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     

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     

Quantitative rheological evaluation of phase inversion in two-phase polymer blends with cocontinuous morphology

 The present work is focused on the rheological properties of two-phase polymer blends in the phase inversion region. A large number of PS/PMMA- and PSAN/PMMA-blends has been investigated in order to establish a rheological criterion which allows the quantitative determination of the phase inversion concentration φ_PI by rheological means. Three rheological criteria based on the viscous and elastic blend properties such as maximum of dynamic viscosity η′, slope of G′, and maximum of G′ at a constant evaluation frequency have been tested. By correlating the rheological results to data from quantitative morphological analysis we could prove that the chosen rheological criteria are differently suitable for the determination of φ_PI. It has turned out that the G′ criterion is the most robust and most suitable one yielding an excellent correlation with morphological data. Based on these findings we propose a new simple equation for the prediction of φ_PI-values. Received: 14 March 2001 Accepted: 15 May 2001     

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.     

Influence of the surface roughness on the third-order moments of velocity fluctuations

Roughness wall effects in a zero pressure gradient turbulent boundary layers were investigated using hot-wire anemometry. The skewness and diffusion factors of u and v, the longitudinal and normal velocity fluctuations, were measured and represented using wall variables. The results indicate that the wall roughness removes the crossover point between sweep and ejection events to the outer region of the layer for a single Reynolds number Re _θ  > 3,000. This behaviour exhibits that the roughness surface favours the maintaining of sweep events obtained by a quadrant analysis. These results show that communication between the wall region and outer region of a turbulent boundary layer exists and the wall similarity hypothesis for a rough wall is questionable. The effect of the wall roughness on the position of the point crossover from sweep to ejection motions with respect to the wall seems to be the same as that obtained when the Reynolds number is higher. Received: 8 March 2000/Accepted: 15 May 2000     

The viscoelasticity of thermotropic liquid crystalline polymers: effects of the chemical composition

In this work, the rheological properties of the wholly aromatic random copolyester HBA/HNA (60/40), the commercial copolyesteramide Vectra B950, and the semiflexible commercial copolyester Rodrun 3000, PET/HBA 40/60, were investigated. All the thermotropic liquid crystalline polymers (TLCPs) show linear viscoelastic behavior at small strain amplitudes. The strain sweep experiments have clearly indicated that the onset for non linearity significantly decreases as the applied frequency increases in all the TLCPs here studied, independent of chemical composition and flexibility. In the case of the Vectra B950, a strain-hardening effect occurred at a strain of about 40% for all the applied frequencies. The frequency behavior showed that the HBA/HNA 60/40 TLCP is characterized by the leveling off of G′ and by a dominant elastic behavior at low frequencies. The inclusion of the flexible PET determines the disappearance of the plateau value for G′ with a viscous response at low frequencies.Paper presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.     

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     

A convenient way of interpreting steady shear rheo-optical data of semi-dilute polymer solutions

Rheo-mechanical and rheo-optical investigations were carried out with the aim of determining the influence of deformation and orientation or disentangling of polymer coils on the flow behavior in the non-Newtonian region of the flow curve, for a moderately concentrated network solution. To avoid the influence of polydispersity this was done on a series of narrowly distributed polystyrene standards (dissolved in toluene). By using steady state shear flow measurements it was possible to detect qualitatively a reduction in the entanglement density within the non-Newtonian flow region. Birefringence experiments were able to show that deformation of the polymer coils also occurs in the Newtonian flow region, which has no effect on the flow behavior in this range, whereas in the non-Newtonian flow region the increase in deformation is lower than in the Newtonian range. The flow birefringence and its orientation can be described over the whole range of the flow curve with a newly developed equation system (Eq. 8 and 14) derived from the stress states of a sheared solution using the stress-optical rule. Starting from these equations, it could be shown, that in the Newtonian flow region a mastercurve in form of a reduced birefringence Δn′/η₀=f(γ˙) and a reduced orientation φ= f(γ˙/γ˙ _crit) can be plotted, independent from concentration and molar mass. A comparison of the experimentally determined orientation angle and birefringence curve form with theoretical deformations and orientations of polymer coils in a solution state, without intermolecular interactions, was able to demonstrate that the flow behavior of a moderately concentrated network solution is determined decisively (approximately to 85%) by the disentanglement. Received: 8 May 2000 Accepted: 12 September 2000     

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     

The Effect of Sweep-Angle Variation on the Turbulence Structure in a Separated,Three-Dimensional Flow

