Rheological properties of peanut butter

The rheological properties of two types of commercial peanut butter have been studied. Both products are concentrated suspensions, and differ by the presence of additives. The first type, referred to as “100% peanuts,” is an unstabilized suspension consisting of solid peanut particles in peanut oil which is a Newtonian fluid. The second type, referred to as “smooth,” consists of the same suspension stabilized with a vegetable oil and contains other ingredients such as salt and sugar in very small quantities. A mean volume particle diameter of 6.6 μm has been determined, the particle diameter distribution was found to be narrow, and the solids volume fraction was estimated to be 0.6. Slip encountered in rheometry was greatly reduced by gluing sandpaper to the parallel plates of the rheometer. Both samples behaved like plastic materials and apparent yield stresses of 24 Pa and 370 Pa have been determined for the unstabilized and the stabilized suspensions, respectively. No linear domain was found for both suspensions and the non-linearity was confirmed by deformed Lissajous curves and higher odd harmonics in the output signal of small amplitude oscillatory shear experiments. The stabilized suspension behaved more like a solid, the elastic modulus being larger than the loss modulus and almost independent of the frequency. This solid-like behavior is supposedly caused by strong repulsive (steric) forces induced by the stabilizing agent. Received: 29 September 1999 Accepted: 9 August 2000     

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.     

Rheological and mechanical properties of silica colloids: from Newtonian liquid to brittle behaviour

Rheological and mechanical properties of aqueous mono-disperse silica suspensions (Ludox? HS40) are investigated as a function of particle volume fraction (ϕ _p ranging from 0.22 to 0.51) and water content, using shear rate tests, oscillatory methods, indentation and an ultrasonic technique. As the samples are progressively dried, four regimes are identified; they are related to the increasing particle content and the existence and behaviour of the electrical double layer (EDL) around each particle. For 0.22 ≤ ϕ _p ≤ 0.30), the suspensions are stable due to the strong electrostatic repulsion between particles and show Newtonian behaviour (I). As water is removed, the solution pH decreases and the ionic strength increases. The EDL thickness therefore slowly decreases, and screening of the electrostatic repulsion increases. For 0.31 ≤ ϕ _p ≤ 0.35, the suspensions become turbid and exhibit viscoelastic (VE) shear thinning behaviour (II), as they progressively flocculate. For 0.35 ≤ ϕ _p ≤ 0.47, the suspensions turn transparent again and paste-like, with VE shear thinning behaviour and high elastic modulus (III). At higher particle concentration, the suspensions undergo a glass transition and behave as an elastic brittle solid (IV, ϕ _p = 0.51).     

Viscosity change in aqueous hectorite suspension activated by DC electric field

The change in the viscosity of deionized aqueous hectorite suspensions by applying an electric field was investigated. The deionized suspensions had low viscosity, which was almost the same as that of its solvent, water. Upon applying a DC electric field of the order of a few volt per millimeter to the deionized suspension, the viscosity started to increase gradually and reached a constant value that was high enough relative to the original value. Regarding the mechanism of the electrically induced stress increase, it is highly plausible that a three-dimensional network structure formed under the electric field due to a deformation of the electrical double layer.     

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.     

Preparation of well-dispersed magnetorheological fluids and effect of dispersion on their magnetorheological properties

In this work, we describe methods for the preparation of suspensions of micron-sized iron particles grafted with different surfactants. The aim is to obtain well-dispersed magnetorheological (MR) fluids. The effectiveness of the surfactants as dispersants was analyzed quantitatively by means of rheological measurements. With this objective, the viscosity of the suspensions was measured, and the results were compared with the prediction of the Batchelor’s formula (Batchelor, J Fluid Mech 83:97–117, 1977). The effect of dispersion on the MR properties of the suspensions was also studied. It was found that the quality of the dispersion of a suspension does not have an important effect on the magnitude of the field-induced yield stress but does on the change of viscosity induced by the field. It was also found that the transition from the solid-like state to the liquid-like one happens very smoothly for well-dispersed suspensions, contrarily to the abrupt transition for poorly dispersed suspensions.     

