Non-linear viscoelastic behavior of fumed silica suspensions

Suspensions of fumed silica exhibit a wide range of rheological properties depending on the nature and magnitude of the interparticle forces. In a non-polar fluid, the particles interact through hydrogen bonding and can form a three-dimensional network. The microstructure formation is responsible for the non-linear viscoelastic behavior of fumed silica suspensions, even at very small strain. These non-linear rheological properties have been studied in small amplitude oscillatory experiments as a function of particle size, surface treatment of particles, suspending medium polarity and solids concentration. The non-linear viscoelastic behavior is characterized by a non-sinusoidal waveform of the signal response. For suspensions in a non-polar fluid, both the elastic and the loss moduli are shown to be sensitive to the strain amplitude: the elastic modulus is decreasing with increasing strain whereas the loss moduli is initially increasing with strain. We have chosen to examine the dissipated energy which is clearly related to the breakup of the suspension structure. A comparison of model predictions and the experimental data shows the limitations of these models, recently proposed in the literature to describe the behavior of colloidal suspensions. Received: 9 March 1998 Accepted: 17 November 1998     

Rhéologie des matériaux en cours de prise : Approche théorique

The rheological behavior of setting heterogeneous materials is studied from a theoretical approach by means of the homogenization technique of periodic medium. These materials considered as suspensions of gas bubbles at finite concentration in a viscoelastic matrix with low compressibility, present the macroscopic behavior of a compressible viscoelastic medium. The shear and volume macroscopic moduli are of the same order of magnitude and directly proportional to that of the fluid. The effective compressibility of the gas (out of thermal equilibrium) is added to these fluid contributions.     

Rheological behavior of needle-like hydroxyapatite nano-particle suspensions

We describe here the preparation and rheological behavior of stable suspensions of needle-like hydroxyapatite nanoparticles dispersed in organic media, including methylethylketone (MEK), polycaprolactone (PCL) solutions in MEK, and PCL melt. These suspensions are the main ingredients in preparing certain biodegradable orthopedic materials that have some advantages over traditional implants. Rheological properties were experimentally determined at shear rates approaching those used in the processing methods such as roll coating, extrusion, and pultrusion. Analysis of the flow behavior suggests possible shear alignment at high Pe number (Pe ≈ 6,000). The linear viscoelastic properties and the paste-like behavior suggest the formation of a network as the particle content increases. These results are critical in designing a process for making composite materials containing highly oriented anisotropic particles.     

Effects of anionic additives on the rheological behavior of aqueous calcium montmorillonite suspensions

Three different experimental measurements, namely, rheology, particle sizing, and x-ray diffraction (XRD), were used to study the effect of anionic additives on the properties of bentonite suspensions. The three additives were sodium carboxymethylcellulose, xanthan gum, and sodium dodecyl sulfate. Flow curves were obtained from shear stress–shear rate measurements, and the viscoelastic properties were determined from oscillatory and transient measurements. Mineralogical data were evaluated by XRD and the particle size analysis performed by light scattering technique. The presence of the surfactant modifies the face-to-face interactions and yields changes of the mixtures rheological behavior at low deformation rates. Polymers act by coating each clay particle and prevent their agglomeration. Therefore, the additives are responsible for the mechanisms of destructuration and structure reorganization as well as the mixtures viscous and viscoelastic behavior.     

Effects of polymer–fiber interactions on rheology and flow behavior of suspensions of semi-flexible fibers in polymeric liquids

Rheological properties of suspensions of fibers in polymeric fluids are influenced by fiber–polymer interactions. In this paper, we investigate this influence from both experimental and modeling standpoints. In the experimental part of this investigation, we have changed the fiber–polymer interactions by treating the surface of the fibers. The resulting effects are observed using scanning electron microscopy and dynamic mechanical analysis techniques and quantified from the measurements of the viscosity in the start-up of shear flows and dynamic tests in the linear viscoelastic range region. The results are interpreted with the help of a mesoscopic rheological model developed for suspensions of fibers in viscoelastic fluids.     

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.     

Linear viscoelastic analysis using frequency-domain algorithm on oscillating circular shear flows for bubble suspensions

To achieve a stable evaluation of the linear viscoelasticity of bubble suspensions, which have difficulties for conventional rheometers from spatial distributions of rheological properties with bubble deformations, we proposed a novel rheometry based on spatio-temporal velocity data obtained by ultrasonic velocity profiling (UVP). A frequency-domain algorithm was adopted to overcome a critical influence of measurement noise on the rheological assessment, which is inferred from error propagation characteristics through the equations of motion in discretized form. Applicability and advantage of the present rheometry with the frequency-domain algorithm were verified by two kinds of fluids: high viscous oil as a Newtonian fluid and polyacrylamide aqueous solution as a shear thinning, viscoelastic fluid. The rheometry was finally adopted for bubble suspensions subject to high oscillatory shear, and it could validly extract elasticity-originated momentum transfer as a function of space.     

