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/Vnd=1−2πkTLZ/peQsh has been obtained (Vnd=classification voltage for non-diffusing particles; k=Boltzmann's constant; T=absolute temperature; L=DMA length; p=number of elementary charges on the particle; e=electron's 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.

► An improved expression relating voltage and mobility in DMAs is proposed.
► The new expression is derived from knowledge of the mean first passage time.
► It is valid for Brownian particles in long DMAs operated at low flow rates.
► The model predictions have been successfully validated by Monte-Carlo simulations.