Page 189 - Book Hosokawa Nanoparticle Technology Handbook

3.7 RHEOLOGY OF SLURRY FUNDAMENTALS
reverse micelle and hot soap methods. Various containing droplets of immiscible liquid, the viscosity
semiconductor nanoparticles and quantum dots can of which is lower than that of medium, also increases
be prepared by this process. However, since it is not at low shear rates.
possible to increase the particle concentration, the Equation. (3.7.1) indicates that the viscosity of
yield is relatively low. Thus the prepared particles dilute suspensions proportionally increases only as a
can only be applied for valuable products. Recently, function of volume fraction of particles, because the
new processes for nanoparticle synthesis using a region subjected to distortion of velocity field is con-
metal–surfactant complex as a reagent have been stant, relative to the particle diameter. However, at
reported [4]. Since these methods can be operated high concentrations the particles cannot behave inde-
under relatively high reagent concentrations, further pendently in shear fields, but the interparticle interac-
development in this research area is expected. tions including collisions are hydrodynamically
Since the viscosity of organic solvent with induced. The flow field outside a particle is influenced
monomer or polymer and high solid content of by the neighboring particles and the overlapping of
nanoparticles is relatively high, the design of mechan- distortion region takes place. The interference between
ical mixing tool such as kneader and mixer is also particles in shear fields leads to additional energy dis-
important to prepare uniform nanoparticle-dispersed sipation. Therefore, when the actual viscosity data are
polymer composites. compared with the Einstein prediction, the former
becomes much higher and exponentially increases in
concentrated suspensions, whereas the same values are
References obtained at low concentrations.
Because of no colloidal interaction between parti-
[1] Z. Sun, J.S. Gutmann: Physica A, 39(1–2), 80–85
cles, the viscosity behavior of non-interacting suspen-
(2004).
sions is governed by the balance between Brownian
[2] C. Lü, C. Fuan, Y. Lju, Y. Cheng, B. Yang: Chem. motion and hydrodynamic forces. The hydrodynamic
Mater., 17, 2448–2454 (2005). forces exerted on a single particle in shear fields are
2
[3] C. Lü, Z. Lui, C. Fuan, J. Guan, B. Yang, J. Shen: given as 6 a
and forces due to thermal motion as
0
Macromol. Mater. Eng., 288, 717–723 (2003). kT/a. Here, is the viscosity of medium, a the parti-
0

[4] J. Park, K. Am, Y. Hwang, J.-G. Park, H.-J. Noh, J.-Y. cle radius,
the shear rate, and kT the thermal energy.
Kim, J.-H. Park, N.-M. Hwang, T. Hyeon: Nat. Mater., The relative importance of shearing forces to
Brownian diffusion can be represented by the Peclet
3, 891–895 (2005). 3
number a
/kT. Referring to the previous work, the
0
relative viscosity / measured using different parti-
0
3.7 Rheology of slurry cle radii, fluid viscosity, and temperatures are super-
imposed when plotted against the Peclet number[1].
The viscosity behavior for suspensions of non-inter-
3.7.1 Fundamentals of suspension rheology acting particles can be scaled on the Peclet number
and this can be treated as a master curve. The impor-
(1) Viscosity behavior of non-interacting suspensions tant feature for concentrated suspensions in which the
The most basic equation on the viscosity of suspen- particles are completely dispersed in a Newtonian liq-
sion is the Einstein equation. For suspensions of uid without flocculation is that the hydrodynamic
monodisperse spherical particles without colloidal effects give rise to shear-thinning flow (often called
interactions in a liquid with viscosity at a volume pseudo-plastic flow), defined as decreasing viscosity
0
fraction , the viscosity is given by the following with increasing shear rate.
equation: When the particle concentration is increased beyond
47 vol%, another unique viscosity behavior appears at
(1 2.5 ) (3.7.1) high shear rates. Figure 3.7.1 shows the effect of par-
0
ticle concentration on the viscosity for concentrated
This equation is theoretically derived for an isolated suspensions of 45 vol% and above [2]. At 45 vol% the
single particle. The viscosity increase in the presence suspension is slightly shear-thinning over the wide
of particles is qualitatively explained by the increase range of shear rates, above 50 vol% the flow becomes
in hydrodynamic energy dissipation due to the distor- shear-thickening flow (often called dilatant flow),
tion of the velocity field in the vicinity of each parti- defined as increasing viscosity with increasing shear
cle. The theory deals with one particle and the rate, and beyond 53 vol% a discontinuous jump of
equation is valid only for very dilute suspensions in viscosity is induced [3]. For suspensions at 53 and
which the hydrodynamic interactions such as colli- 55 vol%, only the data before viscosity jump are plot-
sions in shear fields can be ignored. Since the distor- ted, because the reproducibility is considerably poor at
tion of streamline is responsible for the increase in higher shear rates due to flow instability.
energy dissipation, the Einstein theory leads to a very The viscosity jump is an extreme manifestation of
important conclusion that the viscosity of emulsion shear-thickening flow and peculiar characteristic of
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