Strain stiffening of non-colloidal hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region

Concentrated hard sphere suspensions often show an interesting nonlinear behavior, called strain stiffening, in which the viscosity or modulus starts to increase at critical strain amplitude. Sudden increase of rheological properties is similar to shear thickening; however, the particle dynamics in the strain stiffening under oscillatory shear flow does not necessarily coincide with the mechanism of shear thickening under step shear flow. In this study, we have systematically investigated the nonlinear rheology of non-colloidal (>1???m) hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region in order to better understand the strain stiffening behavior. The suspensions near liquid-and-crystal coexistence region are known to locally form the closed packing structure. The critical strain amplitude which is the onset of strain stiffening was different for the storage and loss modulus. But they converged to each other as the suspension forms a more crystalline structure. The critical strain amplitude was independent of medium viscosity, imposed angular frequency, and particle size, but was strongly dependent upon particle volume fraction. The onset of strain stiffening was explained in terms of shear-induced collision due to particle motion in the closed packing structure. Nonlinear stress wave-forms, which reflect the micro-structural change, were observed with the onset of strain stiffening. During the strain stiffening, enhanced elastic stress before and after flow reversal was observed which originates from changes in the suspension microstructure. Nonlinearity of the shear stress in terms of Fourier intensity was extremely increased up to 0.55. Beyond the strain stiffening, the suspension responded liquid-like and the nonlinearity decreased but the elastic shear stress was still indicating the microstructure rearrangement within a cycle.     

Non-linear viscoelastic response of magnetic fiber suspensions in oscillatory shear

This paper reports the first study on the large amplitude oscillatory shear flow for magnetic fiber suspensions subject to a magnetic field perpendicular to the flow. The suspensions used in our experiments consisted of cobalt microfibers of the average length of 37 μm and diameter of 4.9 μm, dispersed in a silicon oil. Rheological measurements have been carried out at imposed stress using a controlled stress magnetorheometer. The stress dependence of the shear moduli presented a staircase-like decrease with, at least, two viscoelastic quasi-plateaus corresponding to the onset of microscopic and macroscopic scale rearrangement of the suspension structure, respectively. The frequency behavior of the shear moduli followed a power-law trend at low frequencies and the storage modulus showed a high-frequency plateau, typical for Maxwell behavior. Our simple single relaxation time model fitted reasonably well the rheological data. To explain a relatively high viscous response of the fiber suspension, we supposed a coexistence of percolating and pivoting aggregates. Our simulations revealed that the former became unstable beyond some critical stress and broke in their middle part. At high stresses, the free aggregates were progressively destroyed by shear forces that contributed to a drastic decrease of the moduli. We have also measured and predicted the output strain waveforms and stress–strain hysteresis loops. With the growing stress, the shape of the stress–strain loops changed progressively from near-ellipsoidal one to the rounded-end rectangular one due to a progressive transition from a linear viscoelastic to a viscoplastic Bingham-like behavior.     

The solid–fluid transition in a yield stress shear thinning physical gel

We present an experimental investigation of the solid–fluid transition in a yield stress shear thinning physical gel (Carbopol^® 940) under shear. Upon a gradual increase of the external forcing, we observe three distinct deformation regimes: an elastic solid-like regime (characterized by a linear stress–strain dependence), a solid–fluid phase coexistence regime (characterized by a competition between destruction and reformation of the gel), and a purely viscous regime (characterized by a power law stress-rate of strain dependence). The competition between destruction and reformation of the gel is investigated via both systematic measurements of the dynamic elastic moduli (as a function of stress, the amplitude, and temperature) and unsteady flow ramps. The transition from solid behavior to fluid behavior displays a clear hysteresis upon increasing and decreasing values of the external forcing. We find that the deformation power corresponding to the hysteresis region scales linearly with the rate at which the material is being forced (the degree of flow unsteadiness). In the asymptotic limit of small forcing rates, our results agree well with previous steady state investigations of the yielding transition. Based on these experimental findings, we suggest an analogy between the solid–fluid transition and a first-order phase transition, e.g., the magnetization of a ferro-magnet where irreversibility and hysteresis emerge as a consequence of a phase coexistence regime. In order to get further insight into the solid–fluid transition, our experimental findings are complemented by a simple kinetic model that qualitatively describes the structural hysteresis observed in our rheological experiments. The model is fairly well validated against oscillatory flow data by a partial reconstruction of the Pipkin space of the material’s response and its nonlinear spectral behavior.     

