In this paper we investigate the transport properties for rigid spherically symmetric macromolecules, having a segment density distribution falling off as r- lambda . We calculate the rotational and translational diffusion coefficient for a spherically symmetric polymer and the shear viscosity for a dilute suspension of these molecules, starting from a continuum description based on the Debye-Brinkman equation. Instead of numerical methods for solving equations we use perturbative methods, especially methods from boundary-layer analysis. The calculations provide simple analytical formulae for the shear viscosity eta , and the translational and rotational diffusion coefficients DT and DR. The results can also be applied to suspensions of other porous objects, such as aggregates of colloidal particles in which D=3- lambda is called the fractal dimension of the aggregate.
Strating, P., & Wiegel, F. W. (1994). Transport coefficients for rigid spherically symmetric polymers or aggregates. Journal of physics A: mathematical and general, 27(27), 3731-3742. https://doi.org/10.1088/0305-4470/27/11/023