly constant G′ for the suspending fluid and a slightly increasing G′ for the solder paste. From creep experiments, a yield stress of about 40 Pa was determined for the suspending fluid at temperatures between 25 and 40°C, and of 100 Pa at 4°C. A much larger yield stress, 480 Pa, was determined for the solder paste at 25°C.