The classical Beckerndash;Douml;ring homogeneous nucleation theory is rigorously extended to include monomer and cluster removal mechanisms capable of coupling to the usual Beckerndash;Douml;ring equations for evaporation and growth. Exact expressions are obtained in a compact continued fraction form for the steady state cluster distribution and nucleation rate in the presence of an aerosol. The unmodified classical theory is recovered in the limit of a particle free vapor. Recently proposed models for new particle formation in the presence of an aerosol and nucleation in a nonuniform vapor are shown to be contained within the present formulation. Condensation curves are calculated for a series of model condensable vapor species covering a wide volatility range in the presence of an aerosol. For those vapors having low equilibrium vapor pressures (less than 10minus;5Torr at the highest aerosol concentrations considered) significant departures from predictions based on the unmodified classical theory are found.
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