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) |
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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. |
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ISSN: | 1070-6631 1089-7666 |
DOI: | 10.1063/1.4983372 |