Dust suspensions accelerated by shock waves

The motion of dust suspensions accelerated by shock waves has been experimentally investigated in a vertical shock tube, in which a completely developed plane shock wave of moderate strength propagates into a homogeneously distributed dust suspension with a planar interface. Trajectories of the accelerated interfaces as well as transmitted and reflected shock waves are recorded by using a shadowgraph system with a Cranz-Schardin camera. Two kinds of particle samples, i.e. porous lycopodium particles 30 μm in diameter and corn starch particles with a mean diameter of 10 μm, are employed. The effects of shock wave strength and particle loading ratio are also examined. Experimental data are compared with theoretical results, and the agreement is good. Received: 7 October 1998/Accepted: 1 June 1999     

Radial filtration during constant-force squeeze flow of soft solids

Various soft solid suspensions were squeezed at constant force between polished and roughened circular glass plates and the time-dependence of the interplate separation was measured. The filterability of suspensions was quantified by their desorptivity S obtained from measurements of capillary suction time. The squeeze flow (SF) of suspensions for which S < 2 μm s^−1/2 was largely consistent with rheological theory, which neglected radial filtration: the relative motion between the liquid and solid phases of the suspension in the radial pressure gradient. Suspensions having S > 2 μm s^−1/2 showed SF behavior that was consistent with the presence of radial filtration.     

Interparticle interaction and gel characterization of PE microgels using small- and large-strain viscoelastic response

PE microgels were prepared from mechanical fragmentation and from immiscible blends of PS and PE. The surface topology of microgels obtained from mechanical fragmentation was hypothesized to consist of long linear PE chains that are capable of interparticle co-crystallization as suggested by low-strain oscillatory shear experiment results. To investigate this hypothesis, PE microgels with a smooth surface and a PS corona were prepared using immiscible blends of PE and PS, followed by removal of the PS matrix. The rheological response of suspensions of PE microgels with a PS corona in squalane was similar to suspensions of PE microgels with crystallizable surface chains whereby the system would gel and exhibit hysteresis upon a cooling and heating cycle. Suspensions of PE microgels without any surface chains, however, were reversible over multiple cooling and heating cycles. It was determined that the PS corona and the cross-link density of the microgels had an effect (p < 0.01) on the reversibility whereas the microgel concentration in the suspension did not (p = 0.82).     

Shear behaviour of biopolymer suspensions with spheroidal and cylindrical particles

The rheological behaviour of suspensions is influenced by many parameters, one of which is the particle shape. For rigid particle suspensions a number of studies demonstrate the effects of the particle aspect ratio. Indeed, fibres are widely used as rheology modifiers in different materials such as synthetic polymers. This work is concerned with testing the hypothesis that regularly shaped particles with aspect ratios larger than one that are made of gelled biopolymers could be used as rheology modifiers for biopolymer solutions. Biopolymers, and mixtures thereof are a widely used ingredient in foods and other products with structure functionality. Tailoring rheology modifiers by morphology offers an alternative to using different biopolymers. It is demonstrated how biopolymer suspensions with regular spheroidal, or cylindrical particle shapes can be produced by gelling the droplet phase of a liquid two phase biopolymer mixture in a shear field. Biopolymers were chosen such that gelation is initiated by cooling. Shear-cooling at constant stresses leads to the formation of ellipsoidal particles. Cylindrical particles can be generated by stepping up the shear stress prior to gelation, i.e., stretching the droplet phase into fibrils, and trapping the shape prior to break-up through gelation. Morphologies and steady shear rheological data for suspensions of the two biopolymers gellan and κ-carrageenan with an internal phase volume of 0.2 are reported. The influence of particle shape on relative viscosity is pronounced. At high shear stresses particle orientation leads to decreased viscosity with increasing particle aspect ratio. In the low shear region, higher aspect ratio suspensions show higher viscosities. Additionally, the material properties, including the interfacial tension, which influence the suspension morphology are reported. Received: 3 March 2000 Accepted: 22 August 2000     

Simulation of the rheological properties of suspensions of oblate spheroidal particles in a Newtonian fluid

A simulation algorithm was developed to predict the rheological properties of oblate spheroidal suspensions. The motion of each particle is described by Jeffery’s solution, which is then modified by the interactions between the particles. The interactions are considered to be short range and are described by results from lubrication theory and by approximating locally the spheroid surface by an equivalent spherical surface. The simulation is first tested on a sphere suspension, results are compared with known experimental and numerical data, and good agreement is found. Results are then presented for suspensions of oblate spheroids of two mean aspect ratios of 0.3 and 0.2. Results for the relative viscosity η _r, normal stress differences N ₁ and N ₂ are reported and compared with the few available results on oblate particle suspensions in a hydrodynamic regime. Evolution of the orientation of the particles is also observed, and a clear alignment with the flow is found to occur after a transient period. A change of sign of N ₁ from negative to positive as the particle concentration is increased is observed. This phenomenon is more significant as the particle aspect ratio increases. It is believed to arise from a change in the suspension microstructure as the particle alignment increases.     

