Trajectory analysis of nanoparticles under electrostatic/flow field and its application to measurements of electrical mobility

Abstract

The particle trajectory was calculated using the Langevin equation in non-uniform external fields. Validations for incorporating Brownian diffusive deviation in particle trajectory was provided. The size of time step for calculation was discussed and criteria for determining proper size of time step at a given operating condition to minimize an inherent numerical error were suggested. Using the particle trajectory method, the transfer function of a DMA was evaluated for a Low Pressure DMA (LPDMA) and a Long DMA (LDMA). The assumption that the fluid flow in classification region of the LPDMA is laminar and continuum at low-pressure condition was used and validated. In addition, the simplified and complex geometries for the LDMA were used to investigate effects of slit shape on the resulting particle trajectories. The transfer function of DMA obtained by the particle trajectory analysis was compared with experimental results and Stolzenburg diffusional transfer function. The numerical and experimental results were agreed well in comparison of transfer function of LPDMA, however, Stolzenburg diffusional transfer function did not show the de-pendency of transfer function on the pressure change. In comparison of results for the LDMA, there was no significant effect of slit shape on the resulting transfer function. Consequently, the spatial deviation due to Brownian diffusion in non-uniform external fields can not be maintained as a Gaussian distribution assumed in derivation of Stolzenburg diffusional transfer function. For a diffusion dominant regime, this trajectory analysis method has advantages for prediction of DMA transfer function. The evaluation of electrical mobility measurement for nanosized non-spherical particles was also performed using the Gold nano rod particles.