Fundamentals of Particle Dynamics - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 156

6.5 Nanoparticle Transport

With rapid advances in nanotechnology, the potential for exposure to nanoparticles
has increased significantly. Therefore, better understanding of nanoparticle trans-
port and deposition is critical for assessing their potential health hazards and/or the
effectiveness of nanomedicine. Since nanoparticles are in the size range of the mean
free path of air molecules under normal pressure, their behaviour differs markedly
from that of micron size particles. Most notably, nanoparticles are significantly af-
fected by the influence of Brownian motion, and their fluid drags are significantly
reduced due to the molecular slip. When a small particle is suspended in a fluid, it is
subjected to the impact of the gas or liquid molecules. For ultrafine (nano) particles,
the instantaneous momentum imparted to the particle varies randomly, which causes
the particle to move on an erratic path now known as Brownian motion (Fig. 6.13 ).

Fig. 6.13 Brownian motion
of a particle subjected to
impact by fluid molecules
causing the particle to travel
in a random trajectory

Nanoparticle dispersion and deposition can be evaluated by either the Lagrangian
particle tracking or Eulerian diffusion model approach. These two approaches are
described in the following sections.

6.5.1 Lagrangian Particle Tracking

For sub-micron particles, the effects of the Brownian random force generated by the
impact of gas molecules on the particle can be included as an additional force term in
the particle equation of motion given by Eq. (6.1). The intensity of the Brownian force
per unit mass of a particle can be modelled as a white noise stochastic process. White
noise is a zero mean Gaussian random process with a constant power spectrum with
equal power for any frequency. The Brownian excitation is modelled as a Gaussian
white noise random process with a spectral density S o (Li and Ahmadi 1992) given
as,

216 νk b T
π 2 ρ f d 5 ρ p
ρ f

S 0 = (6.38)

2

C c