Mobility shift in the differential mobility analyzer due to Brownian diffusion and space-charge effects

The space-charge field is usually ignored when performing aerosol size measurements with the differential mobility analyzer (DMA). In the case of extremely fine particles requiring low electric fields for their classification, the space-charge field developed within the DMA can even be larger than the applied field and, hence, the mobility of the particles exiting through the sampling port may be very different from that expected. On the other hand, the trajectories of different-sized diffusing particles mix up with each other, resulting also in a shift of the average mobility of the classified particles. When non-uniform electric fields are present, the variance of the particle position probability distribution is larger than in the case of a pure Brownian process. Both phenomena, space charge and diffusion, are thus interrelated and cannot be treated separately. A very simplified theoretical treatment is presented which enables estimation of the order of magnitude of the mobility shift. Experiments with a tandem DMA system have shown that, at very low classification voltages, the measured mobility of the classified particles can be as high as three times the actual mobility. The experimental trends are qualitatively well reproduced by the model calculations.