Diffusional penetration of aerosols through a tube: Comparison between Monte Carlo simulation of Brownian particle trajectory and the numerical solution of the advection–diffusion equation

Abstract

Penetration of nanometer-sized, diffusive aerosol particles through a circular tube has been determined by two numerical methods. One method consisted in the simulation of the trajectories of Brownian particles suspended in a flowing fluid medium. The other was the numerical solution of the advection–diffusion equation. For any given value of the particle diffusion coefficient, penetration, i.e. the fraction of particles that avoid diffusion loss to the wall and exit the tube, calculated by the two methods agreed fairly well with each other for the three types of fluid flow tested (uniform, developing, and fully developed parabolic flows). For the case of parabolic flow there exists an analytical series solution which has been successfully compared with experimental results in a relatively large number of past investigations. The results obtained by the two numerical methods have also shown an excellent agreement with this analytical solution. The Brownian dynamics simulation method requires a larger computer time, but its simplicity allows examination of other aerosol flow processes too difficult to study either experimentally or by means of conventional differential equations. Aerosol penetration in transient, developing flow has never been addressed before, neither experimentally nor theoretically. The results reported in this paper are the first ones.