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On an exact starting expression for macromolecular hydrodynamic models

A calculational method developed by G. K. Youngren and A. Acrivos [J. Fluid Mech. 75, 377 (1975)] expresses the fluid forces exerted over the surface of an immersed body in terms of differences between body and fluid motions. As opposed to bead‐model approaches, this method starts from an essentially exact hydrodynamic expression, and therefore should be of particular interest to those workers trying to obtain accurate coefficients needed to characterize the diffusive and viscoelastic behavior of macromolecules with complex shapes. However, Youngren and Acrivos's treatment has not been widely adopted nor even used as a proper starting place for higher order bead‐model methods. This is probably related to the unfamiliar appearance of their exact expression, which involves two surface integral terms as opposed to the single summation involved in bead models. We show that their expression may be rewritten in the expected analogous form involving one surface integral term whenever stick boundary conditions are applied to a rigid body or a flexible body composed of rigid segments. For spherical segments, we obtain Rotne–Prager‐type bead‐model results by following typical assumptions. Extensions to deformable particles are considered, in which internal friction can be represented by an arbitrarily viscous internal fluid.