Abstract

The finitely extensible nonlinear elastic (FENE) dumbbell model used earlier for dilute polymer solutions may also be used for concentrated solutions and melts if the Brownian motion and hydrodynamic forces acting on the beads are made nonisotropic. This corresponds roughly to imagining that a dumbbell is constrained to move within a capsule-shaped region embedded in the surrounding fluid. The constitutive equation obtained (a modified convected Maxwell model) contains four parameters: σ and β specify the extent of anisotropy in Stokes' law and in the Brownian motion forces respectively; λ is a time constant; and b describes the finite extensibility of the dumbbell. When σ and β are set equal to unity, the dilute-solution constitutive equation is recovered. In this sense the molecular theory given here permits a description of polymeric liquids over the entire concentration range.

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