Abstract
The configurational distribution function of dumbbell macromolecules (rigid and linearly elastic) in a quadratic rectilinear flow is obtained. It is shown that, compared to linear flow results, the inhomogeneity of shear rate alters the distribution function in a significant way when the length scale of the inhomogeneity is comparable to the dumbbell size. Based on these configurational distribution functions, the mean slip velocities, and stress contributions of the dumbbells are computed. The analysis shows that the Kramers expression for the stress tensor must be replaced by the Irving–Kirkwood formulism which admits effects of local spatial variation in shear rate or dumbbell concentration on the ensemble averaging of the dumbbell connector force.
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