(425g) A Model for the Size of Polar and Apolar Nanoparticle Agglomerates in a Fluidized Bed
emerging as a promising but challenging technique for processing of
nanoparticles, for instance, to produce coated nanoparticle. Nanoparticles do
not fluidize individually but form agglomerates due to strong interparticle
forces, dominant at the nano-scale . The type of fluidization and transport phenomena
inside the agglomerates strongly depend on the agglomerates structure and size,
two variables in turn related to the forces present between particles and
The size of the
fluidized agglomerates is commonly estimated with a balance between attractive
interparticle forces, such as van der Waals, electrostatic and capillary force
and separating forces, such as gravity and drag force. When dealing with
hydrophobic (apolar) nanoparticles, capillary is neglected and van der Waals is
the only interparticle attractive force usually considered. In the case of hydrophilic
(polar) nanoparticles, it is common to add a capillary force to the
interparticle forces if the fluidization is carried out with ambient air. If
the fluidizing gas is dry, the approximation is similar to that with apolar nanoparticles
and only van der Waals interactions are included. Tahmasebpoor
et al.  showed that attractive forces between dry and polar
particles is considerably larger than between dry and apolar nanoparticles.
This was attributed to the formation of hydrogen bonds between the surfaces of
the polar nanoparticles.
In this work, we
propose a new model to estimate the average agglomerate size in dry fluidized
beds by taking into account the type of surface, polar or apolar. We do this by
including a term in the inter-particle forces that takes into consideration the
possibility of formation of hydrogen bonds.
In our model,
complex agglomerates are built by porous and spherical primary agglomerates . The attraction between primary agglomerates is
described according to Rabinovichxs model , considering
that the nanoparticles act as asperities in the primary agglomerates. The
Hamaker coefficient has been corrected with the two-body summation approach to
take into account the porosity of the primary agglomerates. The contribution of
the hydrogen bond has been modeled taking into account the geometry of the
contact point between agglomerates. The only separating force considered is
gravity. The average agglomerate size is therefore the size that makes the Bond
number of the agglomerates equal to unity.
The resulting average
agglomerate size is a function of dp, ρp,
Df1, Df2, d*, AH,
N and α, where dp and ρp
are the size and density of the nanoparticles, respectively. Df1,
Df2 are the fractal dimensions of the primary and complex
agglomerates, respectively. d*is the average size
of the primary agglomerates. AH is the Hamaker coefficient of
the nanoparticles material. N is an empirical constant related to the
connectivity of the primary agglomerates, being 1.38 for all the nanopowders.
α is an empirical constant that takes into account the formation of
hydrogen bond between nanoparticles. α is 0 for apolar nanoparticles and
≈1.67e-3 N/m for polar nanoparticles.
The proposed model
successfully approximates the size of most of the nanopowders reported in
literature, both in conventional and in centrifuged beds. It has no systematic
error as a function of the particle size, density or Hamaker coefficient. The
average prediction error of the proposed model is ≈20 %, while for the
model proposed by Valverde and
it is ≈45 %.