An inversion method for the determination of the particle size distribution from diffusion battery measurements

The inverse problem of the determination of the aerosol particle size distribution from a set of deposition measurements taken on the screens of the stages of a diffusion battery is analysed. The mathematical formulation reduces the problem to solving a system of integral equations for the unknown particle size distribution. Since the problem is ill-posed a numerical method which is based on minimising the norm of the derivative function subject to simple bounds of the variables and certain linear constraints, and which does not use any a prior information regarding the parametrised form of the solution is employed. For single- and double (normal or lognormal)-mode particle size distributions the numerical method provides a good estimation of the corresponding analytical solutions provided that, in general, the problem is approximated as a continuous Fredholm integral equation of the firsk kind. For triple-mode distributions a sequential application of the numerical method provides results which give good estimates for the first two modes but the prediction of the third mode is only satisfactory.