Volume 46, Issue 5, September 2002
Index of content:
46(2002); http://dx.doi.org/10.1122/1.1501925View Description Hide Description
The rheological behavior of a monodisperse suspension of non-Brownian particles undergoing simple shear flow in the presence of a weak interparticle force is studied using accelerated Stokesian dynamics. The availability of a faster numerical algorithm permits the investigation of larger systems (typically of 512 particles), and accurate results for the suspensionviscosity, first and second normal stress differences, and the particle pressure are determined as a function of the volume fraction. The system microstructure, expressed through the pair-distribution function, is also studied and it is demonstrated how the resulting anisotropy in the pair-distribution function is correlated with the suspension non-Newtonian behavior. The ratio of the normal to excess shear stress is found to be an increasing function of the volume fraction, suggesting different volume fraction scalings for different elements of the stress tensor. The relative strength and range of the interparticle force is varied and its effect on the shear and normal stresses is analyzed. Volume fractions above the equilibrium freezing volume fraction are also studied and it is found that the system exhibits a strong tendency to order under flow for volume fractions below the hard-sphere glass transition; limited results for however, show that the system is again disordered under shear.
46(2002); http://dx.doi.org/10.1122/1.1501963View Description Hide Description
Ghosh et al. (2001) demonstrated that the Kramers chain captures the optical and rheological properties of dilute polymer solutions in rapidly varying elongational flows better than the finitely extensible nonlinear elastic dumbbell model. A new model, based on introducing an adaptive length scale (ALS) as an internal variable, is developed to reproduce the fine scale physics of the Kramers chain. The resulting ALS-model describes the polymer molecule as a set of identical segments in which each segment represents a fragment of the polymer that is short enough so that it can sample its entire configuration space on the time scale of an imposed deformation and, therefore, stretch reversibly. As the molecule unravels, the number of segments decreases, but the maximum length of each segment increases, so that the constant maximum contour length of the molecule is preserved. The ALS model gives very good predictions of stress growth in startup of uniaxial elongation and stress-birefringence hysteresis in a uniaxial elongational flow followed by relaxation. A closed form of the constitutive equation, the ALS-C model, is proposed. The rheological predictions of the ALS-C model resemble those of the ALS equation. This coupled with its small number of internal degrees of freedom suggests that this constitutive equation may be useful in modeling complex flows.
In situ rheo-x-ray investigation of flow-induced orientation in layered silicate–syndiotactic polypropylene nanocomposite melt46(2002); http://dx.doi.org/10.1122/1.1498284View Description Hide Description
This article describes experimental results for both the rheology and flow-induced orientation of a series of intercalated syndiotactic polypropylene nanocomposites which were prepared by melt intercalation in the presence or absence of an i-PP/maleic anhydride copolymer. The nanocomposites showed typical rheological signatures of well-dispersed interacalated nanocomposites such as a low frequency plateau in dynamic moduli and an apparent yield transition from very high viscosity at low shear stresses to low viscosity above a yield stress.In situx-ray diffraction(XRD)measurements during shear provided direct evidence of rheology-microstructure links in these materials. It was found that the clay tactoids could be easily oriented by shear and that a high degree of orientation can be achieved after the yield transition. Further, the rheo-XRD apparatus allowed measurements of the relaxation of orientation upon the cessation of flow. The orientation relaxation time matched the characteristic relaxation times estimated from independent rheological measurements well.
46(2002); http://dx.doi.org/10.1122/1.1501927View Description Hide Description
We present a theory of the linear viscoelasticity of dilute solutions of freely draining, inextensible, semiflexible rods. The theory is developed expanding the polymer contour about a rigid rod reference state, in a manner that respects the inextensibility of the chain, and is asymptotically exact in the rodlike limit where the polymer length L is much less than its persistence length In this limit, the relaxation modulus exhibits three time regimes: At very early times, less than a time required for the end-to-end length of a chain to relax significantly after a deformation, the average tension induced in each chain and both decay as Over a broad range of intermediate times, where is the longest relaxation time for the transverse bending modes, the end-to-end length decays as while the residual tension required to drive this relaxation and both decay as As later times, the stress is dominated by an entropic orientational stress, giving where is a rotational diffusion time, as for rigid rods. Predictions for and are in excellent agreement with the results of Brownian dynamics simulations of discretized free draining semiflexible rods for lengths up to and with linear viscoelastic data for dilute solutions of poly-γ-benzyl-L-glutamate with
Large amplitude oscillatory shear and Fourier-transform rheology for a high-density polyethylene: Experiments and numerical simulation46(2002); http://dx.doi.org/10.1122/1.1495493View Description Hide Description
Rheological characterization of a high-density polyethylene is performed by means of measurements of the storage and loss moduli with a new viscometric device. Shear viscosity is deduced from both the Cox–Merz rule and capillary measurements. Subsequently, oscillatory experiments are performed in the nonlinear regime, with deformation amplitudes as high as 10. A multimode Giesekus model is selected to describe the rheological behavior of the melt, the parameters of which are successively identified on the basis of the linear properties and the shear viscosity. This model is subsequently used for the numerical simulation of large amplitude oscillatory flows. Fourier-transform rheology is applied to both experimental measurements and simulation results. A comparison is made on the basis of the value of the harmonics, the maximum amplitude of the stress signals, and the phase shift occurring between the applied deformation and the stress output signal. Good quantitative agreement is found between experiments and calculations, demonstrating the relevance of the present approach.