Rheology of physically evolving suspensions

The objective of this work was to investigate the modeling of the whole dynamic rheological behavior of physically evolving suspensions (e.g., polyvinyl chloride plastisols). The evolutions of the complex viscosity with time (isothermal) and with temperature (non-isothermal) were analyzed. To understand the physically involved phenomena, the determination of relationships between the solid volume fraction evolution and the rheological behavior was investigated. Firstly, the evolution of the volume fraction in relation with the variation of radii particle suspensions using a modified Avrami equation was determined. Actually, the rheological study of this physically evolving system is far too complicated due to the many factors involved in the evolving process. Consequently, a phenomenological law using Carreau–Yasuda equation and percolation laws combined with the evolution of the solid volume fraction is investigated to obtain the modeling of the whole dynamic rheological behavior at any frequency and temperature.     

胶凝原油蠕变的时间-温度-应力等效性

黏弹性蠕变是胶凝原油重要的流变特性,要描述胶凝原油的黏弹性蠕变行为,必须同时考虑 应力、时间和温度等参数. 于是对胶凝原油进行了不同应力和不同温度下的蠕变实验,利用 时间-温度-应力等效原理分析了胶凝原油的非线性蠕变行为,得到了参考应力和参考温度下 的蠕变主曲线,并用黏弹性流变模型拟合得到了蠕变主曲线的表达式. 从而可以分别通过较 高温度和应力水平下的短期蠕变行为来预测较低温度和应力水平下的长期蠕变行为.     

A differential model for the rheological properties of concentrated suspensions with weakly viscoelastic matrices

A model for the rheological properties of a concentrated suspension in weakly viscoelastic fluid matrices is proposed. The model is derived according to the Roscoe differential procedure described in 1952. The analytical results produced recently by Greco et al. (J Non-Newton Fluid Mech 147:1–10, 2007) and Housiadas and Tanner (J Non-Newton Fluid Mech 162:88–92, 2009) for dilute suspensions of neutrally buoyant, non-Brownian rigid spheres in weakly viscoelastic matrix fluids are the key results which are used as a base to predict the properties of concentrated suspensions. The results are compared with the few available experimental data from the literature, showing promising trends for the viscometric properties of the suspensions. In particular, one sees the rapidly increasing value of −N₂/N₁ as concentration increases.     

Homogeneous rheological behavior of nanoparticle-based melt

The present work explores nonlinear rheological behavior of a strongly viscoelastic paste made of nano-sized polybutadiene particles. Apart from conventional rheometric measurements, particle-tracking velocimetric observations are carried out to determine the macroscopic state of deformation during startup shear and after step strain. Despite its highly nonlinear rheological characteristics, the system shows no sign of inhomogeneous response to large shear deformations in sharp contrast to well-entangled polymeric liquids made of linear chains. Apparently strongly nonlinear rheological behavior can occur in absence of inhomogeneous macroscopic deformation.     

Linear viscoelastic properties of emulsions and suspensions with thermodynamic and hydrodynamic interactions

We present a new approach to describe the rheological properties of dispersions with non-hydrodynamic interactions (steric, electrostatic and Van der Waals interactions) in the linear viscoelastic domain. Our model is based on the calculation of additional stresses resulting from interaction potentials between spheres and Brownian motion. We start from the statistical mechanical approaches which have been developed by Batchelor and Green and later Lionberger and Russel, to model the viscoelastic properties of emulsions and suspensions. We have extended their calculations to the more general case of viscoelastic deformable inclusions in a viscoelastic matrix. Our contribution lies in the computation of the hydrodynamic functions involved in the term describing interaction stresses. This computation is based on Palierne's results on the deformation field around a viscoelastic inclusion embedded in a viscoelastic matrix. We have also rewritten the conservation equation in the case of interest, over the whole frequency domain. We finally express the complex shear modulus of the dispersion as the sum of two terms : Palierne's complex shear modulus gives the purely hydrodynamic contribution; the interaction contribution depends on both the hydrodynamic properties and the interaction potential.     

Dynamic and rheological properties of soft biological cell suspensions

Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.     

