Page 199 - Book Hosokawa Nanoparticle Technology Handbook

3.8 SIMULATION OF COLLOIDAL DISPERSION SYSTEM FUNDAMENTALS
DPD would become useful as a powerful simulation points is expected to make the LBM stand as a pow-
method for colloidal dispersion, which would be des- erful tool for colloidal simulations.
perately desired at an early date.
3.8.4 Closing remark
(ii) Fluid particle dynamics (FPD)
If any of the computational fluid dynamics (CFD) Many of mesoscale simulation methods have been
simulations can be adapted to a particulate dispersion under research mainly in the field of physics. They
system, it automatically is capable of expressing the have shown, however, not so many examples of
HI. A direct introduction of solid particles into the application to realistic engineering problems, and
CFD simulations, however, would bring a significant have not been organized to a level at which engi-
difficulty to handle moving boundaries in a fluid. neers can use them efficiently without difficulty.
Tanaka et al. [22], who had been conducting Meanwhile the dynamics in the mesoscale should
researches on the phase separations in complex fluids, be the most important phenomena to be pursued for
noticed that the difficulty of moving boundaries the development and production of functional mate-
would be able to be eliminated if a particle is treated rials. We may have to wait until far future if we
as phase-separated component with extremely high would expect the contribution only from the
viscosity, and proposed this method naming as the detailed research in science area. It is, instead,
fluid particle dynamics (FPD). A particle is expressed highly desired that many engineers and researchers
as a concentration field of the high-viscosity compo- in the engineering field have awareness of this issue
nent, and thus the whole system can be treated as a in common, to thrust the development of the meso-
continuum, which can then be expressed by the simulations by tightly connecting them with experi-
Navier–Stokes equation. The value 50 for the ratio of mental knowledge.
the viscosities of the phase-separated component,
which stands for solid particles, was reported to be
enough to simulate colloidal systems. This method
was applied to coagulation process, clarifying inter- References
estingly that the coagulated structure differs signifi- [1] J.F. Brady, G. Bossis: J. Fluid Mech., 155, 105–129
cantly depending on whether the HI exists or not in (1985); G. Bossis, J.F. Brady: J. Chem. Phys., 80,
the system.
5141–5154 (1984).
(iii) Lattice Boltzmann method (LBM) [2] D.L. Ermak, J.A. McCammon: J. Chem. Phys., 69,
Similar to the case of FPD, the Lattice Boltzmann 1352–1360 (1978).
method (LBM) would be able to express colloidal [3] M. Miyahara, S. Watanabe, Y. Gotoh and
dispersion system if it can accommodate particles in K. Higashitani: J. Chem. Phys., 120, 1524–1534
its scheme: The LBM is a method for fluid dynam- (2004).
ics, based, in principle, on the Boltzmann equation: [4] S. Watanabe, M. Miyahara and K. Higashitani: J. Chem.
The fluid is expressed by fictitious particles with Phys., 122 (104704), 1–10 (2005).
some of finite velocities that come from grid spac- [5] H. Shinto, M. Miyahara and K. Higashitani: J. Colloid
ing of a lattice for the flow field, and the time evo- Interface Sci., 209, 79–85 (1999).
lution of the flow field can be followed by the [6] H. Shinto, M. Miyahara and K. Higashitani:
process of translational motion and collision Langmuir, 16, 3361–3371 (2000).
between the fictitious particles employing velocity
distribution functions for all of the velocity compo- [7] H. Shinto, K. Uranishi, M. Miyahara and K.
nents. This method is reported to be capable of fast Higashitani: J. Chem. Phys., 116, 9500–9509
and large-scale calculations, compared with the (2002).
finite-element method, for example, because of its [8] H. Shinto, S. Morisada and K. Higashitani: J. Chem.
simplicity in algorithm and suitability in paralleliza- Eng. Jpn., 37, 1345–1356 (2004).
tion. Typical example of its potential is given by [9] M.P. Allen, D.J. Tildesley: Computer Simulation of
Ladd [23]: By working out with the boundary condi- Liquids, Clarendon Press, pp. 257–269 (Chapter 9)
tions and treatment of velocity distribution functions (1987).
at the particle surface, he succeeded in expressing a [10] S. Kamiyama, A. Sato: Ryutai Micro Simulation,
particle with five units of the grid and conducted Asakura, pp. 52–77 (Chapter 7) (1997).
simulations expressing behavior of tens of thousands
of colloidal particles. The method for accommodat- [11] W.F. van Gunsteren, and H.J.C. Berendsen: Mol.
ing particles in the LBM scheme, however, has not Simul., 1, 173–185 (1988).
yet been well-established, and the method needs fur- [12] M.P. Allen: Mol. Phys., 40, 1073–1087 (1980).
ther study on how to adopt surface forces and [13] F.K. von Gottberg, K.A. Smith and T.A. Hatton:
Brownian motion. Further development on the above J. Chem. Phys, 106, 9850–9857 (1997).

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