Shear and squeeze rheometry of suspensions of magnetic polymerized chains

We present the first experimental results on the magnetorheology of suspensions of non-Brownian magnetic ellipsoidal particles. These particles are made of spherical iron particles linked by polymers and are called polymerized chains. Steady shear, oscillatory shear, and oscillatory squeeze rheological tests have been performed. The rheological properties of the suspension of polymerized chains have been compared with those of the suspension of spherical iron particles. In shear flow, both suspensions develop nearly the same yield stress, while in squeeze flow, the yield stress is several times higher for the suspension of polymerized chains. We show that the squeezing force of a suspension of spherical particles is an increasing function of the magnetic field intensity at low magnetic fields but decreases dramatically at higher fields. Surprisingly, this phenomenon, attributed to cavitation or air entrainment, does not occur in the suspension of polymerized chains.     

Rheological properties and dispersion stability of magnetorheological (MR) suspensions

In the present article, the rheological responses and dispersion stability of magnetorheological (MR) fluids were investigated experimentally. Suspensions of magnetite and carbonyl iron particles were prepared as model MR fluids. Under an external magnetic field (H ₀) and a steady shear flow, the yield stress depends upon H ₀ ^3/2. The Yield stress depended on the volume fraction of the particle (φ) linearly only at low concentration and increased faster at high fraction. Rheological behavior of MR fluids subjected to a small-strain oscillatory shear flow was investigated as a function of the strain amplitude, frequency, and the external magnetic field. In order to improve the stability of MR fluid, ferromagnetic Co-γ-Fe₂O₃ and CrO₂ particles were added as the stabilizing and thickening agent in the carbonyl iron suspension. Such needle-like particles seem to play a role in the steric repulsion between the relatively large carbonyl iron particles, resulting in improved stability against rapid sedimentation of dense iron particles. Furthermore, the additive-containing MR suspensions exhibited larger yield stress, especially at higher magnetic field strength. Received: 4 April 2000 Accepted: 6 November 2000     

Hydrodynamic diffusivity of spherical particles in polymer solution

In this research experiments were performed to examine the hydrodynamic diffusion of spherical particles in a highly filled suspension. The suspension consisted of nearly monodisperse polymethylmethacrylate spheres in a density matched polymer solution. The polymer solution was prepared by dissolving 0–700 ppm of polyacrylamide in a mixture of ethyleneglycol and glycerine. The polymer solution did not show appreciable shear thinning. The particle loading was varied from 30 to 55%. The hydrodynamic diffusivity was estimated by measuring the time-dependent viscosity when the suspension was subjected to a circular Couette flow with an air bubble trapped under the rotor of the Couette apparatus. The results show that the dimensionless diffusivity (D/γ˙a ²) of particles in polymer solution is not proportional to shear rate (γ˙), as in the case of a Newtonian fluid, but that it decreases with increasing shear rate. The diffusivity also decreases with increasing polymer concentration. It is suggested that the elongational thickening behaviour and the increased lubrication force due to the first normal stress difference may be responsible for the reduction of diffusivity in the polymer solution. Received: 18 January 2000 Accepted: 6 April 2000     

Rheological properties and percolation in suspensions of multiwalled carbon nanotubes in polycarbonate

This paper is concerned with several issues related to the rheological behavior of polycarbonate/multiwalled carbon nanotube nanocomposites. The composites were prepared by diluting a masterbatch of 15 wt.% nanotubes using melt-mixing method, and the dispersion was analyzed by SEM, TEM, and AFM techniques. To understand the percolated structure, the nanocomposites were characterized via a set of rheological, electrical, and thermal conductivity measurements. The rheological measurements revealed that the structure and properties were temperature dependent; the percolation threshold was significantly lower at higher temperature suggesting stronger nanotube interactions. The nanotube networks were also sensitive to the steady shear deformation particularly at high temperature. Following preshearing, the elastic modulus decreased markedly suggesting that the nanotubes became more rigid. These results were analyzed using simple models for suspensions of rod-like particles. Finally, the rheological, electrical, and thermal conductivity percolation thresholds were compared. As expected, the rheological threshold was smaller than the thermal and electrical threshold.     