A three-dimensional separated flow behind a swept, backward-facing step is investigated by means of DNS for Re _H = C _∞ H/ν = 3000 with the purpose to identify changes in the statistical turbulence structure due to a variation of the sweep angle α from 0° up to 60°. With increasing sweep angle, the near-wall turbulence structure inside the separation bubble and downstream of reattachment changes due to the presence of an edge-parallel mean flow component W. Turbulence production due to the spanwise shear ∂W/∂y at the wall becomes significant and competes with the processes caused by impingement of the separated shear-layer. Changes due to a sweep angle variation can be interpreted in terms of two competing velocity scales which control the global budget of turbulent kinetic energy: the step-normal component U _∞ = C _∞cosα throughout the separated flow region and the velocity difference C _∞ across the entire shear-layer downstream of reattachment. As a consequence, the significance of history effects for the development into a two-dimensional boundary layer decreases with increasing sweep angle. For α ≥50°, near-wall streaks tend to form inside the separated flow region. Received 7 November 2000 and accepted 9 July 2002 Published online 3 December 2002 RID="*" ID="*" Part of this work was funded by the Deutsche Forschungsgemeinschaft within Sfb 557. Computer time was provided by the Konrad-Zuse Zentrum (ZIB), Berlin. Communicated by R.D. Moser     

Rheological properties of poly(vinyl chloride)/plasticizer systems—relation between sol–gel transition and elongational viscosity

Poly(vinyl chloride) (PVC)/di-isononyl phthalate systems with PVC content of 45.5 (PVC8) and 70.4 wt% (PVC6) were prepared by a hot roller at 150 °C and press molded at 180 °C. The dynamic viscoelasticity and elongational viscosity of PVC8 and PVC6 were measured in the temperature range from 150 to 220 °C. We have found that the storage and loss shear moduli, G′ and G″, of PVC8 and PVC6 exhibited the power-law dependence on the angular frequency ω at 190 and 210 °C, respectively. Correspondingly, the tan δ values did not depend on ω. These temperatures indicate the critical gel temperature T _gel of each system. The critical relaxation exponent n obtained from these data was 0.75 irrespective of PVC content, which was in agreement with the n values reported previously for the low PVC concentration samples. These results suggest that the PVC gels of different plasticizer content have a similar fractal structure. Below T _gel, the gradual melting of the PVC crystallites takes place with elevating temperature, and above T _gel, a densely connected network throughout the whole system disappears. Correspondingly, the elongational viscosity behavior of PVC8 and PVC6 exhibited strong strain hardening below T _gel, although it did not show any strain hardening above T _gel. These changes in rheological behavior are attributed to the gradual melting of the PVC crystallites worked as the cross-linking domains in this physical gel, thereby inapplicability of the of time–temperature superposition for PVC/plasticizer systems.     

Viscoelastic properties of phosphoric and oxalic acid-based chitosan hydrogels

In a previous work, we have shown that chitosan true physical gelation occurs in some organic and inorganic acids (Hamdine et al. 2004). Two systems presenting similar gelation mechanisms were characterized furthermore in order to investigate the sol–gel transition: the chitosan–phosphoric acid and the chitosan–oxalic acid systems. By performing rheological measurements in the framework of linear viscoelasticity, we have investigated the effect of time, temperature, and polymer concentration on the gelation evolution. For both acid-based systems, gelation occurred above a critical polymer concentration around 5% w/v (g/100 ml) of chitosan. Isothermal time sweep experiments showed that the gelation occurs in three stages: (i) incubation; (ii) rapid increase of G′; and (iii) a last stage where G′ slowly reached its equilibrium value due to slow molecular diffusion. At the gel point, G′ and G′′ scaled with ω ⁿ , with n=0.55 for both acid-based systems and a fractal dimension d _f of 1.9. Cooling–heating cycles revealed that the gels showed thermoreversibility after one sequence, but became permanent during subsequent cycles.This revised version was published online in October 2005 with corrections to the author's name.     

Twist viscosity of mixtures of low molar mass nematics

Measurements of the twist viscosity, γ₁(DLS) and twist elastic coefficient, K₂₂(DLS) by electric-field-dependent dynamic light scattering (EFDLS) are reported for low molar mass nematics (LMMNs) 4′-heptyl-4-cyanobiphenyl (7CB) and 4′-octyl-4-cyanobiphenyl (8CB), and their binary mixtures at several temperatures in the nematic state. The results are compared with values (γ₁(Rheol)=α₃–α₂) computed from rheological measurements of the Leslie viscosities α₂ and α₃. For the binary mixtures, at each temperature, the measured twist viscosity γ₁(DLS) and corresponding twist elastic constant K₂₂(DLS) show approximately a linear additive dependence on concentration. The calculated twist viscosity, γ₁(Rheol), agrees with γ₁(DLS) for the pure components, but is significantly smaller for the binary mixtures. Our observations appear to be consistent with a recent report of a discrepancy between values of the tumbling parameter λ, determined using a small-strain oscillatory optical technique, vs those measured by a rheological method. These results suggest that, in the rheological measurements at large strains, the rate of director rotation for mixtures may be affected by a flow-induced change in structure, e.g., shear-induced biaxiality. Received: 17 March 2000 Accepted: 17 July 2000     

Uniaxial elongational behavior of poly(vinyl chloride) physical gel

A poly(vinyl chloride) (PVC,  M_w = 102×10³)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition behavior with elevating temperature. The critical gel temperature (T_gel) characterized with a power–law relationship between the storage and loss moduli, G^′ and G^″, and frequency ω, G￠=G^￠￠/tan  ( np/2 ) μ wⁿ{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the T_gel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations were expressed by the neo-Hookean model at high temperature (135°C) near the T_gel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature. These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions.     

