On Differential Mobility Analyzer Resolution

The resolution of the differential mobility analyzer (DMA) is conveniently described as the ratio of the mobility at the peak of the column transfer function to the full width of the transfer function at 1/2 of its maximum value. The best resolution that can be achieved is that for nondiffusive particles, -_ (nd) = β^ (-1), where β is the flow rate ratio, β = (Qₐ + Qₛ) / (Q_ (sh) + Qₑ). Brownian diffusion causes particles to deviate from the ideal electrophoretic migration trajectories, thereby reducing the resolution. The relative importance of electrophoretic migration to diffusion can be expressed as a function of the migration Peclét number, which can be expressed either in terms of mobilities, dimensions, and flow rates or as Pe_ (m ig) = (qV/kT) f, where q is the charge on the particle, V is the applied voltage, and f is a geometry factor that accounts for nonuniformities in the electric field along the migration pathway. Expressed in this way, the performance of DMAs with different geometries, operating at different flow rates, are, in the absence of distortions in the flows and electric fields, shown to be nearly indistinguishable. Diffusion is shown to dominate at operating voltages below a critical value that is proportional to the square of the limiting resolution. Since the voltage range for DMA measurements is limited, the dynamic range decreases with increasing -_ (nd). Because of the changing size dependence of the mobility, this limitation is more pronounced for free-molecular aerosols than for larger particles.