I am not a specialist of this field but the determination of the bacteria content seems to me quite interesting. However, it depends on the source and location of these aerosols. Since many bacteria are not easy to cultivate, a method based on ATP detection could be relevant as a first step to reveal the presence of bacteria.
I am also working on air purification and surface sensitization for that purpose i used PCS photo catalytic sensor. You can find more detail on my profile. stay in touch if faced problem.
Study of atmospheric particulate matter including transport, composition and transformation is one of the central subjects in physical meteorology. The number of problems to investigate in this field is enormous and it is not easy to prepare the complete list. The answer will depend on the type of measurements conducted with your device. If we assume that you can measure both spectrum of particles and their chemical composition you can certainly perform number of interesting and useful studies.
Just to begin I would like to suggest few subjects
1. Provide additional calibration of data from remote sensing described in the paper discussing mineral aerosol