Analysis of the Rouse model in extensional flow. II. Stresses generated in sink flow by flexible macromolecules and by finitely extended macromolecules

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Abstract
Stresses generated by a solution of Rouse macromolecules in planar and axisymmetric sink flow were analyzed by solving the momentum equation together with the constitutive relation corresponding to the Rouse model (i.e., the generalized convected Maxwell equation). The results show that the additional normal stress in the radial direction is of order [η]c when compared with the corresponding Newtonian viscous stress. However, in the high Reynolds number range where sink flow conditions are valid, the additional stress must be compared with inertial stresses, and in that case the results show that the ratio of non‐Newtonian to Newtonian hydrodynamic stresses is of order [η]c/Re, where Re is the Reynolds number. Since experimental data exceed this small ratio by two orders of magnitude, a new molecular model was developed to accommodate limited molecular extension. The model presumes that, in a converging flow, a molecule initially deforms as a Rouse molecule and then its configuration is frozen after a certain amount of extension. This ‘‘frozen‐necklace’’ model consequently provides an estimate of hydrodynamic effects caused by finite extension, as might be created by intramolecular entanglements. Non‐Newtonian stresses predicted by the model are compared with available data for strictly dilute solutions and agree to the same order of magnitude.