Shear rheometry and visualization of glass fiber suspensions

The nonlinear rheological behavior of short glass fiber suspensions has been investigated in this work by rotational rheometry and flow visualization. A Newtonian and a Boger fluid (BF) were used as suspending media. The suspensions exhibited shear thinning in the semidilute regime and weaker shear thinning in the transition to the concentrated one. Normal stresses and relative viscosity were higher for the BF suspensions than for the Newtonian ones presumably due to enhanced hydrodynamic interactions resulting from BF elasticity. In addition, relative viscosity of the suspensions increased rapidly with fiber content, suggesting that the rheological behavior in the concentrated regime is dominated by mechanical contacts between fibers. Visualization of individual fibers and their interactions under flow allowed the detection of aggregates, which arise from adhesive contacts. The orientation states of the fibers were quantified by a second order tensor and fast Fourier transforms of the flow field images. Fully oriented states occurred for shear rates around 20 s^− 1. Finally, the energy required to orient the fibers was higher in step forward than in reversal flow experiments due to a change in the spatial distribution of fibers, from isotropic to planar oriented, during the forward experiments.     

Prediction of normal stresses under large amplitude oscillatory shear flow

The dynamic response of viscoelastic fluids under large amplitude oscillatory shear (LAOS) has been a subject of long history. In the LAOS flow, the analysis has been mostly focused on shear stress, possibly due to the lack of accurate measurement of normal stress. However, the normal stress may become larger than shear stress at high-strain amplitudes, and thus it is important that we have a good understanding of the normal stress behavior. Furthermore, with the advancement in the instrumentation, it has become possible to get more reliable data. The purpose of this paper is to develop a research platform to analyze and to understand the normal stress behavior of complex fluids under LAOS flow. In this study, we utilized the Giesekus model as a representative constitutive model, and investigated its diverse responses. We defined the dynamic properties corresponding to normal stress, in a similar way to define dynamic moduli from shear stress, and examine their behavior with various analyzing tools. Experimental data were also compared with model predictions. Despite the fact that it is not yet possible to compare all of the predictions because of instrumental limitation, the prediction has been found to fit well with the experimental data. This study is expected to provide a useful framework for further understanding the nonlinear behavior of complex fluids at large deformation.     

矩形截面管内电流变液的流动

基于伽辽金方法，导出了矩形截面直管内泊肃叶流动的一阶和二阶近似解．在此基础上，研究了电流变单链的变形问题，并得到了描述它形状的多项式函数．     

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.     

In situ flow visualization of capillary flow of concentrated alumina suspensions

A new approach was taken to understand the flow behavior of concentrated particle suspensions in pressure-driven capillary flow. The flow of concentrated alumina suspensions in a slit channel was visualized and quantitatively analyzed with modified capillary rheometer. The suspensions showed complex flow behaviors; unique solid–liquid transition and shear banding. At low flow rates, 55 vol% alumina suspension showed a unique transient flow behavior; there was no flow at first and continuous change of flow profile was observed with time. At low shear rates in particular, the suspensions exhibited shear-banded flow profile which could be divided into three regions: the region with low flow rate near the wall, the region with rapid increase of flow velocity to maximum, and the region of velocity plateau. Based on both flow visualization and measurement of shear stress, it was found that the shear-banded flow profile in pressure-driven slit channel flow was strongly correlated with shear stress. The banding in pressure-driven flow was different from that in Couette flow. The banding of concentrated alumina suspensions was unique in that sluggish velocity profile was pronounced and two inflection points in velocity profile was exhibited. In this study, shear banding of concentrated alumina suspensions in slit channel flow was visualized and quantitatively analyzed. We expect that this approach can be an effective method to understand the flow behavior of particulate suspensions in the pressure-driven flow which is typical in industrial processing.     

Theoretical and experimental investigation of the flow of a viscoelastic fluid in the gap between two rotating disks

A theory of the nonlinear viscoelastic behavior of polymer fluids has been constructed in [1]. The theory was used in [2] to investigate the motion of a nonlinear viscoelastic medium under steady and unsteady deformation rates in simple shear flow, and a comparison was made with experiment. The experiments in [2], which were performed on a cone-plate Weissenberg rheogoniometer, indicate that this arrangement is unsuitable for measurements of normal stresses under unsteady conditions in fluids with a fairly high viscosity. Below, we will show the suitability of using a disk-disk Weissenberg rheogoniometer to measure normal stresses in this case for unsteady conditions (transition to steady flow and stress relaxation). In this regard, a theoretical study of the flow of a viscoelastic fluid in the gap between rotating disks is needed. Note that in this case new information will be obtained from a comparison with simple uniform shear flow, since in the flow of a polymer between two disks all three normal stress components contribute to the axial force, while in the gap between a cone and a plate only the first normal stress difference contributes to the normal force.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 25–30, March–April, 1976.     

