An approximate treatment of aerosol coagulation and removal

The evolution of an aerosol undergoing removal with a rate Avm, and coagulation with constant kernel K is investigated. For an initial number density N0 and mean particle volume , the removal timescale and the coagulation timescale tc=(KN0)−1 are defined. For tr tc, accurate approximations for the suspended aerosol number density and volume as a function of time t are derived from the analytical solution, avoiding the need for quadrature. For tr tc, an argument based on equating rates of coagulation and removal to identify the peak mean particle volume suggests that the suspended aerosol volume (as a fraction of its initial value) plotted against t/(tr1/(m+1)tcm/(m+1)) should be independent of tr, tc and the parameters of the initial distribution. Numerical results for m=2/3 plotted in this way do indeed exhibit this independence provided tr/tc is greater than about 100. The case of an aerosol source is also considered. Here the relevant coagulation timescale is , where is the number of source particles flowing into unit container volume per second. The size distribution in the chamber depends on the ratio tr/tcs and plots of various features of this distribution in the steady-state as a function of tr/tcs, as well as estimates of the time to reach the steady state are presented. Although many of the proposed scalings were derived assuming the coagulation kernel is constant, they also apply to the case of Brownian coagulation of large particles.