Calculating the rotational friction coefficient of fractal aerosol particles in the transition regime using extended Kirkwood-Riseman theory.

We apply our extended Kirkwood-Riseman theory to compute the translation, rotation, and coupling friction tensors and the scalar rotational friction coefficient for an aerosol fractal aggregate in the transition flow regime. The method can be used for particles consisting of spheres in contact. Our approach considers only the linear velocity of the primary spheres in a rotating aggregate and ignores rotational and coupling interactions between spheres. We show that this simplified approach is within approximately 40% of the true value for any particle for Knudsen numbers between 0.01 and 100. The method is especially accurate (i.e., within about 5%) near the free-molecule regime, where there is little interaction between the particle and the flow field, and for particles with low fractal dimension (≲2) consisting of many spheres, where the average distance between spheres is large and translational interaction effects dominate. Our results suggest that there is a universal relationship between the rotational friction coefficient and an aggregate Knudsen number, defined as the ratio of continuum to free-molecule rotational friction coefficients.