A rheological approach to the study of concentrated milk clotting

The aim of the present work is to analyze the complex phenomena involved in the concentrated milk clotting process in order to define general criteria applicable to the design of a continuous coagulator. A full characterization of the rheological properties of completely hydrolyzed milk as a function of two different parameters, i.e., the coagulator temperature and the concentration degree of the milk, is presented. The dynamic evolution of loss, G′′, and storage, G′, moduli has been obtained at different frequency values and for different concentration degrees during the clotting process. Time cure tests have been performed on completely hydrolyzed milk samples showing that the rate of curing is very high and that the time for rheological experiments is much too short for testing Winter's theory of gelation. To overcome this problem, the intersect of loss and storage moduli was used for estimating the coagulation. Coagulation is faster when higher temperatures are used and the consistency of the final curd is greater if a more concentrated milk is used. A tentative physical explanation based on the network theories is presented. If an observation time far enough from the crossover point is chosen it can be seen that the curd strength estimated at 40 °C is about 50 times higher than that one evaluated at 25 °C. Among the considered temperatures, a good processing value was evaluated at 40 °C. Received: 6 February 2000 Accepted: 24 October 2000     

Viscoelastic properties of dibenzylidene sorbitol (DBS) physical gels at high frequencies

The rheological behavior of Dibenzylidene D-Sorbitol (DBS) gels formed in ethylene glycol, glycerol, mineral oil, ethanol, and chlorobenzene was studied using oscillatory squeezing flow viscometry. The storage (G ^′) and loss (G ^″) moduli were measured as a function of gellant concentration (0.5–2 w/w) and type of solvent. As expected greater values of gel strength (G ^′) were observed for gels containing higher concentrations of DBS. In addition, both storage and loss moduli of 2% systems were mostly frequency independent over the studied range, whereas 0.5% gels did exhibit some degree of dependence. We also found that the solvent plays an important role in the properties of the gels. Among the parameters that affect the viscoelastic properties of DBS gels, the solvent polarity and its ability to form hydrogen bonding may have significant effects on the gel rheology.     

High-frequency viscoelasticity of crosslinked actin filament networks measured by diffusing wave spectroscopy

We study the short-time relaxation dynamics of crosslinked and uncrosslinked networks of semi-flexible polymers using diffusing wave spectroscopy (DWS). The networks consist of concentrated solutions of actin filaments, crosslinked with increasing amounts of α-actinin. Actin filaments (F-actin) are long semi-flexible polymers with a contour length 1–100μm and a persistence length of 5–15μm; α-actinin is a small 200kDa homodimer with two actin-binding sites. Using the large bandwidth of DWS, we measure the mean-square-displacement of 0.96μm diameter microspheres imbedded in the polymer network, from which we extract the frequency-dependent viscoelastic moduli via a generalized Langevin equation. DWS measurements yield, in a single measurement, viscoelastic moduli at frequencies up to 10⁵Hz, almost three decades higher in frequency than probed by conventional mechanical rheology. Our measurements show that the magnitude of the small-frequency plateau modulus of F-actin is greatly enhanced in the presence of α-actinin, and that the frequency dependence of the viscoelastic moduli is much stronger at intermediate frequencies. However, the frequency-dependence of loss and storage moduli become similar for both crosslinked and uncrosslinked networks at large frequencies, G′(ω)∝G′′(ω)∝ω^0.75±0.08. This high-frequency behavior is due to the small-amplitude, large-frequency lateral fluctuations of actin filaments between entanglements. Received: 20 January 1998 Accepted: 12 February 1998     

Rheostructural studies of a discotic mesophase pitch at processing flow conditions

The flow-induced microstructure of a mesophase pitch was studied within custom-made dies for changing wall shear rates from 20 to 1,100 s^− 1, a flow scenario that is typically encountered during fiber spinning. The apparent viscosity values, measured at the nominal wall shear rates ranging from 500 to 2,500 s^− 1 using these dies, remain fairly constant. The microstructure was studied in two orthogonal sections: r–θ (cross section) and r–z (longitudinal mid plane). In these dies, the size of the microstructure gradually decreases toward the wall (to as low as a few micrometers), where shear rate is highest. Furthermore, as observed in the r–θ plane of the capillary, for a significant fraction of the cross section, discotic mesophase has a radial orientation. Thus, the directors of disc-like molecules were aligned in the vorticity (θ) direction. As confirmed from the microstructure in the r–z plane, most of the discotic molecules remain nominally in the flow plane. Orientation of the pitch molecules in the shear flow conditions is consistent with that observed in controlled low-shear rheometric experiments reported earlier. Microstructral investigation suggests that the radial orientation of carbon fibers obtained from a mesophase pitch originates during flow of pitch through the die.     

