The Rheology of Two-Phase Flows

SYNOPSISPolarized light microscopy shows that polypropylene crystallizes from the melt into a welldistinguished spherulitic structure. Therefore, it provides a useful model for molten-filled polymers, where the growing spherulites are considered to be filler particles dispersed in a matrix fluid. Although spherulites are randomly dispersed in the space, two dispersion models (simple cubic and centered cubic) are discussed to correlate the transformed fraction a ( t ) with the volume fraction of filler q5 (t). The combination of these results with those of differential scanning calorimetry (DSC) shows that the transformed fraction a(t) is a direct indication of the volume fraction of filler q5(t). The rheological study, using oscillatory experiments coupled with DSC results, shows the relative sensitivity of the rheological functions to structural changes of the liquid during crystallization. Furthermore, they reveal the existence of a yield effect above a certain critical value of the filler content (& = 0.4). In the absence of this yield effect, a model is proposed to predict the variation of the rheological functions with the filler content. This model shows not only a variation of the plateau modulus, but also the modification of the characteristic times of relaxation of the polymer matrix, whereas the shape of the relaxation spectrum remains unchanged. 0 1996 John Wiley & Sons, Inc. INTRODUCTION Rheological BehaviorThe rheological behavior of filled polymers strongly depends on a large number of parameters such as volume fraction, shape and size of particles, fillerfiller and filler-matrix interactions. The influence of the volume fraction on the main flow functions such as viscosity and normal stress coefficients has been the most extensively discussed in the literat~r e . ' -~ In order to overcome problems arising from the shape or anisometry of the particles, several author^'^^-'^ have used spherical particles such as glass beads and metal spheres. In general, the models proposed are concerning the steady shear flow. They are derived from theories established for suspensions of elastic particles in a Newtonian fluid. LeonovZ0 has proposed another approach wherein he described the rheological behavior of filled polymers by a model in which the total mean stress 7 is represented by the following sum:where 7, represents the mean stress arising in a suspension of inactive particles in a matrix, and 7p is an additional mean stress due to the particle-toparticle interactions in the particulate phase. The matrix mode was described using viscoelastic equations known for pure polymers (Maxwellian modes). In this description, the dependencies of the rheological parameters on the particle loading 4 was included. For the particle mode, he took into account both the effect of finite elasticity and the dissipative effect. Therefore, assuming that the matrix parameters are independent of the particle size, only hydrodynamic interactions between particles of filler are assumed to have an effect on the behavior of the pol...

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“…In the case of the moduli, the function of 4 of the right side of Eq. (19) seems to be also a frequency-dependent term. cubic models).…”

Section: Correlation Between Dsc and Polarized Light Microscopymentioning

confidence: 91%

Polypropylene during crystallization from the melt as a model for the rheology of molten-filled polymers

Boutahar¹,

Carrot²,

Guillet³

1996

J. Appl. Polym. Sci.

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“…The attention is drawn to the solidlike behavior at small deformation rates, claiming that the nonterminal flow region is the most important PNC characteristic. However, such behavior has been observed in all MPSs having a percolated three-dimensional network i.e., in suspensions, ionomers, polymer alloys (e.g., compatibilized, low concentration blends [Utracki and Kamal, 2002]), composites, and foams [Utracki, 1988[Utracki, , 1995[Utracki, , 2004Krishnamoorti and Yurekli, 2001;Solomon et al, 2001]. Thus, such behavior is not unique for PNCs, but related to the presence of three-dimensional structures.…”

Section: Melt Rheologymentioning

confidence: 99%

“…Within the linear viscoelastic region the modified Krieger-Dougherty [1959] dependencies might be used [Utracki, 1988;Utracki and Lyngaae-Jørgensen, 2002]:…”

Section: Small-amplitude Oscillatory Shear Flowmentioning

confidence: 99%

“…Since in most MPSs the morphology of a given material controls its performance, testing the same MPSs under different flow conditions is equivalent to testing different materials. In consequence, the test method selected should reflect the final use of the data (e.g., when simulation of the flow through dies is important, capillary data are useful, but in general, for MPS characterization, low strain dynamic tests are preferred [Utracki, 1988[Utracki, , 1989[Utracki, , 1995). Recognizing the flow effects on the structure and physical properties, simultaneous methods of the structure characterization in flow have been developed.…”

Section: Introductionmentioning

confidence: 99%

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Rheology of Polymers with Nanofillers

2010

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“…The expression derived for the relative viscosity over the full range of concentration had two theoretical parameters, the intrinsic viscosity and the maximum packing volume fraction, which could be measured independently. With their experimental values, the theoretical expression was proved valid for numerous suspensions of not necessarily spherical monodispersed particles [Utracki, 1988]. Moreover, a start was made, with a graduate student, Jacques Zakin, on adapting hard-sphere theory to develop a corresponding-states principle for the viscosity of concentrated solutions of flexible coils Zakin, 1960, 1962].…”

Section: New York-washington 1938-1958mentioning

confidence: 99%