Approximate relationship between voltage and mobility for Brownian particles in cylindrical DMAs

This work presents the results of a theoretical investigation aimed at the determination of the relationship between applied voltage V and mobility Z for highly diffusive particles classified in a concentric cylindrical differential mobility analyzer (DMA). Based on knowledge of the mean of the first passage time probability distribution, the expression V / V n d = 1 − 2 π k T L Z / p e Q s h has been obtained (Vnd=classification voltage for non-diffusing particles; k=Boltzmannʹs constant; T=absolute temperature; L=DMA length; p=number of elementary charges on the particle; e=electronʹs charge; Qsh=sheath air flow rate). Numerical simulations of particle trajectories have shown that the above expression is only approximate and that the last term, accounting for the effect of diffusion, has to be multiplied by a geometrical factor which is approximately given by the fitting expression 2.49ln−0.66(R2/R1), where R1 and R2 are the inner and outer electrode radii, respectively. The V/Vnd ratio departs from one only in extreme cases, namely, classification of particles with very high mobility in a quite long DMA operated at relatively low flow rates. For other situations the difference between V and Vnd is negligible.