Clear and pigmented water epoxy systems: a study on the hardening kinetics on the basis of the variations of the viscoelastic moduli

The hardening reaction of a two-can water epoxy polyamide system was investigated on the basis of the variation of the viscoelastic moduli G′ and G′′. Unpigmented (clear varnish) and TiO₂ pigmented formulations, at two different TiO₂ concentrations, were taken into account. Time and frequency sweep procedures were carried out using the stress-controlled rheometer Haake RS 150. The behavior of G′ and G′′ vs time was fitted to a four-parameter asymptotic model through the whole course of the hardening process. Frequency sweep data, obtained at increasing times during the whole hardening process, were plotted to the generalized Cole and Cole behavior model and the corresponding mechanical spectra were drawn. An interpretation for some aspects of the cross-linking progress is discussed and possible future developments are briefly outlined. Received: 15 January 2000 Accepted: 13 November 2000     

Viscoelastic behavior of polymerizing systems

Experimental data of the dynamic viscoelastic properties, storage modulus (G′), loss modulus (G′′), and phase shift (δ) as well as of the viscosity, η, are reported for the polymerization of a free radical polymerization system (methyl methacrylate) which exhibits the Trommsdorff effect. A rheometer-reactor assembly developed in our laboratory is used for this purpose. It is observed that in the early stages of reaction, data lie in the terminal zone. As the polymerization progresses, the Trommsdorff effect leads to a sharp increase in both the polymer concentration and the weight average molecular weight, and the viscoelastic properties then lie in the entanglement zone. A modulus crossover point (when G′ = G′′) is identified that could be used as an identification of the point where the Trommsdorff effect starts assuming significance. Received: 17 September 1998 Accepted: 9 December 1998     

Extensional and shear rheometry of oriented triblock copolymers

 The effects of extensional flow orientation on the rheological properties of two poly(styrene)-poly(ethylene-co-butylene)-poly (styrene) (PS-PEB-PS) triblock copolymers containing either spherical or cylindrical PS microdomains were studied by oscillatory shear and oscillatory extensional experiments. Extensional measurements revealed that below the PS block glass transition temperature pre-oriented triblocks display highly anisotropic mechanical properties. For both polymers, the storage modulus E ′ is higher along the flow direction. Above the PS glass transition temperature the materials are no longer anisotropic and the same storage moduli are obtained along the flow direction and perpendicular to it. Above the PS glass transition temperature the rheological behaviour parallel and perpendicular to the flow direction was also probed in pre-oriented and non-oriented samples by oscillatory shear rheometry. At high frequencies, the mechanical response of the triblocks was found to be independent of the orientation for both copolymers while at low frequencies a strong effect of the flow orientation could be observed. For both polymers the value of the storage modulus was found to be lower along the flow direction that perpendicular to it. This was explained by the ability of PS blocks to relax more easily along the flow direction. Received: 10 September 1999/Accepted: 1 October 1999     

Effect of ionic interaction on linear and nonlinear viscoelastic properties of ethylene based ionomer melts

The effect of ionic interaction on linear and nonlinear viscoelastic properties was investigated using poly(ethylene-co-methacrylic acid) (E/MAA) and its ionomers which were partially neutralized by zinc or sodium. Dynamic shear viscosity and step-shear stress relaxation studies were performed. Stress relaxation moduli G(t, y) of the E/MAA and its sodium or zinc ionomers were factorized into linear relaxation moduli G°(t) and damping functions h(y). The relaxation modulus at the smallest strain in each ionomer agreed with the linear relaxation modulus calculated from storage modulus G and loss modulus G. In the linear region, the ionic interaction shifted the relaxation time longer with keeping the same relaxation time distribution as E/MAA. In the nonlinear region, the ionic interaction had no influence on h(y) when the ion content was low. At higher ion content, however, the ion bonding enhanced the strain softening of h(y).     

