The sedimentation
half-times t
s of
initially monodisperse dispersions of 750, 505, and 350 nm silica
microspheres were measured in water, in ethanol, and in aqueous NaBr
solutions of concentration c
NaBr ranging
from 50 to 1000 mM, where the particles may have formed clusters.
In water and in ethanol, t
s was about
8, 18, and 33 h for the 750, 505, and 350 nm particles, respectively.
These values were the same as the ones predicted by Stokes’
law, suggesting that the particles were monodisperse and remained
so during sedimentation; t
s values remained
the same with increasing particle weight fraction up to 0.03, indicating
no hydrodynamic interactions. Three regions of NaBr concentrations
with different settling behavior were found for each size. In region
I or at lower c
NaBr, the t
s values were the same as at no salt conditions, implying
that there was no significant agglomeration before particles settled.
In region II, t
s decreased with increasing c
NaBr, suggesting that the agglomeration and
sedimentation half-times of medium-size clusters were comparable.
In region III, the t
s values were quite
similar for all particles, and independent of the NaBr concentration,
indicating that at short times the particles formed large clusters
which settled rapidly. The zeta potentials of the particles in water
or in NaBr solutions were measured and used to predict the corresponding
Fuchs–Smoluchowski stability ratios, which were sensitive to
the chosen Hamaker constant values and the NaBr concentrations. Two
models, based on the Smoluchowski steady-state and the more general
unsteady-state agglomeration rates, were developed for obtaining the
agglomeration times t
an
for forming clusters of size 2
N
m
, where N
m = 1, 2, 3, ..., and
the net predicted sedimentation half-time t
s
* for these clusters.
The clusters were described by a fractal model with a fractal dimension d
f. Diffusion-limited clusters (d
f = 1.8) were compared to the coalescence-limit clusters
(d
f = 3). The models provide some useful
and accurate upper bounds of t
an
and t
s
*. Moreover, the effective sizes, density differences,
and volume fractions of the clusters were obtained as a function of
time. The predicted trend of t
s
* was consistent with the experimental
data. The predictions supported the inferences that the particles
were unagglomerated in region I, formed medium size clusters in region
II, and rapidly formed large clusters in region III.