Abstract
A detailed survey has been carried out to assess the usefulness of the gamma and modified gamma distributions for representing particle size spectra in coagulating aerosols. By taking moments of the kinetic equation for the aerosol spectrum n( v, t) we have obtained a closed set of first-order, coupled nonlinear differential equations for the parameters in the gamma distribution. Using two model coagulation kernels K( u, v) ∞ uv and u + v, for which exact results may be obtained, we have assessed the accuracy of the method. It is found that the modified gamma distribution has a number of advantages over the conventional log-normal representation. We have, in addition, made calculations using the exact Brownian hydrodynamic, Brownian free-molecule, shear, and gravitational kernels and where possible have compared these with exact numerical solutions and similarity results. In general, we find much to commend the modified gamma distribution as a concise representation of aerosol size spectra.
Published Version
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