Synthesis and electrorheological properties of polar molecule-dominated TiO 2 particles with high yield stress

Two types of amorphous TiO₂ particles with different particle sizes were synthesized by a simple sol–gel method and were characterized by X-ray diffraction analysis, field emission scanning electron microscopy, and Fourier transform infrared spectrometry. The electrorheological (ER) results show that the TiO₂/silicone oil suspensions exhibited a remarkable ER effect. The static shear stress can be up to 130 kPa (shear rate 0.2 s^− 1) under the DC electric field of 4 kV/mm at room temperature. The polar molecules present on the particles’ surface play a decisive role for the observed giant ER effect, which arises from the alignment of polar molecules in the gap between neighboring particles.     

Spatially periodic suspensions of convex particles in linear shear flows. I. Description and kinematics

Preparatory to a subsequent dynamical study in Part II, aimed at calculating the rheological properties of geometrically-ordered models of concentrated suspensions, a purely kinematical study is here presented of the motion of a mobile spatially periodic array of identical convex particles, typically spheres, participating in a macroscopically homogeneous linear shear flow to which the suspension as a whole is subjected. The geometrical configuration of such particle-lattice suspensions is shown to evolve temporally in a manner dependent upon the initial lattice configuration and the specific bulk shearing motion to which the suspension is subjected. Under certain circumstances the particle-lattice system is found to reproduce itself periodically in time—or, less stringently—“almost” periodically. Precise circumstances under which this occurs are exhaustively delineated for the entire class of two-dimensional isochoric spatially homogeneous shearing motions, parametrized by a scalar λ expressing the relative amounts of shear and vorticity present in the flow. This investigation is performed for both two- and three-dimensional lattices. (Eventual time averaging of the local, instantaneous, dynamical, interstitial fluid properties of these almost self-reproducing systems in Part II furnishes the rheological properties of the suspension.) Using concepts borrowed from Minkowski's geometry of numbers, calculations are outlined for establishing the maximum volume fraction of suspended particles that is kinematically possible for each shearing motion. This is observed to be always less than would obtain in a comparable static system.     

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.     

Correlation between the high-frequency elastic modulus and the interparticle interaction potential in zirconium oxide colloidal suspensions

In this work, we study the high-frequency elastic modulus of aqueous suspensions made with two kinds of zirconium oxide particles, one commercially available and the other synthesized as monodisperse spheres. The effect of volume fraction of solid, ionic strength (sodium chloride as indifferent electrolyte) and particle geometry is taken into account in the study on this viscoelastic property of the suspensions. Frequency sweeps were performed at a fixed value of the applied shear-stress in order to obtain the frequency-limiting value of the elastic modulus by rheometrical methods. On the other hand, the high-frequency modulus is theoretically calculated independently by means of the models proposed by Buscall and co-workers, Wagner and Bergenholtz and co-workers, which correlate the interaction potential between particles with this rheological parameter. The approach to the interparticle potential is the extended DLVO theory, which considers the electrical repulsion between charged colloidal particles, the van der Waals attraction and the acid–base interaction that can be attractive or repulsive depending on the thermodynamic nature of the solid–liquid interface.     

Concentration dependence of the linear viscoelastic properties of particle suspensions

The response under small amplitude oscillatory deformations of a suspension of non-Brownian spheres dispersed in a viscoelastic fluid is investigated. The correspondence principle of linear viscoelasticity is used to derive a simple constitutive model from a model for a suspension in a Newtonian liquid. The theory predicts that for a specific particulate system the concentration dependence of the viscoelastic properties should collapse to a single master curve when the values are normalized with those of the carrier fluid alone. Measurements with the micro-Fourier rheometer using oscillatory squeeze flow are carried out on two suspensions of 60 and 80 μm sized particles dispersed in polymeric fluid and in silicon oil, and the master curve is verified. Received: 27 April 1999/Accepted: 15 October 1999