(70dh) Numerical Simulations of Sedimentation Behaviour of Microparticles in Suspensions

Suspensions of fine particles in liquids have a widespread application in a number of industrial sectors including personal and health care, energy, pharmaceutical, materials, food and drink, and pigment. However, with increasing particle size, gravitational effect becomes important, and suspension may become unstable particularly when the density of particles is higher than the liquid. This is significant and is not always possible to overcome by matching the buoyancy. One of possible solutions to this is nanoparticles. When highly charged nanoparticles are added to a suspension, it normally undergoes a remarkable transition between a gel-like structure and a stable fluid with increasing nanoparticle addition. Recent researches have opened up new avenues in the stabilization of micro-and macrosuspensions using nanoparticle. A pioneering work related to this topic can be seen in the paper by Tohver et al. (2001), who experimentally validated the above methodology. The aim of this work is to gain a fundamental understanding of the stability of suspensions of microsizes particles (microparticle) denser than the host medium with an aid of nanoparticels. To achieve this, we have developed a 3-dimensional model to simulate the dynamic of micropartile and medium solvent consisting of the suspension. In this model, the Distinct Element Method (DEM) is used to model the solid phase (microparticle) and the continuous approach to simulate the fluid field, and the two-way coupling is considered. On the other hand, the effect of nanoparticle is obtained by a statistical mechanics approach. The details of these methodologies is given following. The so-called Distinct Element Method (DEM) is established by Cundall and Strack (1979) for granular system, and has been emerged as an important tool in particle technology research over the past years. However, it has not been used in the problem of particle sedimentation. In the DEM, we consider almost all important forces acting on the sedimenting particles, including, buoyancy, gravitational force, Brownian force, drag force, and contact force between two colliding particles. The equation of particle motion can be expressed in a vector form as followed, (1) where and are the van der Waals attractive force and electrostatic repulsive force, which consists of the well-known ?DLVO' effect. On the other hand, when the sedimentation occurs, the motions of particles induce the fluid flow in the spatial domain. Meanwhile this fluid flow in turn affects the movement of individual particles. For incompressible fluids, the governing equations, i.e., continuity equation and momentum equation, take the following forms, respectively: (2) (3) where is the volumetric fluid-particle interaction force. The algorithm adopted in this work for solving the Navier-Stokes equation is the so-called ?SIMPLE' algorithm developed by Patanker (1980). Another important task in this model is the coupling of DEM and CFD. In the this work, the combination of DEM and CFD is achieved by considering the volumetric fluid-particle interaction force between solid particle and liquid phase (i.e., Ffp in Eq. ) applying Newton's third law of motion. Recently the interest of research activities has been extended to so-called ?non-DLVO' effect induced by nanometer-sized particle on the phase behaviour of colloidal suspensions. The interaction potential of this effect can be determined by the distribution of nanoparticles surrounding macroparticles, as suggested by Boltzmann equation: (4) where g(r) is the radial distribution function of nanoparticle. To obtain g(r) of binary systems, Henderson et al. (2004) has developed an approach, in which the Ornstein-Zernike (OZ) equation is solved numerically with Percus-Yevivk (PY) closure. Details of the derivation can be seen in the cited paper. In the simulation results, first presented are the simulation results under different conditions of monodispersed microparticle and liquid, in which solid lines represent the prediction of Baichelor's theory (Batchelor, 1972). On the other hand, with application of DEM, trajectory of individual particle can be tracked for every time step. Here we present the visualized representation of the sedimentation of particles of different size in Fig. 2. In the investigation of nanoparticle effect, the normalized sedimentation velocity of microparticle is shown as a function of volume fraction of nanoparticle in Fig. 3. Solid line stands for the result of Bachelor's prediction for binary system (Batchelor, 1972). To summarize, we have developed a mathematical model combining DEM and CFD to simulate the phase behaviours of colloidal suspension composed of microparticle. Effect of nanoparticle, which is obtained by a statistical mechanic approach with numerical solution, can be also implied in this model. Initial simulations show very promising results, which agree well with the theoretical observation for monodispersed and binary systems by some other author (Batchelor, 1972). The accuracy of the present model can also be guaranteed through these comparisons. Further development under way includes modification of present model, which is made for the systems with higher volume fraction.

Reference: Batchelor, G. K. (1972), Sedimentation in a dilute dispersion of spheres. J. Fluid. Mech. 52, 145 Cundall, P.A., and Strack, O.D.L., (1979), A discrete numerical model for granular assemblies. Geotechnique, 29, 47 Henderson, D., Trokhymchuk, A. D., and Wassan, D. T. (2004) Interaction energy and force a pair of colloidal particles in a bidisperse hard-sphere solvent J. Mole. Liq. 112, 21 Patankar, S. V. (1980) Numerical Hear Transfer and Fluid Flow. Hemisphere, New York, U.S.A. Tohver, V., Chan, A., Sakurada, O., and Lewis, J. A. (2001), Nanoparticle engineering of complex fluid behaviour. Langmuir, 17, p 8414-8421