We apply a self-consistent field method (Corson et al. 2017c) to calculate the rotational friction coefficient for fractal aerosol particles in the transition flow regime. Our method considers hydrodynamic interactions between spheres in a rotating aggregate due to the linear velocities of the spheres. Results are consistent with electro-optical measurements of soot alignment. Calculated rotational friction coefficients are also in good agreement with continuum and free molecule results in the limits of small (Kn = 0.01) and large (Kn = 100) primary sphere Knudsen numbers. As we previously demonstrated (Corson et al. 2017b) for the translational friction coefficient, the rotational friction coefficient approaches the continuum limit as either the primary sphere size and the number of primary spheres increases. We apply our results to develop an analytical expression Equation (26) for the rotational friction coefficient as a function of the primary sphere size and number of primary spheres. One important finding is that the ratio of the translation to rotational diffusion times is nearly independent of cluster size. We include an extension of previous scaling analysis for aerosol aggregates to include rotational motion.
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