A self-similar behavior for the relative viscosity of concentrated suspensions of rigid spheroids

A viscosity model for suspensions of rigid particles with predictive capability over a wide range of particle volume fraction and shear conditions is of interest to quantify the transport of suspensions in fluid flow models. We study the shear viscosity of suspensions and focus on the effect of particle aspect ratio and shear conditions on the rheological behavior of suspensions of rigid bi-axially symmetric ellipsoids (spheroids). We propose a framework that forms the basis to microscopically parameterize the evolution of the suspension microstructures and its effect on the shear viscosity of suspensions. We find that two state variables, the intrinsic viscosity in concentrated limit and the self-crowding factor, control the state of dispersion of the suspension. A combination of these two variables is shown to be invariant with the imposed shear stress (or shear rate) and depends only on the particle aspect ratio. This self-similar behavior, tested against available experimental and numerical data, allows us to derive a predictive model for the relative viscosity of concentrated suspensions of spheroids subjected to low (near zero) strain rates. At higher imposed strain rates, one needs to constrain one of the state variables independently to constrain the state of dispersion of the suspension and its shear dynamic viscosity. Alternatively, the obtained self-similar behavior provides the means to estimate the state variables from the viscosity measurements made in the laboratory, and to relate them to microstructure rearrangements and evolution occurring during deformation.     

Transient phenomena in thixotropic systems

A nonlinear rheological model which accounts for the time-dependent elastic, viscous and yielding phenomena is developed in order to describe the flow behavior of thixotropic materials which exhibit yield stress. A key feature of the formulation is a smooth transition from an ‘elastically’ dominated response to a ‘viscous’ response without a discontinuity in the stress–strain curve. The model is phenomenological and is based on the kinetic processes responsible for structural changes within the thixotropic material. As such, it can predict thixotropic effects, such as stress overshoot during start-up of a steady shear flow and stress relaxation after cessation of flow. Thus this model extends a previously proposed viscoplastic model [J. Rheol. 34 (1991) 647] to include thixotropy.An analysis and comparison to experimental data involving oscillatory shear flow are provided to evaluate the accuracy of the model and to estimate the model parameters in a prototype concentrated suspension. The experiments were conducted using a series of concentrated suspensions of silicon particles and silicon carbide whiskers in polyethylene. The data obtained with this experimental system indicated much better agreement between the theory and experiments that obtained in earlier work.     

Shear rate dependence of the normal force of a magnetorheological suspension

An experimental study was made of the normal force in a magnetorheological suspension under shear flow with the magnetic field applied normally to the shear planes. Under no deformation, the normal force was found to increase with magnetic flux density, and acted to push apart the rheometer plates. At the start-up of shearing under a constant shear rate, the normal force decreased with strain and reached a plateau value which became smaller as shear rate was raised. This behaviour can be interpreted in terms of the aggregate model of magnetorheological suspensions: the normal force arises from the elongated aggregates spanning the gap between the plates, and these are broken up into smaller particle clusters under shearing.     

Phase structure change and ER effect in liquid crystalline polymer/dimethylsiloxane blends

The mechanism of the electrorheological (ER) effect in two types of liquid crystalline polymer (LCP)/dimethylsiloxane (DMS) blends was investigated by rheological measurements and by structure observation under electric field and shear flow. The results show that the phase structures of these immiscible blends can be categorized into slipping (low viscosity) and non-slipping (high viscosity) states. In the non-slipping state, higher viscosity LCP domains connect the electrodes. In the slipping state, on the other hand, LCP domains do not connect the electrodes and the shear is mainly confined in the lower viscosity DMS domains. The ER effect (electrically induced viscosity increase) originates from the electrically induced slipping to non-slipping transition. In one of the blends, the ER effect occurs only at high shear rate, since this blend is in non-slipping state even under no field if the shear rate is low. Received: 29 April 1997 Accepted: 3 November 1997     

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.     

Electrorheological properties of PDMS/carbon black suspensions under shear flow

Suspensions of polydimethylsiloxane (PDMS) containing low amounts (1 wt.% or less) of a highly conducting carbon black (CB) filler are rendered conductive and exhibit electrorheological (ER) responses under shear flow when exposed to an externally applied AC electric field. The presence of columnar structures, consisting of CB particles aligned in the direction of the electric field is evidenced through optical microscopy experiments. The appearance of yielding behavior and positive ER response, manifested by an increase in the viscosity of the suspensions, depend strongly on the filler loading, strength of the electric field, magnitude of the shear field, and viscosity of the medium. The responses are stronger at low filler loadings, below the percolation threshold, and at very low shear rates, where the microstructure of the dispersed phase remains intact. At higher shear rates, corresponding to Mason numbers (Mn) above 1, the structure is disrupted and thus does not contribute to the observed shear stress. The rheological characterization is accompanied with admittance measurements, to demonstrate that the induced polarization forces between particles lead to the formation of electrically conductive structures within the polymer matrix. A critical comparison with the qualitative predictions based on the theory of induced dipole–dipole interactions shows that the theory is valid for these dilute systems.     

