The DMA Transfer Function with Brownian Motion a Trajectory/Monte-Carlo Approach
The transfer function for the Differential Mobility Analyzer (DMA) is derived based on particle trajectories for both nondiffusing particles and diffusing particles. The effect of particle diffusion is assessed by using a Monte-Carlo method for particles of sizes 1, 3, 10, 30, and 100 nm. This approach includes both the effect of wall losses and axial diffusion. The range of validity of the Stolzenburg analysis is assessed by comparing his transfer function, the peak of his transfer function, and its dimensionless width with similar calculations based on the Monte-Carlo. For particle sizes smaller 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 skewness of the transfer function. It is shown that Stolzenburg's approximate formula for the standard deviation of the width of the transfer function agrees with Monte-Carlo simulations for particle sizes of 3 nm and larger.