Analytical expression for the rotational friction coefficient of DLCA aggregates over the entire Knudsen regime

ABSTRACT

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)[26] $\frac{{\zeta }_r}{8\pi \mu a^3}=\frac{1+5.988{\text{Kn}}_{\text{1}}}{C_r({\text{Kn}}_{\text{1}})}{\{{\left[0.713N^{1.63}+0.287\right]}^{-1}+5.988{\text{Kn}}_{\text{1}}{\left[1.184N^{2.02}-0.184\right]}^{-1}\}}^{-1}$[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.

Copyright © 2018 American Association for Aerosol Research

EDITOR:

• Yannis Drossinos

Notes

¹ These are bounding estimates. Note that the algorithm we use to generate our aggregates yields particles whose radii of gyration are ∼30–33% of the maximum length.

² Note that if one applies the simple scaling arguments from Section 2.3 (translational friction coefficient proportional to the radius of gyration in the continuum and to the number of primary spheres in the free molecule regime, and rotational friction coefficients given by Euations (20)[20] ${\zeta }_r^c\sim k_0^{-3/d_f}{\zeta }_{r0}^c{N}^{3/d_f}$[20] and (21[21] ${\zeta }_r^{FM}\sim k_0^{-2/d_f}{\zeta }_{r0}^{FM}{N}^{1+\left(2/d_f\right)}$[21] )), one predicts that the ratio is independent of N in the continuum and free molecule regimes.