Pressure-driven flows of concentrated alumina suspensions depending on dispersion states of particles

The flow developments of 25 vol% alumina suspensions in slit channel were visualized and analyzed depending on the dispersion states. For the coagulated alumina suspension, the shear stress showed an N curve that included a region of stress decrease with an increase in shear rate followed by a monotonic increase. Depending on the region in the stress curve, the flow profile changed from a shear-banded profile to a plug-like flow profile similar to the Newtonian fluid. In addition, it was observed that the transient flow behavior over time at high shear rate in liquid state experienced all of the steady state flow profiles at lower shear rates in solid-liquid transition. During the solid-liquid transition, the flow profile was found to be shear banded, and the pressure profile did not reach a steady state but fluctuated with a characteristic time period. In contrast, the well-dispersed suspension showed only a monotonic increase of shear stress in the range of shear rates we could measure, indicating that the suspension was in liquid state. The flow profile was plug-like, and the pressure was fluctuating without any characteristic time period.     

On constitutive equations for electrorheological materials

Constitutive equations for electrorheological (ER) fluids have been based on experimental results for steady shearing flows and constant electric fields. The fluids have been modeled as being rigid until a yield stress is reached. Additional stress is then proportional to the shear rate. Recent experimental results indicate that ER materials have a regime of solid-like response when deformed from a rest state. They behave in a viscoelastic-like manner under sinusoidal shearing and exhibit time-dependent response under sudden changes in shear rate or electric field. In this work, a constitutive theory for ER materials is presented which accounts for these recent experimental observations. The stress is given by a functional of the deformation gradient history and the electric field vector. Using the methods of continuum mechanics, a general three-dimensional constitutive equation is obtained. A sample constitutive equation is introduced which is then used to determine the response of an ER material for different shear histories. The calculated shear response is shown to be qualitatively similar to that observed experimentally.     

Strain-thickening transition in ferric-oxide suspensions under oscillatory shear

Shear-strain-thickening transition under oscillatory flow was observed in flocculated ferric-oxide suspensions in mineral oil. The value of the dynamic modulus of the suspensions that was measured at small strain amplitude after cessation of shear also became higher when the strain amplitude of the applied shear had been within or above the transition region.The ferric-oxide powders used were an acicular submicron maghemite (magnetic) and the hematite (non-magnetic) that was converted from the maghemite by heat treatment. The powders were treated with a dispersing agent and the suspensions were prepared in 33% by particle weight. The strain-thickening transition was observed in both the magnetic and the non-magnetic suspensions. However, the onset of the strain-thickening in the magnetic suspension was found at about one decade larger strain amplitude than that in the non-magnetic analog suspension, indicating particle interactions affect to the appearance of the phenomenon.A qualitative interpretation was made in view of site percolation for the enhancement of modulus at rest after the application of the large-amplitude oscillatory shear, where the process of the strain-thickening transition under shear and the development of the modulus after stopping the shear was described with a floc model in which the flocculation phase dilates as a result of the reduction of the particle linkages under higher shear.     

Microstructure of shear-thickening concentrated suspensions determined by flow-USANS

Reversible shear thickening in colloidal suspensions is a consequence of the formation of hydroclusters due to the dominance of short-ranged lubrication hydrodynamic interactions at relatively high shear rates. Here, we develop and demonstrate a new method of flow-ultra small angle neutron scattering to probe the colloidal microstructure under steady flow conditions on length scales suitable to characterize the formation of hydroclusters. Results are presented for a model near hard-sphere colloidal suspension of 260 nm radius (10% polydisperse) sterically stabilized silica particles in poly(ethylene glycol) at shear rates in the shear thinning and shear thickening regime for dilute, moderately concentrated, and concentrated (ordered) suspensions. Hydrocluster formation is observed as correlated, broadly distributed density fluctuations in the suspension with a characteristic length scale of a few particle diameters. An order–disorder transition is observed to be coincident with shear thickening for the most concentrated sample, but the shear-thickened state shows hydrocluster formation. These structural observations are correlated to the behavior of the shear viscosity and discussed within the framework of theory, simulation, and prior experiments.     

颗粒材料内部滑动变形局部化的离散元模拟

颗粒材料在加载过程中表现出非常复杂的变形性质.在微观尺度上,单个颗粒的运动、单个孔隙胞元内的变形都是非均匀的,但也不是完全随机、没有规律可循的,而是呈现一定结构性的分布,如微带、剪切带等.本文用基于孔隙胞元的离散元方法对颗粒体进行双轴加载数值试验,模拟了以滑动变形表征的变形局部化现象.数值结果发现,对应加载过程中的不同...