Particle clustering hydrodynamics

Hydrodynamic interactions with particles may certainly play a role in clustering. Horio and Clift [30] noted that particle clusters, a group of loosely held together particles, are the result of hydrodynamic effects. Squires and Eaton [31] proposed that clustering resulted from turbulence modification from an isotropic turbulent... 

It is noted that a cluster as referred to here is a lump of solid particles over which flow properties such as voidage do not vary substantially. It is formed mainly as a result of hydrodynamic effects. The mechanism of particle clustering is different from that of agglomeration, in which particles adhere to one another mainly by surface attraction (e.g., van der Waals force and electrostatic forces), and mechanical or chemical interaction [Horio and Clift, 1992],... 

On the basis of the observations in the macroscale, the flow of a fast fluidized bed can be represented by the core-annulus flow structure in the radial direction, and coexistence of a bottom dense region and a top dilute region in the axial direction. Particle clusters are an indication of the heterogeneity in the mesoscale. A complete characterization of the hydrodynamics of a CFB requires the determination of the voidage and velocity profiles. There are a number of mathematical models accounting for the macro- or mesoaspects of the flow pattern in a CFB that are available. In the following, basic features of several types of models are discussed. 

Thus, the disperse nanofiller particles aggregation in elastomeric matrix can be described theoretically within the framewoiks of a modified model of irreversible aggregation particle-cluster. The obligatory consideration of nanofiller initial particles size is a feature of the indicated model application to real systems description. The indicated particles diffusion in polymer matrix obeys classical laws of Newtonian liquids hydrodynamics. The offered approach allows to predict nanoparticles aggregates final parameters as a function of the initial particles size, their contents and other factors number. 

Solomentsev Y, Rohmer M, Anderson JL (1997) Particle clustering and pattern formation during electrophoretic deposition a hydrodynamic model. Langmuir 13 6058... 

In a gas—sohd CFB with heterogeneous reactions and mass transfer, in Hne with the structural characteristics of the SFM model (Hong et al, 2012), as shown in Fig. 12, the mass transfer and reaction in any local space can be divided into components of the dense cluster (denoted by subscript c), the dilute broth (denoted by subscript f), and in-between (denoted by subscript i), respectively. And these terms can be represented by Ri (1 = gc, gf, gi, sc, sf, si). Both the dense and dilute phases are assumed homogenous and continuous inside, and the dense phase is fiarther assumed suspended uniformly in the dilute phase in forms of clusters of particles. Then the mass transfer terms can be described with Ranz-Marshall-hke relations for uniform suspension of particles (Haider and Basu, 1988). In particular, the mesoscale interaction over the cluster will be treated as is for a big particle with hydrodynamic equivalent diameter of d. Due to dynamic nature of clusters, there are mass exchanges between the dilute and dense phases with rate ofTk (k = g, s), pointing outward from the dilute to the dense phase. 

Heat transfer models are usually written in terms of either clusters or dense wall layers, based on the hydrodynamics of fast fluidization. For cluster models (Fig. 26), heat can be transferred between the suspension and wall by (1) transient conduction to particle clusters arriving at the wall from the bulk, supplemented by radiation (2) convection and radiation from the dispersed phase (gas containing a small fraction of solid material). The various components are usually assumed to be additive, ignoring interaction between the convective and radiation components. 

The structures of cluster-cluster (C-C) and particle-cluster (P-C) fractal-like agglomerates have been investigated by Brasil et al. [4], In the applied numerical scheme, simplified models based on the Langevin dynanucs have been used in which the hydrodynamic interaction between fluid and particles is not accounted... 

FIGURE 13.5 Time evolution of the average hydrodynamic radius of BSAp-functionalized particle clusters for two different net charges. 

Attention may be drawn to the fact that Fleming et al. (1991) suggested that clusters formed at concentrations in excess of 1% of high molecular weight gelatins, with hydrodynamic radii of the component particles in the clusters of around 75 nm. However, they also suggested that the radii were around 60 nm when the molecular... 

In dispersive mixing the clusters of particles held together by cohesive forces (agglomerates) are successively broken apart by hydrodynamic stresses imposed on the external surfaces of the deforming liquid matrix, which in turn generate internal stresses within the cluster (40). A detailed review of dispersive mixing was given by Manas-Zloczower (41), and in this section we will follow her discussion. 

Fig. 1 Schematic view of filler morphology in three concentration regimes. For reinforcement is due to hydrodynamic amplification by particles ( < 1) or clusters (cp> +) with eff= or cpeff= / A) respectively. For > reinforcement is due to the deformation of a flexible filler network...

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

The theory reflects the solvent properties through the thermody-namic/hydrodynamic input parameters obtained from the accurate equations of state for the two solvents. However, the theory employs a hard sphere solute-solvent direct correlation function (C12), which is a measure of the spatial distribution of the particles. Therefore, the agreement between theory and experiment does not depend on a solute-solvent spatial distribution determined by attractive solute-solvent interactions. In particular, it is not necessary to invoke local density augmentation (solute-solvent clustering) (31,112,113) in the vicinity of the critical point arising from significant attractive solute-solvent interactions to theoretically replicate the data. 

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