Multiple particle systems

Cornish(128) considered the minimum possible value of the Nusselt number in a multiple particle system. By regarding an individual particle as a source and the remote fluid as a sink, it was shown that values of Nusselt number less than 2 may then be obtained. In a fluidised system, however, the inter-particle fluid is usually regarded as the sink and under these circumstances the theoretical lower limit of 2 for the Nusselt number applies. Zabrodsky 1 291 has also discussed the fallacy of Cornish s argument. 

Understanding the behavior of single particles is, however, a solid foundation upon which to build knowledge of multiple-particle systems. In addition, the literature on single particles is already so extensive that it warrants a book of its own. 

Niiyama and Suzuki (1982) studied hydrogenation of ethylene over Ni—A1203. Oscillations in particle temperature were observed. Similarly in a packed bed flow reactor, a multiple-particle system, the temperature of the catalyst bed and the... 

When many particles flow in a fluid in close proximity to each other the motion of each particle is influenced by the presence of the others. The simple analysis for the fluid particle interaction for a single particle is no longer valid but can be adapted to model the multiple particle system. 

As far as the first term of the fluid—particle interaction force F ofEq. (5) is concerned in a uniform homogeneous steady flow of the fluid, it results in a term — Vp (Tchen, 1947) or a gravity term (Bird et al, 1960) in the equation of motion for a single particle see also, e.g., SokoHchin et al (2004). Derksen (2003) includes both the — Vp term and the viscous p U term. In a multiple particle system with N particles contained within a volume element of volume A, the first term of Eq. (5) results in a contribution to the fluid-particle interaction force per unit of volume of the multiple particle system that runs hke... 

In multiple particle systems, particularly when the mutual distances between the particles become smaller, the flow field around a particle in a swarm—i.e., the development and separation of the boundary layer and the formation and dynamic behavior of the wake behind particles—is really affected by the presence and motion of neighboring particles. There are two effects first of all, there is simply not sufficient space for boundary layer and wake to develop without interference with the adjacent particles and their boundary layers and wakes—and, second, for a given superficial velocity (or... 

Yet, the majority of the hterature on ffuid—particle interaction starts from the base case of a single particle (or bubble), carries out experiments, derives model equations for the behavior of a single particle under various flow conditions (as discussed), and/or appHes single-phase correlations in multiple particle systems. In the pre-CFD era and in the domain of process design and optimization, the usual focus is on the steady-state drag and one takes refuge to simple correlations such as that proposed decades ago by Richardson and Zaki (1954) ... 

The topic of the drag coefficient in multiple particle systems has regained interest because of the CFD simulations of turbulent multiple particle systems such as agitated sohd suspensions, aerated stirred vessels, solid—liquid fluidized beds, and gas-sohds cyclones. A recent review on this topic can be found in Ghatage et al (2013) who also presented new experimental data on the shp velocity of a foreign particle in sohd—Uquid fluidized beds. 

---