The DMA transfer function with Brownian motion a trajectory/Monte-Carlo approach

The transfer function for the Differential Mobility Analyzer (DMA) is deriv ed based on particle trajectories for both nondiffusing particles and diffu sing particles. The effect of particle diffusion is assessed by using a Mon te-Carlo method for particles of sizes 1, 3, 10, 30, and 100 mm. This appro ach includes both the effect of wall losses and axial diffusion. The range of validity of the Stolzenburg analysis is assessed by comparing his transf er function, the peak of his transfer function, and its dimensionless width with similar calculations based on the Monte-Carlo. For particle sizes sma ller than 10 nm, the Monte-Carlo method indicates large wall losses, which result in a reduction in the peak of the transfer function by as much as a factor of 10 to 30, sensitivity to the flow-field, and skewmess of the tran sfer function. It is shown that Stolzenburg's approximate formula for the s tandard deviation of the width of the transfer function agrees with Monte-C arlo simulations for particle sizes of 3 nm and larger.