Elongation flow rheology

The rheological constitutive equation of the Rouse model is that of an upper-convected Maxwell model, with the consequence that steady-state elongational flow only exists for strain rates lower than l/(2A,i). The steady-state elongational wscosity depends then on strain rate ... 

Part 2 presents a summary of the theoretical considerations and basic assumptions that lead to the model equations. Part 3 discusses some experimental aspects and focuses on the measmements in various shear and uniaxial elongational flow situations. Part 4 and 5 are devoted to the comparisons between experimental and predicted rheological functions. Problems encountered in the choice of correct sets of parameters or related to the use of each type of equation will be discussed in view of discrepancies between model and data. 

Doi and Edwards (1978) and Kuzuu and Doi (1980) have solved the Smoluchowski equation (6-47)-(6-48) for simple shearing and elongational flows, and they obtained predictions of rheological behavior that are similar to those of the reptation theory for concentrated flexible polymers discussed in Section 3.7.5.1. Figure 6-19, for example, shows the shear-rate-dependence of the shear viscosity and first and second normal stress coefficients predicted by the Doi-Edwards theory for semidilute rods these results are similar to those predicted by the Doi-Edwards theory for entangled flexible molecules. At... 

The stress in viscoelastic liquids at steady-state conditions is defined, in simple shear flow, by the shear rate and two normal stress differences. Chapter 13 reviews the evolution of both the normal stress differences and the viscosity with increasing shear rate for different geometries. Semiquantitative approaches are used in which the critical shear rate at which the viscosity starts to drop in non-Newtonian fluids is estimated. The effects of shear rate, concentration, and temperature on die swell are qualitatively analyzed, and some basic aspects of the elongational flow are discussed. This process is useful to understand, at least qualitatively, the rheological fundamentals of polymer processing. 

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. 

Lee et al. (1981) highlighted the importance of shear and elongational flows for SMC polyesters in flow modelling. They described the following rheological models ... 

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

We have illustrated the many ways in which elongational flow behavior can provide novel information about the behavior of macromolecules. Special emphasis has been given to rheological changes associated with extensional flow fields. 

Mixing rheology - elongational flow. The above considerations are obviously oversimplified and neglect the particular behaviour of viscoelastic materials. On one hand, we have already pointed out that it is difficult to introduce the more realistic viscosity function n = f ( y> T), and,on the other hand, it is quite clear that the mixing process is not isothermal. Furthermore, Tokita and White (13, 14) demonstrated that the lubrication theory can be applied to a nip of length L and depth H providing that... 

Lee, S. H., Cho, E., and Youn, J. R., Rheological behavior of polypropylene/layered silicate nanocomposites prepared by melt compounding in shear and elongational flows, J. Appl. Polym. Sci, 103, 3506-3515 (2006). 

Theoretical description of dendritic structures is an active but difficult topic because the length between branched points is close to or even smaller than the Kuhn length, above which the segments can be thought of as if they are freely jointed with each other. Most modeling or simulation work has focused on the quasi-static and rheological properties of hyperbranched polymers and dendrimers in shear flow [240, 244, 255-263]. Limited amounts of data were published for dendrimers and hyperbranched polymers within elongational flow field. 

Muller AJ, Odell JA, Keller A (1988) Elongational flow and rheology of monodisperse polymers in solution. J Nonnewton Fluid 30 99-118... 

Gabriel, G., and H. Miinstedt. 2003. Strain hardening of various polyolefins in uniaxial elongational flow. Journal of Rheology 47 619-630. 

Hingmann, R., and B. L. Marczinke. 1994. Shear and elongational flow properties of polypropylene melts[sup a)]. Journal of Rheology 38 573-587. 

La Mantia, F. R, R. Scaffaro, G. Carianni, and P. Mariani. 2005. Rheological properties of different film blowing polyethylene samples under shear and elongational flow. Macromolecular Materials and Engineering 290 159-164. 

Mighri, R, A. Ajji, and P. J. Carreau. 1997. Influence of elastic properties on drop deformation in elongational flow. Journal of Rheology 41 1183-1201. 

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