Dilute solutions of macromolecules in a rectilinear Poiseuille flow

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Abstract
Rheological results for a dilute solution of elastic and rigid dumbbells in a rectilinear Poiseuille flow are obtained within the framework of the kinetic theory of polymeric liquids. The values of the stresses and viscometric functions resulting from the two models of a macromolecule are calculated and compared. In both cases some of the stress tensor components show contributions due to the coupling of Brownian motion to convection in the nonhomogeneous velocity field of the solvent. The coupling parameter ε∼λγ̄L/B is assumed small and used to develop a perturbation scheme. Here, γ̄ is the shear rate at the wall, B is the half-width of the channel, and L and λ are the characteristic length and relaxation time of the macromolecule. Unlike the elastic dumbbell model, the rigid dumbbell model predicts a viscosity increase with increasing channel width and a negative value for the second normal stress difference.