Fokker-Planck equation solution of aerosol Brownian coagulation with an interparticle potential

For the Brownian coagulation of aerosol particles in the transition regime of Knudsen number in the presence of an interparticle potential, the Fokker-Planck equation is solved by using Grad's 13-moment method. Mass and energy accommodation coefficients are interfaced with the Fokker—Planck moment equations through the use of half-range fluxes. Analytical solutions of the potential-free situation are obtained for arbitrary values of the accomodation coefficients. Numerical solutions of the number and energy flux profiles for a repulsive or an attractive interparticle potential of power-law form are obtained by a two-dimensional shooting scheme. This numerical algorithm is further applied to calculate the coagulation coefficient between two transition regime particles under either a van der Waals potential or a Coulombic potential. The results are in good agreement with those predicted by the flux-matching method of Fuchs. The present fundamental approach, therefore, provides theoretical support of the coagulation coefficient expression obtained by the empirical flux-matching method in the presence of an interparticle potential.