46(2002); http://dx.doi.org/10.1122/1.1495492View Description Hide Description
Rheological data are reported for five fractions of poly(diethylsiloxane) (PDES) with molar masses of PDES ranging from 45 to 200 kg/mol. At room temperature, the samples exhibit a stable mesomorphic (biphasic) structure consisting of a mesophase (condis crystal) and an amorphous phase. The effects of molar mass and temperature on the rheological properties of PDES are examined. At ambient temperatures, the high molar mass samples are highly elastic, as evident from the weak dependence of and on the frequency. This elastic behavior is attributed to the presence of mesophase domains that act as effective crosslinks in the melt. The mesophase melts to an amorphous phase on heating past an isotropization temperature that depends on molar mass. The biphasic and amorphous states exhibit large differences in their low frequency rheological responses. The kinetics of mesophase formation is found to be dependent on the molar mass.
46(2002); http://dx.doi.org/10.1122/1.1501924View Description Hide Description
The rheological properties of a dilute solution of polymers in a good solvent are predicted by incorporating excluded volume effects and hydrodynamic interactions into a Hookean dumbbell model. We use a narrow Gaussian repulsive potential between the beads of the dumbbell to model the effect of excluded volume. The linear viscoelastic relaxation modulus is estimated using Brownian dynamics simulations and a Green–Kubo relation. When excluded volume interactions dominate, a stretched-exponential function is shown to better describe the decay of the relaxation modulus with time, than a simple exponential decay. Although the excluded volume and hydrodynamic interactions are nonlinear phenomena,Brownian dynamics simulations show that their influence on viscosity and first normal stress difference coefficient is approximately additive. This linear coupling, however, is not true for the second normal stress difference coefficient. Results of Brownian dynamics simulations also show enhanced shear thinning as the solvent quality improves. The results of the simulations are compared with predictions obtained by assuming that the configurational distribution function is Gaussian. The Gaussian approximation is accurate in certain ranges of the model parameters and in overall qualitative agreement with the Brownian dynamics simulations.
Effects of solvent quality on the dynamics of polymer solutions simulated by dissipative particle dynamics46(2002); http://dx.doi.org/10.1122/1.1498285View Description Hide Description
The rheology and configurational properties of dilute polymer solutions in steady shear flow are modeled by dissipative particle dynamics (DPD), a new mesoscopic simulation method. The simulations represent the polymer as a 10-bead chain of FENE connector springs and the solvent as a sea of free DPD particles. Thermodynamic interactions between the polymer and solvent are modeled by varying the strength of the repulsive forces acting between unlike particle species. Since DPD simulations model the full hydrodynamics of the polymer–solvent system, instantaneous hydrodynamic interactions among beads of the polymer chain emerge naturally from the simulations. The predicted rheological material functions include realistic features such as shear thinning of the viscosity and first normal stress coefficient, and negative values for the ratio The enhancement of η, and by means of chain expansion in good solvents is also realistically represented by the model predictions. The DPD simulations accurately describe the variation of the orientation angle of polymer chains with the shear rate, and predict macromolecular expansion ratios that are in good agreement with the recent flow light scattering measurements of Lee and Muller [Polymer40, 2501–2510 (1999)].