A rheological approach to drill-in fluids optimization

The aim of this work is to propose design criteria, based on rheological characterisation for improving drill-in fluids performance. In particular, it reports an example in which rheological approaches helped improve drill-in fluids resistance to temperature. As a starting system a commercial drill-in fluid containing xanthan gum and calcium carbonate was chosen and evaluated. Different samples were then prepared by changing the initial formulation in order to increase the system's stability to temperature. Drill-in fluids' performance have been compared by considering their “damaging potential”, filtration properties and, “cakes”. All drill-in fluids have been tested before and after aging at a given temperature with “hot rolling tests”. The systems' gel structure was characterized by measuring dynamic moduli (G′ and G′′) in the linear viscoelastic range and all samples were compared by evaluating their “melting” temperature and gel network strength during time cure tests. The results obtained from this work suggest that the rheological tests carried out on the whole drill-in fluid can provide insights into fluids' damaging potential and “cake” structure. In particular, rheology proved to be able to provide quantitative information about gel strength and temperature stability that permitted one to improve drill-in fluids' formulation in order to preclude formation damage and to meet industrial requirements. Received: 6 February 2000 Accepted: 15 November 2000     

Exact Connections of Warping Fields and Torsional Rigidities of Symmetric Composite Bars

Saint-Venant's torsion of symmetric cylindrical bars consisting of two or four homogeneous phases is studied. A symmetric section is meant that the cross section of the cylindrical bar possesses reflectional symmetry with respect to one or more axes. Each constituent region may have different shear modulus. The idea of the analysis is to superimpose suitably reflected potentials to obtain the torsion solution of the same composite section but with different moduli. For two-phase sections, we show that, if the warping fields for a given symmetric section with phase shear moduli μ₁ and μ₂ are known a priori, then the warping fields for the same configuration but with a different set of constituent moduli μ₁ ^′ and μ₂ ^′ are readily found through simple linear superpositions. Further, suppose that the torsional rigidities T(μ₁,μ₂) and T(μ₁ ^′,μ₂ ^′) for any two sets of phase moduli can be measured by some experimental tests or evaluated through numerical procedures, then the torsional rigidity for any other combinations of constituent moduli T(μ₁ ^′′,μ₂ ^′′) can be exactly determined without any recourse to the field solutions of governing differential equations. Similar procedures can be applied to a 4-phase symmetric section. But the coefficients of superposition are only found for a few branches. Specifically, we find that depending on the conditions of μ and μ^′, admissible solutions can be divided into three categories. When the correspondence between the warping field is known to exist, a link between the torsional rigidities can be established as well. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effect of nanofillers on the phase separation and rheological properties of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) blends

The viscoelastic characteristics of the blends of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) (PMMA/SAN) were investigated at various temperatures below, near, and above the phase separation temperature. The investigated polymer system is characterized by a lower critical solution temperature. Rheological behavior of the blends in the region of a phase separation was compared with change of the light scattering intensity. The presence of nanofillers in the blend results in that the phase separation occurs at a higher temperature. At the isothermal conditions, the phase separation begins earlier and proceeds with a higher rate as compared with the same blend without filler. The results of the study show the considerable change of the viscoelastic characteristics of PMMA/SAN when the polymer system passes from the homogeneous state to the heterogeneous one. Such characteristics as the dependence of the storage modulus (G ^′) on the loss modulus (G ^″), the dependence of the loss viscosity (η ^″) on the dynamic viscosity (η ^′), the dependences of the complex viscosity (η*), and the free volume fraction (f) on the blend composition are the most sensitive to the phase separation. The phase separation affects the characteristics G ^′(ω), where ω is the frequency only in a low-frequency range. Temperatures of phase separation were estimated using dependence G ^′(T) at ω, which is the constant in the range of low frequencies.     

Dynamic melt flow of nanocomposites based on poly-ɛ-caprolactam

 The dynamic flow behavior of polyamide-6 (PA-6) and a nanocomposite (PNC) based on it was studied. The latter resin contained 2 wt% of organoclay. The two materials were blended in proportions of 0, 25, 50, 75, and 100 wt% PNC. The dynamic shear rheological properties of well-dried specimens were measured under N₂ at T=240 °C, frequency ω=0.1–100 rad/s, and strains γ=10 and 40%. At constant T, γ, and ω the time sweeps resulted in significant increases of the shear moduli. The γ and ω scans showed a complex rheological behavior of all clay-containing specimens. At γ=10% the linear viscoelasticity was observed for all compositions only at ω>1 rad/s, while at γ=40% only for 0 and 25 wt% of PNC. However, the effect was moderate, namely decreasing G′ and G′′ (at ω=6.28 rad/s; γ=50%) by 15 and 7.5%, respectively. For compositions containing >25 wt% PNC two types of non-linearity were detected. At ω≤ω_c=1.4 ± 0.2 rad/s yield stress provided evidence of a 3-D structure. At ω > ω_c, G′ and G′′ were sensitive to shear history – the effect was reversible. From the frequency scans at ω > ω_c the zero-shear relative viscosity vs concentration plot was constructed. The initial slope gave the intrinsic viscosity from which the aspect ratio of organoclay particles, p=287 ± 9 was calculated, in agreement with the value calculated from the reduced permeability data, p=286. Received: 24 May 2001 Accepted: 27 August 2001     

Generalized Rouse model for a dilute solution of clustered polymers

A theory analogue to tha of Rouse is given, to describe the rheological behavior of dilute solutions consisting of clusters of crosslinked polymers. The frequency-dependent behavior of the dynamic moduli of these fluids differs substantially from that of the well-known Rouse-like fluid (GG^1/2). In our case the storage modulus becomes proportional to ^3/2, while the loss modulus is proportional to . The loss modulus dominates the dynamic behavior for frequencies smaller than the largest normal frequency of the clusters.     

