Numerical Evaluation of the Transfer Function of a Low Pressure DMA by Using the Langevin Dynamic Equation

Nanoparticle cross-flow differential mobility analyzer (NCDMA): Theory and design

“…Accounting for the axial velocity distribution along the radial position at the starting position of particles, the transmission efficiency was calculated by changing the applied voltage between the inner and outer electrodes (Song et al, 2005). Particles are injected at the aerosol inlet in 50 equally spaced annular sections.…”

“…Monte Carlo simulations of the Langevin equation (Song et al, 2005) are used to compare the diffusional transfer functions of the NCDMA and nano-DMA (Chen et al, 1998;TSI Inc.). In calculation of particle trajectories, the Langevin equation was solved with a time step of 1 ms, established as the minimum time step size required for accurate position calculations (Fig.…”

“…A number of authors have analyzed the effect of diffusional broadening on the performance of sizing instruments using theoretical, experimental, and numerical analysis (Hagwood, Sivathanu, & Mulholland, 1999;Kousaka, Okuyama, Adachi, & Mimura, 1986;Stolzenburg, 1988;Song, Chang, Kim, & Okuyama, 2005;Song et al, 2006). Generally, as particle sizes decrease, the particle population distributions experience increasing spatial broadening in the DMA classifier section due to Brownian diffusion.…”

Change in distributions of particle positions by Brownian diffusion in a non-uniform external field

“…It is, however, difficult to determine the characteristic time associated with the external force. Here, we use numerical modeling to obtain as the largest time step that results in a time-step independent result (Song et al, 2005(Song et al, , 2006. Fig.…”

“…The effect of Brownian diffusion on DMA measurements has been studied by a number of authors using different approaches (Alonso & Kousaka, 1996;Hagwood, Sivathanu, & Mulholland, 1999;Kousaka, Okuyama,Adachi, & Mimura, 1986;Rosell-Llompart, Loscertales, Bingham, & Fernández de la Mora, 1996;Salm, 2000;Seol et al, 2000;Seto et al, 1997, Song, Chang, Kim, & Okuyama, 2005Stolzenburg, 1988;Zhang & Flagan, 1996). Of these, the semi-analytical expression for the DMA diffusional transfer function derived by Stolzenburg (1988) based on the assumption that particle positions have a Gaussian distribution about the non-diffusing particle trajectory is most widely used.…”