Environmental Engineering Reference
In-Depth Information
Brownian diffusion leads to dispersion of particles into the air. Dispersion may
also occur from mechanical mixing during industrial processes, interfacial instabil-
ity between immiscible layers of solvents and differences in molecular structures of
particles. A velocity-based model describes the spreading of a solute in time and
space. The convection-dispersion equation (CDE) for dispersion of non-reactive
solute can be given as:
∂
∂
C
t
∂
∂
2
C
x
∂
∂
C
x
=
K
−
v
2
Where C is the concentration of solute, t is time, x is distance, K is the diffusion-
dispersioncoeficientandvisthemeanvelocity.ThisequationpredictsthattheK
and v do not vary in space or with direction. K and v are related to the mean and
varianceofthenormaldistributionofdistancestraversedbythesolute(Perfectand
Sukop
2001
).
Another ENP transport mechanism in air is via agglomeration. Herein, individ-
ual particles agglomerate through Brownian motion and collide, leading to increased
size.Thesmallsizeofnanoparticlesmakesthemunstableandthusassiststheircol-
lision with each other. Repeated collisions form particle agglomerates
(Bandyopadhyaya et al.
2004
). Nanoparticle agglomerates may collide with the
molecules of surrounding gas (Lall and Friedlander
2006
) (Table
4
). Friedlander
(
2000
) suggested that Brownian movement was responsible for the highest collision
rates of nanoparticles and was more influential than other transport mechanisms
suchasturbulentlow(Table
4
). Friedlander described the fractal nature of ENPs
agglomerates mathematically as:
NK
R
d
g
=
D
p
f
f
/2
p
Where,
N
p
is the number of primary particles that forms agglomerates,
d
p
is
diameter of particles,
K
f
is fractal prefactor,
R
g
is radius of gyration (mean root
squareofthedistancesbetweenthespherulesandthecentreofmassoftheagglom-
erate) and
D
f
is fractal dimension.The above mentioned equation can be used to
estimate the number of ENPs undergoing agglomeration.
The physico-chemical characteristics of ENPs affect their fate as does how they
aretransportedinair.Lowryetal.(
2012
) reported the possible mechanisms by which
nanoparticles behave and are transformed in the environmentAitken et al. (
2004
)
reported that particles having diameters ≤100 nm remain suspended in air for longer
times and are capable of diffusing. Particle size bears an inverse relationship with
diffusion rate, whereas gravitational settling is directly proportional. ENPs have been
classiiedbytheirsizesandbehavior,whenpresentintheatmosphere.Smallparticles
(<80nm)tendtobeshortlivedandtoagglomerate.Largeparticles(>2,000nm)are
coarseandaresubjectedtogravitationalsettlingorsedimentation.Particlesofinter-
mediatesize(>80nmand<2,000nm)persistforlongerperiodsintheatmosphere
(
http www epa gov osa pdfs nanotech epa nanotechnology whitepaper 0207 pdf
).
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