Validity of the superposition approximation in an application of the modified Oseen tensor to rigid polymers

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Abstract
The validity of the superposition approximation in the Kirkwood–Riseman formulation of polymer transport problems with the modified Oseen tensor is examined. For rigid polymers composed of spherical beads, the frictional forces exerted by them are obtained as the iterative solutions of coupled integral equations equivalent to the Stokes equation under the nonslip boundary condition. From a comparison with these exact solutions, it is found that the Kirkwood–Riseman formulation with the modified Oseen tensor gives correct results to terms of order σ3 in the case of uniform translation in a fluid at rest, but not for these terms in the case of uniform rotation in linear or vanishing flow, where σ is the ratio of the radius of the bead to the separation between the two.