Rheological behavior of concentrated suspensions as affected by the dynamics of the mixing process

The rheological characterizations of concentrated suspensions are generally carried out assuming “well-mixed” suspensions. However, the variation of the concentration distributions of the ingredients of the formulation, i.e., the “goodness of mixing”, the size and shape distributions of the particle clusters and the rheological behavior of the suspension all depend on the thermo-mechanical history that the suspension is exposed to during the mixing process. Here, various experimental tools are used for the characterization of the degree of mixedness (concentration distributions) of various ingredients along with the characterization of rheological material functions, wall slip behavior and the maximum packing fraction of a graphite/elastomer suspension. The degree of mixedness values of the ingredients of the suspensions processed using batch and continuous processes and under differing operating conditions were characterized quantitatively using wide-angle X-ray diffraction and thermo gravimetric analysis and were elucidated under the light of the electrical properties of the suspension as affected by the mixing process. Upon achieving better homogeneity of the graphite particles and the binder and decreases in the size and breadth of the size distributions of particle clusters (as inferred from electrical measurements and maximum packing fraction values), the elasticity (storage modulus) and the shear viscosity (magnitude of the complex viscosity from small-amplitude oscillatory shear and shear viscosity from steady torsional and capillary rheometry) of the suspension decreased significantly and the wall slip velocity values increased. These findings demonstrate the intimate relationships that exist between the rheological behavior of concentrated suspensions and the thermo-mechanical history that they are exposed to during the processing stage and suggest that the preparation conditions for suspensions should be carefully selected and well documented to achieve reproducible characterization of rheological material functions.     

Suspension-like hardening behavior of HDPE and time-hardening superposition

The rheology of solidifying high-density polyethylene (HDPE) is investigated. Experiments on an HDPE were performed with a novel RheoDSC device. Results agree quantitatively with simulations for a suspension of elastic spheres in a viscoelastic matrix except for very low values of space filling (<5%), indicating that the rheological behavior of the crystallizing melt in the frequency range investigated is purely suspension like. The hardening behavior of the material is characterized in two different ways; a normalized rheological function and a time-hardening superposition (THS) master curve of rheological properties. An improvement is proposed to the procedure for performing THS that was previously used in the literature. Based on this procedure, a novel method for predicting the rheological properties of crystallizing melts is presented.     

Rheology of carbon black suspensions. I. Three types of viscoelastic behavior

Dynamic viscoelastic properties were investigated for carbon black (CB) suspensions in three suspending media, an alkyd resin (AR), a rosin-modified phenol resin (PR), and a polystyrene/dibutyl phthalate solution (PS/DBP). The affinity of the medium toward the CB particles decreased in this order, and different types of rheological behavior were observed accordingly. In AR having a high affinity, the CB particles were well dispersed to form no agglomerates. These particles exhibited a slow relaxation process attributable to their diffusion. In PR having a moderate affinity, the suspension showed a sol-gel transition with increasing CB concentration, and the critical gel behavior characterized with a power-law relationship between the modulus and frequency (P), G' = G"/tan(n?/2)œPⁿ with n=0.71, was observed at a critical concentration. This behavior suggested formation of a self-similar, fractal agglomerate of the CB particles in PR. These two suspensions in AR and PR exhibited a moderate nonlinearity. In contrast, in PS/DBP, the suspension exhibited a strong nonlinearity attributable to strain-induced disruption of a fully developed three-dimensional (3D) network structure of the CB particles therein. Thus, the structure and rheology of the CB particles changed with the affinity of the suspending medium. This result in turn posed a caution to a conventional structural interpretation that the CB particles in the actually used ink/paint (always) form the fully developed 3D agglomerates.     

Free vibration analysis of the axially moving Levy-type viscoelastic plate

In this paper, the viscoelastic theory is applied to the axially moving Levy-type plate with two simply supported and two free edges. On the basis of the elastic – viscoelastic equivalence, a linear mathematical model in the form of the equilibrium state equation of the moving plate is derived in the complex frequency domain. Numerical calculations of dynamic stability were conducted for a steel plate. The effects of transport speed and relaxation times modeled with two-parameter Kelvin–Voigt and three-parameter Zener rheological models on the dynamic behavior of the axially moving viscoelastic plate are analyzed.     

A photographic study of shapes of bubbles and coalescence in non-Newtonian polymer solutions

This communication reports (photographically) on the shapes of bubbles of different gases in several Newtonian and polymer solutions, encompassing a wide range of rheological behavior. Effects of a surface active agent are mentioned and bubble coalescence in viscoelastic solutions is visualized.     

Analysis of rheological deformation of soil by means of finite element method

A linear time-dependent viscoelastic behavior of soil is analyzed by the finite element method (FEM), which has great advantage in obtaining an approximate numerical solution of deformation or stress of a continuous body under complex boundary conditions, as known nowadays worldwide. A rheological three-element model, which is easily handled and represents rationally the actual behavior of soil, is suggested to obtain the rheological constants and the constitutive equation of soil. As actual examples of soil behavior, a stress relaxation of a soil block and a time-dependent sinkage of a rigid wheel are calculated by FEM and are also compared with test results and theoretical values.