On the equivalence of simplest non-linear rheological equations for viscoelastic polymer media

Some equivalence conditions are formulated for non-linear models of polymer melts and solutions that are analogous to known conditions for three-constant linear rheological equations. The resulting model is analysed in simple shear and elongational flows. The kinematics of finite elastoviscous strains is considered in an appendix.     

Grid-shell theory,a new concept to explain thixotropy

Some rheological phenomena of the thixotropic pseudoplastic crude oils can not be accounted for by the earlier theories: e.g. stabilized hysteresis curve, no regeneration during motion, irreversible change of paraffin structure by shearing, anisotropic network after relaxation, influence of shear history on flow properties. The grid-shell theory seems to be adequate to interpret these characteristics.     

An improved simple version of a nonlinear theory of elasto-viscous polymer media

Summary Some rheological equations describing the elastoviscous behavior of concentrated polymer solutions and melts were suggested using a two-parameter elastic potential. These equations, containing a small number of parameters, are based upon a representation involving a set of nonlinear noninteracting relaxators (the Maxwellian models). As examples, shear and extension deformations are considered. The reasons for the choice of rheological constants are given. A comparison between the theory and some experiments for a simplest four-parameter model (two noninteracting nonlinear relaxators) has shown that it describes the tests much better than the simplest three parameter model developed previously.

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Zusammenfassung Ausgehend von einem zweiparametrigen elastischen Potential werden rheologische Stoffgleichungen abgeleitet, die das viskoelastische Verhalten von konzentrierten Polymerlösungen und Schmelzen beschreiben sollen. Diese Gleichungen, die nur wenige Parameter enthalten, basieren auf der Superposition einer Anzahl nichtlinearer, nicht miteinander in Wechselwirkung stehender Maxwell-Modelle (Relaxatoren). Als Beispiele werden Scher- und Dehnvorgänge betrachtet, wobei die Wahl der rheologischen Konstanten begründet wird. Ein Vergleich der Theorie für das einfachste Vier-Parameter-Modell (d. h. Parallelschaltung zweier nichtlinearer Relaxatoren) mit einigen Experimenten zeigt, daß diese hiermit wesentlich besser zu beschreiben sind als mit einem früher entwickelten einfachen Drei-Parameter-Modell.

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With 6 figures     

Dynamic viscoelastic properties of polymer melts

Summary An apparatus has been designed and constructed to measure the dynamic viscoelastic properties of polymer melts over the frequency range 10^–2–10³ Hz. The measurements made on two samples of polythene are discussed, the samples differing in their molecular weight distributions. Some fractions from these two parent polymers have also been studied. The results are compared with the modifiedRouse (3) theory for polymer melts, and with the liquid model proposed byBarlow,Erginsav andLamb (4).

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Zusammenfassung Mit Hilfe einer neuentwickelten Apparatur wurden Messungen der dynamischen viskoelastischen Eigenschaften von polymeren Schmelzen im Frequenzbereich 10^–2 bis 10^–3 Hz durchgeführt. Die Meßergebnisse, die an zwei Polyäthylenproben unterschiedlicher Molekulargewichtsverteilung erhalten wurden, werden diskutiert. Einige Fraktionen dieser beiden Polymeren wurden auch untersucht. Es wurden schließlich die Ergebnisse mit derRouseschen Theorie über polymere Schmelzen (3) und mit dem vonBarlow, Erginsav undLamb (4) vorgeschlagenen Flüssigkeitsmodell verglichen.

     

Non-linear viscoelastic behavior of polymer melts interpreted by fractional viscoelastic model

Very recently, researchers dealing with constitutive law pertinent viscoelastic materials put forward the successful idea to introduce viscoelastic laws embedded with fractional calculus, relating the stress function to a real order derivative of the strain function. The latter consideration leads to represent both, relaxation and creep functions, through a power law function. In literature there are many papers in which the best fitting of the peculiar viscoelastic functions using a fractional model is performed. However there are not present studies about best fitting of relaxation function and/or creep function of materials that exhibit a non-linear viscoelastic behavior, as polymer melts, using a fractional model. In this paper the authors propose an advanced model for capturing the non-linear trend of the shear viscosity of polymer melts as function of the shear rate. Results obtained with the fractional model are compared with those obtained using a classical model which involves classical Maxwell elements. The comparison between experimental data and the theoretical model shows a good agreement, emphasizing that fractional model is proper for studying viscoelasticity, even if the material exhibits a non-linear behavior.     

Stable crack growth in viscoelastic media

Conclusions It follows from the last two examples, that for unsteady creep, with the creep effect diminishing in time, the crack grows at a diminishing rate, and after a certain time crack growth comes almost completely to a stop. For steady creep, however, crack growth does not diminish, but proceeds at a constant rate. These conclusions are in good agreement with results obtained earlier by L. M. Kachanov [3, 4] and G. P. Cherepanov [12].Prikladnaya Mekhanika, Vol. 4, No. 6, pp. 74–79, 1968     

Particle-liquid mass transfer in viscoelastic media

The problem of mass transfer from a solid sphere to a viscoelastic fluid has been examined theoretically. It is shown that fluid elasticity increases marginally the mass transfer rate in the creeping flow regime. This will have serious implications on the mass transfer from bubbles if impurities are present. Some conclusions on mass transfer at high Reynolds numbers are also offered.     

A model for the nonisothermal behavior of viscoelastic media

Summary A new constitutive model is derived for the viscoelastic behavior of polymers under non-isothermal loading. The model extends the concept of adaptive links (entanglements) between polymeric molecules to thermoviscoelastic media. By using experimental data for Nylon-6 and polyisobutylene in the vicinity of the glass-transition temperature, we find parameters of the model and study their dependence on temperature. The model is employed for the numerical analysis of the material response to time-periodic loads under isothermal conditions and to time-varying loads under heating. The results of numerical simulation demonstrate fair agreement with experimental data. Accepted for publication 23 May 1996     

Rheology of compatibilized immiscible viscoelastic polymer blends

Rheological behavior of a PS/PE model viscoelastic immiscible blend compatibilized by two types of interfacial modifiers was investigated. Dynamic, steady shear, and transient experiments were performed to probe the effect of the interfacial modification on the rheological behavior of the blend. While the effect was relatively small in dynamic and steady shear experiments, significant signature of the presence of the copolymer was observed in transient experiments after start up of shear flow. The magnitude of the departure from Doi-Otha theory (worked out for non-compatibilized blends) was evaluated. Received: 6 March 2000 Accepted: 15 June 2000