In elongational flow

In packed beds of particles possessing small pores, dilute aqueous solutions of hydroly2ed polyacrylamide will sometimes exhibit dilatant behavior iastead of the usual shear thinning behavior seen ia simple shear or Couette flow. In elongational flow, such as flow through porous sandstone, flow resistance can iacrease with flow rate due to iacreases ia elongational viscosity and normal stress differences. The iacrease ia normal stress differences with shear rate is typical of isotropic polymer solutions. Normal stress differences of anisotropic polymers, such as xanthan ia water, are shear rate iadependent (25,26). 

Fig. 9. Stress distribution on a solid cylinder in elongational flow (the flow direction is x)...

Fig. 15. Simulation of conformational changes in elongational flow by preferred rotation of bonds perpendicular to flow direction (according to Ref. [70])...

In elongational flow, the entanglement regime was observed at much lower concentrations, even below [r ] c = 0.1 [169], The effect was initially thought to be the result of coil expansion in flow, but was later discarded in favor of the lifetime for entanglement formation, under dynamic conditions of flow. 

Hill JW, Cuculo JA (1976) In Elongational flow behavior of polymeric fluids, Rev in Macromol Chem 14 B, Marcel Dekker, New York, p 143... 

As in PP-based nanocomposite systems, the extended Trouton rule, 3r 0 (y t) = r E (so t), also does not hold for PLANC melts, in contrast to the melt of pure polymers. These results indicate that in the case of P LANC, the flow induced internal structural changes also occur in elongation flow [48], but the changes are quite different in shear flow. The strong rheopexy observed in the shear measurements for the PLA-based nanocomposite at very slow shear rate reflects the fact that the shear-induced structural change involved a process with an extremely long relaxation time. 

A simple RIS model of polymers in elongational flows is developed and used to analyze the coil stretching and chain retraction as a function of polymer and flow parameters. The results are in agreement with available experimental data on dilute polymer solutions in strong elongation flows. 

Swartjes, F.H.M. (2001) Stress induced crystallization in elongational flow, Ph.D. thesis, University of Technology Eindhoven, the Netherlands... 

The function F(t — t ) is related, as with the temporary network model of Green and Tobolsky (48) discussed earlier, to the survival probability of a tube segment for a time interval (f — t ) of the strain history (58,59). Finally, this Doi-Edwards model (Eq. 3.4-5) is for monodispersed polymers, and is capable of moderate predictive success in the non linear viscoelastic range. However, it is not capable of predicting strain hardening in elongational flows (Figs. 3.6 and 3.7). 

The pom-pom polymer reptation model was developed by McLeish and Larson (60) to represent long chain-branched LDPE chains, which exhibit pronounced strain hardening in elongational flows. This idealized pom-pom molecule has a single backbone confined in a reptation tube, with multiple arms and branches protruding from each tube end, as shown in Fig. 3.12(a). Mb is the molecular weight of the backbone and Ma, that of the arms. 

In 4.3 we have already seen that polymers, in the rubber or fluid condition, crystallize much more rapidly when their chains are oriented. Therefore a stretched rubber, if stereospecific in its molecular structure, is able to crystallize at a temperature considerably above its equilibrium thermodynamic melting point. Also a thermoplast such as polyethylene, when in the molten state or in solution, can crystallize spontaneously when the chains are being orientated in elongational flow. The latter case is utilized when polyethylene is spun from a diluted solution (gel spinning process), resulting in fibres of super-high strength and stiffness ( Dyneema fibres). 

Miles, M. J., Tanaka, K., and Keller, A. (1983). The behaviour of polyelectrolyte solutions in elongational flow the determination of conformadonal relaxation times (with an Appendix of an anomalous adsorption effect). Polymer 24 1081-1088. 

Nguyen TQ and Kausch H-H, "Flexible Polymer Chain Dynamics in Elongational Flow", Springer, Berlin, 1999. Reiner M, "Deformation and Flow", Lewis, London, 1948. 

In any case, the new parameter of the generalized invariant has now to be obtained from additional experiments in elongational flows. But the Wagner equation can now be written in the unified form ... 

The validity of the stress optical relationship for flowing liquids has been proved for ideal rubbers and flexible macromolecules at low extension. Many authors have shown that this relationship holds for a broader range of materials, providing the stresses are lower than 10 Pa in shear flow or 1 MPa in elongational flow (see Refs. [6, 13, 14] and part 3 of the present Chapter). Table 1 summarizes values of the stress optical coefficient C for some classical polymers. 

LDPE, and with polypropylene, PP, was studied In steady state shear, dynamic shear and uniaxial extenslonal fields. Interrelations between diverse rheological functions are discussed In terms of the linear viscoelastic behavior and Its modification by phase separation Into complex morphology. One of the more Important observations Is the difference In elongational flow behavior of LLDPE/PP blends from that of the other blends the strain hardening (Important for e.g. fllm blowing and wire coating) occurs In the latter ones but not In the former. 

Henderson, N. and Thurston, G., Society of Rheology Annual Meeting, Viscoelastic Effects in Elongational Flow A New Orifice Impedance Method, Minnesota, October, 2002. 

Fig. 9. Stress growth in elongational flow as calculated from Eq. (18.9)...

In elongational flow of the same velocity gradient, the viscous stresses are greater see Eq. (5.2). Anisometric solid particles become aligned in the direction of flow flexible particles become extended, i.e., anisometric, and aligned. Particles that are close to each other become separated from each other, while they can stay together in simple shear flow a doublet of spheres then continues rotating as one dumbbell-shaped particle. 

The magnitude of most of the effects mentioned also depends on flow type. In elongational flow, for instance, rodlike particles may obtain a parallel orientation in the direction of flow, which tends to decrease the viscosity increase caused by the particles. In turbulent flow, the relations are more complicated. 

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