Elasticity and dynamics of particle gels in non-Newtonian melts

We investigate the relation between the structure and the viscoelastic behavior of a model polymer nanocomposite system based on a mixture of titanium dioxide (TiO₂) nanoparticles and polypropylene. Above a critical volume fraction, Φ _c, the elasticity of the hybrids dramatically increases, and the frequency dependence of the elastic and viscous moduli reflects the superposition of the independent responses of the suspending polymer melt and of an elastic particle network. In addition, the elasticity of the hybrids shows critical behavior around Φ _c. We interpret these observations by hypothesizing the formation of a transient network, which forms due to crowding of particle clusters. Consistent with this interpretation, we find a long-time, Φ-dependent, structural relaxation, which emphasizes the transient character of the structure formed by the particle clusters. For times below this characteristic relaxation time, the elasticity of the network is Φ-independent and reminiscent of glassy behavior, with the elastic modulus, G^′, scaling with frequency, ω, as G^′∼ω ^0.3. We expect that our analysis will be useful for understanding the behavior of other complex fluids where the elasticity of the components could be superimposed.     

On the use of the model proposed by Leonov for the explanation of a secondary plateau of the loss modulus in heterogeneous polymer–filler systems with agglomerates

The purpose of the presented work was to test the capability of the model proposed by Leonov (J Rheol 34:1039–1068, 1990) for the prediction of secondary plateaus on the storage and loss moduli during small-amplitude oscillatory shear flow experiments on filled or heterogeneous polymer melts. Though the occurrence of a plateau on the storage modulus can be well explained in the frame of a filler network, a plateau on the loss modulus can hardly be described with the classical models. In the Leonov model, the continuum of dissipative processes is attributed to the rupture of flocs of particles. Experiments with polyolefins filled with magnesium hydroxide show that there is a clear connection between the amount of agglomerates and the occurrence of a plateau on the loss modulus. However, the value of the critical strain for floc rupture that can be calculated from the experiment shows that the processes responsible for the low-frequency dissipation are rather changes of configuration within the agglomerates than floc rupture. These processes are not described by the Leonov model, and the predicted strain dependence of the plateau is not observed experimentally.     

Estimating the viscoelastic moduli of complex fluids using the generalized Stokes–Einstein equation

We obtain the linear viscoelastic shear moduli of complex fluids from the time-dependent mean square displacement, <Δr ²(t)>, of thermally-driven colloidal spheres suspended in the fluid using a generalized Stokes–Einstein (GSE) equation. Different representations of the GSE equation can be used to obtain the viscoelastic spectrum, G˜(s), in the Laplace frequency domain, the complex shear modulus, G ^*(ω), in the Fourier frequency domain, and the stress relaxation modulus, G _r (t), in the time domain. Because trapezoid integration (s domain) or the Fast Fourier Transform (ω domain) of <Δr ²(t)> known only over a finite temporal interval can lead to errors which result in unphysical behavior of the moduli near the frequency extremes, we estimate the transforms algebraically by describing <Δr ²(t)> as a local power law. If the logarithmic slope of <Δr ²(t)> can be accurately determined, these estimates generally perform well at the frequency extremes. Received: 8 September 2000/Accepted: 9 March 2000     

Reological behaviour of concentrated monodisperse suspensions as a function of preshear conditions and temperature: an experimental study

 The influence of preshearing on the rheological behaviour of model suspensions was investigated with a stress-controlled cone-and-plate rheometer. The used matrix fluids showed Newtonian behaviour over the whole range of applied shear stresses. Highly monodisperse spherical glass spheres with various particle diameters were used as fillers. By applying steady preshearing at a low preshear stress, where a diffusion of particles can be expected, it was found for all model suspensions investigated at volume fractions ranging from 0.20 to 0.35 that the time-temperature superposition in the steady shear and in the dynamic mode holds within the chosen temperature range. Furthermore, all presheared model suspensions displayed a high and a low frequency range which are either separated by a shoulder or by a plateau value of G′ at intermediate frequencies. It could clearly be demonstrated that the low frequency range strongly depends on the preshear conditions. Hence, the features observed in the low frequency range can be attributed to a structure formation of a particulate network. In the high frequency range a frequency-dependent behaviour was observed which obeys the classical behaviour of Newtonian fluids (G′∝ω², G′′∝ω). The resulting temperature shift factors from the dynamic and the steady shear mode are identical and independent of the volume fraction and the particle size of the filler. Received: 29 November 2000 Accepted: 12 July 2001     

