Three-Dimensional Simulation of Brownian Motion of Nano-Particles In Aerodynamic Lenses

Abstract

A computer code for analyzing nano-particle motions in an aerodynamic particle beam focusing system was developed. The code uses an accurate three-dimensional model for the Brownian diffusion of nano-particles in strongly varying pressure field in the aerodynamic lens system. Lagrangian particle trajectory analysis was performed assuming a one-way coupling model. The particle equation of motion used included drag and Brownian forces.The prediction of the 3-D model for penetration efficiency, beam divergence angle, beam diameter and radial cumulative fraction were evaluated and were compared with those of the axisymmetric models. The simulation results showed that for particle diameters less than 30 nm in helium gas, the Brownian force could significantly affect the beam focusing and particle penetration efficiency. Some potential errors in the naïve usage of axisymmetric model were discussed. It was shown that the earlier axisymmetric models lead to the incorrect mean square radial displacement of Brownian particles. The present 3-D approach, however, leads to the correct value of the radial mean square displacement of 4Dt.The effect of the inlet orifice and relaxation region on the performance of the lens system was also investigated. It was shown that the major losses of the 4 to 10 nm particles occur in the inlet orifice and relaxation region walls. For 15 to 30 nm particles, the main losses occur at the inlet orifice walls. Some alterations of the shape of the inlet orifice were examined and a new design is suggested to reduce the loss of the particles at the inlet flow control orifice.

Numerical investigation of the flow field and cut-off characteristics of supersonic/hypersonic impactors

“…Two important forces for the particles are drag and Brownian forces. The details of the governing equations and the method of solving can be found in the following references (Abouali et al, 2009;Nikbakht et al, 2007).…”

“…Having the flow field, the particle equations of motion were solved with a Lagrangian approach. A computer code developed for numerical analysis of aerodynamic lenses (Abouali, Nikbakht, Ahmadi, & Saadabadi, 2009;Nikbakht, Abouali, & Ahmadi, 2007) was modified for solving the equations of nano-particle motion in supersonic/hypersonic impactors. Two important forces for the particles are drag and Brownian forces.…”

Microstructural Parameter-Based Modeling for Transport Properties of Collagen Matrices

“…To mimic particle random motion, a particle transport equation was solved by taking two forces into consideration: drag force and Brownian force. The particle transport equation used in this study is given by [33] …”

Influence of particle location on the number of charges per charged nanoparticle at the outlet of a needle charger

“…is the Brownian random force (Abouali et al, 2009;Li and Ahmadi, 1992), b is the inverse of the particle relaxation time, G is a zero-mean, unit variance independent Gaussian random number, Át is the time step, and U p ! is the particle velocity.…”