1,721,073 research outputs found
Stress induced demixing in simple shear flow: suitable formulation of the two-fluid theory
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On compatibility of the Cox-Merz rule with the model of Doi and Edwards
No full textA recently suggested relaxation mechanism which is expected to be dominant in fast flows of polymer melts is combined here with the tube model of Doi and Edwards, and the corresponding constitutive equation is derived. The mechanism consists of the renewal of topology by convective displacement of entanglements. Detailed predictions for the flow curve in steady shear are obtained in order to test the agreement with the Cox-Merz rule. With respect to the basic tube model, significant progress is achieve
Stress tensor and stress-optical law in entangled polymers
No full textThe molecular origin of the stress in entangled polymers is reconsidered here, in order to ascertain whether or not the pressure that the confined chain exerts on its 'tube of constraints' should be accounted for. Indeed, the classical expression for the stress includes only traction along the chain. The analysis shows that the pressure terms significantly contribute to the stress provided flow or deformation creates a long-lasting local anisotropy of the chain confinement. The effects of such anisotropy is described by means of elliptical cross-sections of the constraining tubes. The new expression for the stress tensor thus obtained properly degenerates into the classical one for circular cross sections. It is also shown that the stress-optical law remains obeyed. (C) 1998 Elsevier Science B.V. All rights reserve
A simple constitutive equation for entangled polymers with chain stretch
No full textWe propose a simple way of including chain stretch effects in convective constraint release theories for entangled polymers. The main idea is that the characteristic time of orientational relaxation depends in a series-parallel way on all three relevant mechanisms, i.e., reptation, constraint release (thermal and convective), and Rouse relaxation. As usual, a separate equation describes chain stretch, which however is assumed not to be affected by constraint release. The model is further simplified by writing the orientational equation in differential form. For step strains, the successful damping function of the Doi-Edwards theory is exactly preserved. Predictions in steady shear also favorably compare with typical data of nearly monodisperse polymer
Falling spheres in polymeric solutions. Limiting Results of the Two-Fluid Theory of Migration
No full textIn this paper we derive a few analytical results for the case of polymeric solutions flowing past a spherical obstacle. The calculations are meant to ascertain the possible importance of flow-induced migration (i.e., of changes in concentration), making use of the, recent two-fluid theory of Doi and Milner. In order to obtain solutions in closed form, the problem is suitably linearised; in particular, we have considered both the case of Newtonian behaviour of the polymeric liquid flowing past the sphere, and that of a linearly elastic polymeric gel perturbed by a localised force. The results, though confirming migration effects, indicate that, in these linear limits at least, the concentration change decays quadratically with the reciprocal distance from the centre of the perturbation, i.e., no long ''wake'' is predicted. Another outcome of these calculations refers specifically to the viscous case. The classical Stokes result is recovered only as a singular solution of the two-fluid proble
Open problems in tube models for concentrated polymers
No full textIn this work we examine the Doi-Edwards (D-E) theory corrected with convective constraint release (CCR) to show that open problems still remain. One of them is incomplete fulfilment of the Cox-Merz rule. Another problem is underprediction of the normal stress ratio in shear in the limit of low stresses. The latter problem is directly linked with deformation tensor Q of D-E theory. We then show that in order to solve these problems one should account for the fact that the deformation process makes the constraining tubes elliptical in cross-section, an assumption consistent with the affine deformation of the grid of topological constraints. It is shown, however, that the affine deformation of the tube segments overpredicts the desired corrections. It so appears that, although the tube section must change during deformation to become elliptical, the constraint deformation is less than affine
Letter to the Editor: A note added to “Prediction of rheometrical and complex flows of entangled linear polymers using the double-convection-reptation model with chain stretching” [J. Rheol. 47, 247 (2003)]
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