Friction factor for aerosol fractal aggregates over the entire Knudsen range

We develop an approach for computing the hydrodynamic friction tensor and scalar friction coefficient for an aerosol fractal aggregate in the transition regime. Our approach involves solving the Bhatnagar-Gross-Krook equation for the velocity field around a sphere and using the velocity field to calculate the force on each primary sphere in the aggregate due to the presence of the other spheres. It is essentially an extension of Kirkwood-Riseman theory from the continuum flow regime to the entire Knudsen range (Knudsen number from 0.01 to 100 based on the primary sphere radius). Our results compare well to published direct simulation Monte Carlo results, and they converge to the correct continuum and free molecule limits. Our calculations for clusters with up to 100 spheres support the theory that aggregate slip correction factors collapse to a single curve when plotted as a function of an appropriate aggregate Knudsen number. This self-consistent-field approach calculates the friction coefficient very quickly, so the approach is well-suited for testing existing scaling laws in the field of aerosol science and technology, as we demonstrate for the adjusted sphere scaling method.