Page 276 - Environmental Nanotechnology Applications and Impacts of Nanomaterials

Nanoparticle Transport, Aggregation, and Deposition 261

the particles transported to the collector surface will attach; therefore,
the single collector efficiency must be modified.
Indeed, transport is only part of the story. The surface chemistry of
nanoparticles rather than their size is likely to be the factor that deter-
mines mobility. Just as aggregation was described mathematically to
be the product of factors transport ( ) and attachment ( ), the proba-
bility that a particle approaching a single collector deposits on the col-
lector can be written[38] as the product of the collector contact efficiency
and the attachment efficiency:

5 a (19)
0
When particle removal is calculated for a lower value of the attachment
or stickiness coefficient, particle removal decreases, corresponding to an
increase in mobility (Figure 7.17).
The ratio of the rate of particle deposition on a collector to the rate of
collisions with that collector is the attachment efficiency factor, , and
is analogous to the stickiness coefficient or 1/W. Theoretical predictions
of the attachment efficiency in this case are identical to those for par-
ticle aggregation, typically based on DLVO-type calculations that con-
sider the balance of forces arising from interactions at very small
separation distances between particles and the collector surface. These
phenomena may be important over length scales that are large by com-
parison with nanoparticle dimensions. Similar to the case where the
stickiness coefficient is treated as a fitting variable in the particle pop-
ulation models, the attachment efficiency can be treated as an empiri-
cal parameter that captures all aspects of particle deposition not
described by the more extensively validated particle transport models.
The empirically determined attachment efficiency should vary with
changes in surface and solution chemistry.
Measurements of particle removal across a length (L) of a homoge-
) and
neous porous medium composed of spherical grains of radius (r c
porosity [38] can be combined with calculations of particle transport to
yield estimates of the attachment efficiency factor [38]:

4a c n j
a 5 lna ^ b (20)
3s1 2 ed L n 0
0
where n and n are respectively the particle number concentrations
0
j
present at distance L in the column effluent and influent to the column;
is the clean bed single collector contact efficiency, which describes the
0
particle transport to an individual collector and can be calculated as a
function of the Darcy velocity, porous medium grain size, porosity, and
temperature among other variables using Eq. 18. Using experimentally
/n values (fraction of influent particles remaining after
measured n j 0