Abstract
In this paper properties of planar incompressible (viscoelastic) flows for which the constitutive equation is given by the Bird-DeAguiar model are examined. This is a nonlinear differential dumbbell model which was derived from molecular theory allowing the Brownian motion and hydrodynamic forces acting on the beads to be nonisotropic. The model is considered with no solvent contribution which corresponds to zero retardation time, and for the range of parameters for which it is considered to be valid. When the constitutive equation is coupled with the equations of conservation of mass and momentum, the flow is governed by a system of seven first order nonlinear partial differential equations. This system is examined for uniform, shear and extensional flows for stability and, for the time-independent case, for its type. It is found that there is always a stable base flow. Moreover, the corresponding time-independent linearized system does change type and may have three, five, or even seven real eigenvalues within the flow region. this last feature, all eigenvalues real, is a new feature and is associated with (among other factors) the Weissenberg number.
Published Version
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