The mobility, charging, coagulation and mass-transfer properties o f aerosol agglomerates were related to the particle and the background gas mean free path λ. The mobility-equivalent diameter d_m of a self-similar cluster of spheres in the continuum regime (λ≪d_m) was calculated to be proportional to the radius of gyration Rg_g of the cluster for fractal dimension D_f>1.3. Slender-body behavior is approached for D_f<1.3. In the free-molecule regime (dm≪λ) , d_m is nearly equal to the projected-area diameter d_A. In the transition regime (d_m~λ) , d_m depends on both d_A and R_g. In general, there is a divergence of d_A and R_g as the agglomerate size increases, but it is very gradual for typical aerosol agglomerates, for which d_m~d_A in the transition regime.

The mass transfer of nanometer-sized ²¹¹Pb clusters to TiO₂ agglomerates was investigated with an Epiphaniometer. The measured mass-transfer-equivalent diameters of the agglomerates were within 10% of d_m. The lead cluster mean free path was nearly the same as λ. For an analogous phenomenon, the bipolar diffusion charging of agglomerates, it was found that the charging-equivalent diameter of the agglomerates was ~10% larger than d_m.

These measurements were incorporated into a model describing the coagulation of agglomerates in the transition regime. Particles smaller than the primary particle diameter d \ were assumed to coalesce rapidly, while large particles were assumed to be solid with a fractal structure. In the transition regime, the agglomerate mean free paths are much smaller than d_m even when d_m<λ. This leads to distinctly different dynamic behavior than predicted by previous models developed for the continuum or free-molecule regimes. The enhancement of coagulation over that of dense spheres is large for aerosols with median diameters slightly greater than d₁ but smaller for aerosols consisting of much larger particles.