DMA Transfer Function With Brownian Motion: A Trajectory/Monte-Carlo Approach.
DMA Transfer Function With Brownian Motion: A
Hagwood, C.; Sivathanu, Y. R.; Mulholland, G. W.
Aerosol Science and Technology, Vol. 30, 40-61, January
particle trajectories; diffusion; brownian motion; monte
carlo method; particle size; equations
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.