Heat-induced gelation of globular proteins. Part 5. Creep behaviour of β-lactoglobulin gels

 Creep and recovery experiments have been used to investigate the behaviour of heat set protein gels exemplified by those prepared from β-lactoglobulin (β-Lg). Some initial experiments were also performed on heat set BSA gels to establish appropriate experimental conditions. The latter illustrated the importance of a well-controlled thermal regime and the use of an appropriate solvent trap. Results from the concentration dependence of compliance for β-Lg were in good agreement with previously published results for the long time extrapolated storage modulus, G ^′ _∞ we introduced previously, especially considering the necessarily different experimental conditions. The exponent of creep and recovery phase viscosity vs concentration was extremely high, ∼30, but reflects the nature of such gelling systems close to their critical concentration. In this respect, the behaviour of the creep phase viscosity was in qualitative agreement with our recently postulated viscosity vs concentration state diagram for a gelling system. Received: 12 July 2001 Accepted: 29 October 2001     

Rheo-dielectric behavior of low molecular weight liquid crystal 2. Behavior of 8CB in nematic and smectic states

Rheo-dielectric behavior was examined for 4−4^′−n-octyl-cyanobiphenyl (8CB) having large dipoles parallel to its principal axis (in the direction of the C≡N bond). In the quiescent state at all temperatures (T) examined, orientational fluctuation of the 8CB molecules was observed as dielectric dispersions at characteristic frequencies ω_c>10⁶ s⁻¹. In the isotropic state at high T, no detectable changes of the complex dielectric constant ɛ^*(ω) were found under slow flow at shear rates ˙γ≫ω_c. In the nematic state at intermediate T, the terminal relaxation intensity of ɛ^*(ω) was decreased under such slow flow. In the smectic state at lower T, the flow effect became much less significant. These results were related to the flow-induced changes of the liquid crystalline textures in the nematic and smectic states, and the differences of the rheo-dielectric behavior in these states are discussed in relation to a difference of the symmetry of molecular arrangements in the nematic and smectic textures. Received: 1 October 1998 Accepted: 13 January 1999     

A rheological approach to the stability of humic acid/clay colloidal suspensions

Steady-state, oscillatory, and transient rheological determinations were used to assess the stability of homoionic sodium montmorillonite (NaMt) suspensions at constant ionic strength (10^–2 mol/l NaCl) and different pH values, after adsorption of humic acid (HA) on the particles. The adsorption of the latter was first spectrophotometrically determined, at pH 3 and 9. While at pH 9 adsorption saturation was observed, at pH 3 the adsorption density continued to grow up to the maximum equilibrium HA concentration reached (∼200 mg/l). Considering the similarity between the structure of edge surfaces of NaMt particles and the surfaces of silica and alumina, the adsorption of HA was also investigated on the latter solids. The results suggest that at pH 3 humic acids adsorb preferentially on edge surfaces, mainly through electrostatic attraction with positively charged aluminol groups. This hypothesis is indirectly confirmed by zeta potential, ζ, values: while HA concentration has little effect on ζ for silica, the addition of HA yields the zeta potential of alumina increasingly negative for all pH values. Using shear stress vs shear rate plots, the yield stress of NaMt was determined as a function of particle concentration, C, for pH 3, 5, 7, and 9, with and without addition of 50 mg/l HA. The yield stress, σ_y, was fitted with a power law σ_y∝C ⁿ ; it was found that n values as high as 12 are characteristic of NaMt suspensions at pH 9 in the presence of HA. This indicates a strong stabilizing effect of humic acid. This stabilization was confirmed by oscillometric measurements, as the storage modulus G′ in the viscoelastic linear region also scales with C, displaying large n values at neutral and basic pHs in the presence of HA. The modulus (in the viscoelastic linear region, for a frequency ν=1 Hz) was found to increase with time, but G′ was lower at any time when HA was added, a consequence of the stabilization provided by HA. Similarly, creep-recovery experiments demonstrated that NaMt suspensions containing HA displayed a less elastic behavior, and a permanent deformation. Modeling the results as a Kelvin-Voigt model allowed one to establish a new scaling law of the reciprocal instantaneous deformation with C. As before, high values of n were found for suspensions at pH 9 in the presence of HA.