Hydrodynamics clustering

It is important to note here that the presence of rigid filler clusters, with bonds in the virgin, unbroken state of the sample, gives rise to hydrodynamic reinforcement of the mbber matrix. This must be specified by the strain amplification factor X, which relates the external strain of the... 

Time intervals permitting displacement values in the scaling window a< )tortuous flow as a result of random positions of the obstacles in the percolation model [4]. Hydrodynamic dispersion then becomes effective. For random percolation clusters, an anomalous, i.e., time dependent dispersion coefficient is expected according to... 

Resulting maps of the current density in a random-site percolation cluster both of the experiments and simulations are represented by Figure 2.9.13(b2) and (bl), respectively. The transport patterns compare very well. It is also possible to study hydrodynamic flow patterns in the same model objects. Corresponding velocity maps are shown in Figure 2.9.13(d) and (c2). In spite of the similarity of the... 

In this section, we consider flow-induced aggregation without diffusion, i.e., when the Peclet number, Pe = VLID, where V and L are the characteristic velocity and length and D is the Brownian diffusion coefficient, is much greater than unity. For simplicity, we neglect the hydrodynamic interactions of the clusters and highlight the effects of advection on the evolution of the cluster size distribution and the formation of fractal structures. 

Kanthale PM, Gogate PR, Wilhelm AM, Pandit AB (2005) Dynamics of cavitational bubbles and design of a hydrodynamic cavitational reactor cluster approach. Ultrason Sonochem 12 441 -52... 

Ishii and Murakami (1991) evaluated the CFB scaling relationships of Horio et al. (1989) using two cold CFB models. Solids flux, pressure drop, and optical probe measurements were used to measure a large number of hydrodynamic parameters to serve as the basis for the comparison. Fair to good similarity was obtained between the beds. Dependent hydrodynamic parameters such as the pressure drop and pressure fluctuation characteristics, cluster length and voidage, and the core diameter were compared between the two beds. The gas-to-solid density ratio was not varied between the beds. As seen in Table 7, the dimensionless solids flux decreased as the superficial velocity was increased because the solids flux was held constant. 

Pulsation in a spray is generated by hydrodynamic instabilities and waves on liquid surfaces, even for continuous supply of liquid and air to the atomizer. Dense clusters of droplets are projected into spray chamber at frequencies very similar to those of the liquid surface waves. The clusters interact with small-scale turbulent structures of the air in the core of the spray, and with large-scale structures of the air in the shear and entrainment layers of outer regions of the spray. The phenomenon of cluster formation accounts for the observation of many flame surfaces rather than a single flame in spray combustion. Each flame surrounds a cluster of droplets, and ignition and combustion appear to occur in configurations of flames surrounding droplet clusters rather than individual droplets. 

The total electro-osmotic coefficient = Whydr + mo includes a contribution of hydrodynamic coupling (Whydr) and a molecular contribution related to the diffusion of mobile protonated complexes—namely, H3O. The relative importance, n ydr and depends on the prevailing mode of proton transport in pores. If structural diffusion of protons prevails (see Section 6.7.1), is expected to be small and Whydr- If/ ori the other hand, proton mobility is mainly due to the diffusion of protonated water clusters via the so-called "vehicle mechanism," a significant molecular contribution to n can be expected. The value of is thus closely tied to the relative contributions to proton mobility of structural diffusion and vehicle mechanism. ... 

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... 

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... 

Fig. 3.4 Showing the coexistence of molecules and micelles via dynamic light scattering. Intensity fraction versus the apparent hydrodynamic radius for solutions of PBO, PEOwPBOs (120gem 3, 20 and 40°C) (Booth et al. 1997 Yang et al. 1996a). Here PBO denotes poly(oxybutylene) and PEO poly(oxyethylene). The peaks correspond to molecules (or molecular clusters) at small values of / hi>pp and to micelles at large values Ol f h.app ...

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