Binary particle interactions

Fig. 2.1 A binary particle interaction or scattering event as viewed in the laboratory coordinate system...

As a second example, consider the partitioning of Cd(II) between two adsorbents—a-TiC and (am)Fe20j.H20. Figure 11 shows Cd(II) fractional adsorption as a function of pH for binary mixtures of these adsorbents under experimental conditions such that Cddl) and SOUp are constant only the surface site mole fraction varies from one end-member to the next. As the site mole fraction shifts between the end-members, the fractional adsorption edges for the binary adsorbent mixtures varies between the limits defined by end-members. In the absence of particle-particle interactions, the adsorbents should act as independent ligands competing for complexa-tion of Cd(II). If this is the case, then the distribution of Cd(II) in such binary mixtures can be described by a composite mass-action expression (13) which includes a separate term for the interaction of Cd(II) with each adsorbent. 

P. Fede, O. Simonin, and L. Zaichik. Pdf approach for the collision modelling in binary mixture of particles. In Symp. on Fluid-particle Interactions in Turbulence. ASME-FED, 2006. 

In a hard sphere approach, particles are assumed to interact through instantaneous binary collisions. This means particle interaction times are much smaller than the free flight time and therefore, hard particle simulations are event (collision) driven. For a comprehensive introduction to this type of simulation, the reader is referred to Allen and Tildesley (1990). Hoomans (2000) used this approach to simulate gas-solid flows in dense as well as fast-fluidized beds. There are three key parameters in such hard sphere models, namely coefficient of restitution, coefficient of dynamic friction and coefficient of tangential restitution. Coefficient of restitution is discussed later in this chapter. Detailed discussion of these three model parameters can be found in Hoomans (2000). 

As discussed in Chapter 2, the one-particle NDF does not usually provide a complete description of the microscale system. For example, a microscale system containing N particles would be completely described by an A-particle NDF. This is because the mesoscale variable in any one particle can, in principle, be influenced by the mesoscale variables in all N particles. Or, in other words, the N sets of mesoscale variables can be correlated with each other. For example, a system of particles interacting through binary collisions exhibits correlations between the velocities of the two particles before and after a collision. Thus, the time evolution of the one-particle NDF for velocity will involve the two-particle NDF due to the collisions. In the mesoscale modeling approach, the primary physical modeling step involves the approximation of the A-particle NDF (i.e. the exact microscale model) by a functional of the one-particle NDF. A typical example is the closure of the colli-sionterm (see Chapter 6) by approximating the two-particle NDF by the product of two one-particle NDFs. 

Particle Interactions in Binary Mixtures of Carbon Black and White Solid Acids... 

A conceptual and mechanistic model of particle interactions in silica-iron binary oxide suspensions is described. The model is consistent with a process involving partial Si02 dissolution and sorption of silicate onto Fe(OH)3. The constant capacitance model is used to test the mechanistic model and estimate the effect of particle interactions on adsorbate distribution. The model results, in agreement with experimental results, indicate that the presence of soluble silica interferes with the adsorption of anionic adsorbates but has little effect on cationic adsorbates. 

Details on the adsorbent preparation and experimental and analytical techniques are presented elsewhere (9). This paper briefly reviews the experimental results for the Fe(OH)3 and Si02 suspensions and describes a conceptual and mechanistic model for particle interactions which is qualitatively consistent with the experimental observations. Similar results were obtained for binary Al(OH)3 and Si02 suspensions (9). The constant capacitance surface complexation model is then used to test the mechanistic model and estimate the quantitative influence of the particle-particle interactions on adsorbate distribution. 

Figure 12.3 The green overhang of linker A is self-complementary therefore, DNA-AuNPs hybridized to linker A are self-complementary and behave as a single component system. Maximizing the number of particle-particle interactions results in a close-packed structure depicted by an FCC unit ceU. The red and blue overhang of linker X and linker Y are complementary and DNA-AuNPs hybridized to linkers X and Y are complementary and behave as a binary system. Maximizing the number of particle-particle interactions results in a nonclose-packed structure depicted by a BCC unit cell. (Adapted from S. Y. Park et al., Nature 2008, 451, 553.) (See color insert.)...

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