Predicting the linear viscoelastic properties of monodisperse and polydisperse polystyrenes and polyethylenes

 For linear homopolymers the linear viscoelastic predictions of the double reptation model are compared to those of a recent, more detailed model, the “dual constraint model” and to experimental data for monodisperse, bidisperse, and polydisperse polystyrene melts from several laboratories. A mapping procedure is developed that links the empirical parameter K of the double reptation model to the molecular parameter τ_e of the dual constraint model, thereby allowing the parameter K to be related to molecular characteristics such as the monomeric friction coefficient ζ. Once K (or τ_e) are determined from data for monodisperse polymers, the double reptation model predicts that for fixed weight-average molecular weight M_w, the zero-shear viscosity η₀ increases slightly with increasing polydispersity M_w/M_n for log normal distributions, while for the dual constraint model η₀ is almost independent of M_w/M_n. Experimental data for polystyrenes show no increase (or even a slight decrease) in η₀ with increasing M_w/M_n at fixed M_w, indicating a deficiency in the double reptation model. The dual constraint theory is also applied to hydrogenated polybutadienes and commercial high-density polyethylenes, where we believe it can be used to indicate the presence of long side branches, which are difficult to detect by other analytic methods. Received: 11 October 2000 Accepted: 17 May 2001     

Slip coefficients and macroparameter jumps of a diatomic gas with rotational degrees of freedom on a weakly curved spherical surface

Using the half-space moment method, the problem of the slip of a diatomic gas along a rigid spherical surface is solved within the framework of a model kinetic equation previously proposed which takes into account the rotational degrees of freedom of the gas. Second-order slip coefficients (correctionsC _m ^′ , β _R ^′ , and β _R to the isothermal and thermal slip which are linear with respect to the Knudsen number Kn) are obtained. The gas macroparameter jump coefficientsC _v andC _q, which are of the second order in the Knudsen number and characterize the discontinuity of the normal mass and heat fluxes on the gas-rigid phase interface, are calculated. These coefficients are given as functions of the tangential momentum accommodation coefficient, the translational and rotational energy accommodation coefficients, and the Prandtl number. The coefficients are calculated for certain diatomic gases. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–173, January–February, 2000.     

Identification of Heterogeneous Constitutive Parameters in a Welded Specimen: Uniform Stress and Virtual Fields Methods for Material Property Estimation

Local strain data obtained throughout the entire weld region encompassing both the weld nugget and heat affected zones (HAZs) are processed using two methodologies, uniform stress and virtual fields, to estimate specific heterogeneous material properties throughout the weld zone. Results indicate that (a) the heterogeneous stress–strain behavior obtained by using a relatively simple virtual fields model offers a theoretically sound approach for modeling stress–strain behavior in heterogeneous materials, (b) the local stress–strain results obtained using both a uniform stress assumption and a simplified uniaxial virtual fields model are in good agreement for strains ɛ _xx < 0.025, (c) the weld nugget region has a higher hardening coefficient, higher initial yield stress and a higher hardening exponent, consistent with the fact that the steel weld is overmatched and (d) for ɛ _xx > 0.025, strain localization occurs in the HAZ region of the specimen, resulting in necking and structural effects that complicate the extraction of local stress strain behavior using either of the relatively simple models.

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     

Supersonic leeside flow topology on delta wings revisited

The leeside vortex structures on delta wings with sharp leading edges were studied for supersonic flow at the Institute of Theoretical and Applied Mechanics of the Russian Academy of Sciences in Novosibirsk. The experiments were carried out with three wings with sweep angles of χ=68°, 73°, and 78° and parabolic profiles in the 0.6 × 0.6 m² test section of the blow-down wind tunnel T-313 of the institute. The test conditions were varied from Mach numbers M=2 to 4, unit Reynolds numbers from Re _l=26 × 10⁶ to 56 × 10⁶ m⁻¹, and angles of attack from α=0° to 22°. The results of the investigations revealed that for certain flow conditions shocks are formed above, below, and between the primary vortices. The experimental data were accurate enough to detect the onset of secondary and tertiary separation as well as other boundaries. The various flow regimes discussed in the literature were extended in several cases. The major findings are reported. Received: 6 September 1999/Accepted: 24 January 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.