46(2002); http://dx.doi.org/10.1122/1.1498283View Description Hide Description
Steady shear rheology of entangled polystyrene (PS)-diethyl phthalate (DEP)solutions are investigated using mechanical rheometry and optical birefringencemeasurements.Polymer solutions are formulated using narrow molecular weight distribution polymers that cover a broad range of molecular weights and concentrations of In polymer systems with cone-and-plate and narrow-gap parallel plate shear flowmeasurements reveal an unusual transition to non-Newtonian behavior at The transition is evidenced by early power law deviations from Newtonian fluid response, and is consistent with earlier observations reported by Bercea et al. [Macromolecules26, 7095–7096 (1993)] and by Islam and Archer [J. Polym. Sci., Part B: Polym. Phys. 39, 2275–2289 (2001)] for solutions of ultrahigh molecular weight polymers in good solvents. The power-law flow regime extends well beyond for most systems studied and its breadth is proportional to the number of entanglements in solution. Arguments ranging from supramolecular complex formation in concentrated polymer solutions to tube distortion at low shear rates have previously been advanced to explain this behavior. Using gap-dependent steady shear measurements and a slip constitutive equation suggested by theory, we show that the behavior is caused by interfacial slip. A procedure based on attachment of micron-sized silica glass beads to parallel-plate, cone-and-plate, and Couette shear fixtures is shown to be highly effective for reducing slip errors in steady shear rheometry of entangled PS/DEP solutions. Steady-state shear stress and first normal stress difference results obtained using several well entangled PS/DEP solutions are compared with predictions from two recently proposed molecular-based constitutive models.
46(2002); http://dx.doi.org/10.1122/1.1501962View Description Hide Description
The flow-induced morphology of aqueous mixtures of gelatin and dextran was investigated during gelation of the dispersed phase. Mixtures with 5% volume fraction of the gelatin-rich phase dispersed in the dextran-rich phase were sheared in a translating parallel plate apparatus coupled with an optical microscope. Gelation of the dispersed phase was brought about by decreasing mixture temperature under flow. As a consequence of gelation, the dispersed phase aggregated, forming clusters of gelled, partially coalesced, spherical particles. Cluster size was found to depend on the shear rate applied during gelation and on the temperature profile. Indeed, smaller clusters were formed: (a) under faster flows, (b) if the temperature was decreased to lower levels, and (c) if gelation was induced under quiescent conditions and the flow started only afterwards. By acting on these parameters, it is possible to suppress or enhance cluster formation and to tune cluster size. When the temperature was increased again above the gelation temperature, the gelled particles melted and the clusters rapidly coalesced.
Experimental observation and matching numerical simulation for the deformation and breakup of immiscible drops in oscillatory shear46(2002); http://dx.doi.org/10.1122/1.1501960View Description Hide Description
This paper describes experimental results on the way immiscible drops of a Newtonian fluid can deform and breakup when subject to oscillatory shear deformation. The paper also reports a matching three-dimensional numerical simulation of corresponding events. Using an optical shearing apparatus and a modified rheometer, experimental observations on the deformation of drops with a viscosity ratio of unity were carried out for a range of strain amplitudes and frequencies. For moderate strain deformations, it was discovered experimentally that the dropdeformation oscillates between a maximum and a nonzero minimum deformation parameter and that the numerical simulation was able to capture both this and start up effects. For large strain deformations it was experimentally observed that breakup occurred only by one mechanism; namely, end pinching, and this was successfully matched by the numerical simulation. The results for oscillatory deformation and breakup are compared with those obtained in steady shear.
46(2002); http://dx.doi.org/10.1122/1.1501961View Description Hide Description
The yield behavior of concentrated carbonyl ironmagnetorheological fluids (MRF) is investigated measuring the normal force during shear flow in a plate–plate controlled-stress rheometer. For high enough external magnetic fields, a positive normal force is obtained below the yield point. This result is not explained using affine deformation chain models. However, the assumption of gapspanning particle chains and spheroidal aggregates of spheres predicts not only a positive normal force but also a maximum if we plot the normal force as a function of the strain, a result also found experimentally. The field dependence of the normal force suggests the existence of a threshold field, likely associated to the formation of gapspanning structures in the MRF. Another possible explanation for the maximum in the normal force lies on the phase transition from homogeneous to layered structures with cylindrical symmetry in the suspension. Steady-state and oscillometry studies show that the maximum in the normal force is associated to the onset of flow, most probably due to the fact that at that moment the aggregates no longer link the plates. We also find that the yield stress obtained from the extrapolation of the rheogram to zero shear rate is above the one predicted by dynamic investigations.