An exploration and further study of an enhanced Oldroyd model

The Oldroyd 6-constant constitutive model for polymeric liquids [J. G. Oldroyd, “On the formulation of rheological equations of state,” Proc. R. Soc. A 200, 523 (1950)] was shown in the work of Bird [“A modification of the Oldroyd model for rigid dumbbell suspensions with Brownian motion,” Z. Angew....

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Veröffentlicht in:Physics of fluids (1994) 2017-05, Vol.29 (5)
Hauptverfasser: Bird, R. Byron, Drugan, W. J.
Format: Artikel
Sprache:eng
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Zusammenfassung:The Oldroyd 6-constant constitutive model for polymeric liquids [J. G. Oldroyd, “On the formulation of rheological equations of state,” Proc. R. Soc. A 200, 523 (1950)] was shown in the work of Bird [“A modification of the Oldroyd model for rigid dumbbell suspensions with Brownian motion,” Z. Angew. Math. Phys. 23, 157 (1972)] to have insufficient flexibility even to describe all second-order time-dependent behaviors of the simple molecular model of rigid dumbbells in solution. Bird proposed an enhancement of the Oldroyd model that would remove this deficiency. The advantage of such a continuum constitutive model is that it is far easier to use in solving specific flow problems than the more physical, but far more cumbersome, molecular models. Thus, if this enhanced constitutive model is indeed able to replicate the results of the molecular models, it should be extremely useful over the applicable range. Here, we employ the enhanced constitutive model of Bird [Z. Angew. Math. Phys. 23, 157 (1972)] to solve four different flow problems, and we verify that our solutions coincide exactly with those of a molecular model: through third order for rectilinear steady shear flow and steady extensional flow, and for one steady non-rectilinear flow (eccentric disk rheometer flow); and through second order for one unsteady (i.e., oscillatory) shear flow, thus providing strong confirmation of the physical veracity and utility of this continuum constitutive model, at least for small and moderate shear or extension rates.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.4983372