Determination of the aerosol particle size distribution by means of the diffusion battery: Analytical inversion

The algorithm of the analytical inversion of aerosol size distribution is proposed in this work. As the diffusion battery separates particles into several fractions according to their diffusivity, the total spectrum can be represented as the sum of spectra of fractions. Analytical formulas are derived to calculate mean diameters for particles in different fractions using diffusion battery penetrations as input parameters. The spectra of fractions are approximated by lognormal functions. Two analytical solutions for the aerosol size distribution inversion problem are discussed. The sizing accuracy of analytical solutions is investigated, comparing them with the measurements through transmission electron microscopy using the laboratory-generated NaCl aerosol. The agreement is demonstrated to be within 10% accuracy. It is shown that in case of two-mode size distribution, the spectrum components are well resolved for rather distant peaks (modal diameters of 10 and 300 nm) and poorly resolved for nearby modes (50 and 300 nm). To improve the peak resolution, the procedure of spectrum correction is applied demonstrating an excellent peak separation. Finally, the peak resolution is experimentally verified for the laboratory-generated two-mode spectra of tungsten oxide–NaCl aerosol with the modal diameters of 10 and 60 nm, respectively. Both analytical solutions demonstrated good peak resolution.