Particle-dominated regime

With increasing fluid velocity, a particle-fluid system starts with the particle-dominated fixed bed terminating at UmC, spans the particle-fluidcompromising regimes of particulate, bubbling, turbulent and fast fluidization,... 

The computer model is based upon a continuum description of fluidization in coal gasification reactors. In general, fluidized flows are dominated by specific physicochemical processes and, hence, require particular theoretical representations. For example, in the heavily loaded gas-particle regime appropriate to fluidization, the solid particles dominate the transport of momentum and energy. This aspect of fluidization is reflected in the mathematical descriptions which have been used in the fluidized bed model. 

The effect of ac, rather than dc, fields on the steady shear viscosity has also been investigated. An ac field might be desirable as a means of periodically reversing, and thereby minimizing, electrically induced migration or chemical reactions. High-frequency ac fields are also required if one is to avoid a crossover to a conduction-dominated regime in which the effective polarizability is controlled by conductivities rather than polarizabilities of the particles and medium (see Section 8.2.1.1). Klass and Martinek (1967) found that at a fixed... 

A homogeneous nucleation model was proposed [20, 21] in which radicals react in the aqueous phase with solubilized monomer to form growing oligomeric species (Fig. 3). These species will form particles when the critical water solubility length is reached (/crit-iner). The consequence is that in cases where homogeneous nucleation is the dominating regime of particle nucleation, the water solubility of the monomer, the initiator concentration, and the water solubility of the initiator become important parameters in the emulsion polymerization process. 

This equation has interesting physical consequences. In the diffusion-dominated regime, Nr I r > 1, the probability of translocating is small transport time displays the familiar scaling with the channel length I r. 

The activation observed in titania-supported Au electrocatalysts is unlikely to arise from electronic effects in monolayer or bilayer Au [Valden et al., 1998 Chen and Goodman, 2004], since the electrocatalytic activity was correlated with the size of three-dimensional titania-supported Au particles [Guerin et al., 2006b Hayden et al., 2007a, c]. The possibility that titania-induced electronic modification of three-dimensional particles below 6.5 nm is responsible for the induced activity, however, could not be excluded. It was pointed out, though, that such electronic effects should dominate for the smaller particle regime (<3 nm), where deactivation of the Au is observed on all supports. 

Regime of transport limitation, here

diffusion through the hydrodynamic boundary layer. The apparent activation energy under these conditions gets close to zero. Every educt molecule reacts instantaneously on the outer catalyst surface, no educt diffusion inside the catalyst particle takes place. 

The fu st term is a modified Archimedes number, while the second one is the Froude number based on particle size. Alternatively, the first term can be substituted by the Reynolds number. To attain complete similar behavior between a hot bed and a model at ambient conditions, the value of each nondimensional parameter must be the same for the two beds. When all the independent nondimensional parameters are set, the dependent parameters of the bed are fixed. The dependent parameters include the fluid and particle velocities throughout the bed, pressure distribution, voidage distribution of the bed, and the bubble size and distribution (Glicksman, 1984). In the region of low Reynolds number, where viscous forces dominate over inertial forces, the ratio of gas-to-solid density does not need to be matched, except for beds operating near the slugging regime. 

When external gradients correspond to substantial differences in concentration or temperature between the bulk of the fluid and the external surface of the catalyst particle, the rate of reaction at the surface is significantly different from that which would prevail if the concentration or temperature at the surface were equal to that in the bulk of the fluid. The catalytic reaction is then said to be influenced by external mass or heat transfer, respectively, and, when this influence is the dominant one, the rate corresponds to a regime of external mass or heat transfer. 

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