A Review of Transfer Theory and Characterization of Measured Performance for Differential Mobility Analyzers

Particle transfer theory for steady-state differential mobility analyzers with and without diffusion is reviewed in detail with a particular focus on the assumptions and approximations made in the analysis. Impacts of the approximations are discussed and, where available, methods to reduce the errors of these approximations are suggested. The non-diffusing theory uses just one approximation, affecting the centroid calculation, which can be readily addressed via numerical modeling of the electric field. The diffusing theory makes numerous approximations to achieve an analytical expression. One of the most serious of these, neglecting secondary flows in the vicinities of the aerosol entrance and exit slits, could be improved upon using a numerical model of the flow field. Losses in the aerosol entrance plumbing can perturb the inlet profile to the classification region. The maximum effects on the transfer function are estimated to be a 1% increase in the mean mobility and a 14% reduction of the non-diffusing contribution to the variance. Methods of fitting transfer theory to measurements are also reviewed. TDMA measurements generally do not have the resolving power to distinguish different shapes of the transfer function but newer measurements using truly monomobile ions have the potential to more rigorously test the diffusive transfer model. In adjusting the width of the theoretical transfer function to fit measurements from a real DMA demonstrating non-ideal performance, it is physically more meaningful and accurate to use an additive adjustment to the variance as opposed to a multiplicative adjustment to the width.