Local Solids Flow Structure

The prediction of overall solids holdups can be obtained by integrating the axial profile of the solids concentration over the axial length. In terms of Eq. (10.12), the overall solids holdup can be expressed as 

The equation is applicable for aa = 0.85-0.93. For comparison, the typical solids concentration ranges for the bubbling and turbulent regimes are, respectively, 0.4-0.55 and 0.22-0.4 [Kunii and Levenspiel, 1990]. 

The preceding sections are concerned with the time-averaged flow behavior in a macroscale. The time-variant flow behavior is complex. Analyses of the instantaneous flow 

These factors lead to localized particle accumulation in the wall region. The particle accumulation alters the large-scale motion in the gas-solid flow, which in turn affects the cluster size and motion. 

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Other than the particle dimension d, the porous medium has a system dimension L, which is generally much larger than d. There are cases where L is of the order d such as thin porous layers coated on the heat transfer surfaces. These systems with Lid = 0(1) are treated by the examination of the fluid flow and heat transfer through a small number of particles, a treatment we call direct simulation of the transport. In these treatments, no assumption is made about the existence of the local thermal equilibrium between the finite volumes of the phases. On the other hand, when Lid 1 and when the variation of temperature (or concentration) across d is negligible compared to that across L for both the solid and fluid phases, then we can assume that within a distance d both phases are in thermal equilibrium (local thermal equilibrium). When the solid matrix structure cannot be fully described by the prescription of solid-phase distribution over a distance d, then a representative elementary volume with a linear dimension larger than d is needed. We also have to extend the requirement of a negligible temperature (or concentration) variation to that over the linear dimension of the representa-... 

Figure 12 Snapshots of the solid particle distribution and the local flow structure from a DNS of gas-solid flow carried out by Chen et al (2009). Reprinted from Chen et al (2009) with permission from Eisevier.

Individual Coefficient of Heat Transfer Because of the comphcated structure of a turbulent flowing stream and the impracti-cabifity of measuring thicknesses of the several layers and their temperatures, the local rate of beat transfer between fluid and solid is defined by the equations... 

The solidity of gel electrolytes results from chain entanglements. At high temperatures they flow like liquids, but on cooling they show a small increase in the shear modulus at temperatures well above T. This is the liquid-to-rubber transition. The values of shear modulus and viscosity for rubbery solids are considerably lower than those for glass forming liquids at an equivalent structural relaxation time. The local or microscopic viscosity relaxation time of the rubbery material, which is reflected in the 7], obeys a VTF equation with a pre-exponential factor equivalent to that for small-molecule liquids. Above the liquid-to-rubber transition, the VTF equation is also obeyed but the pre-exponential term for viscosity is much larger than is typical for small-molecule liquids and is dependent on the polymer molecular weight. 

Containment systems are typically designed with solid, impermeable floors with perimeter curbing, dikes, berms, or walls to contain the released material within the area of the release. The containment should be designed such that a flammable spill and fire water runoff flow away from and do not collect under process equipment. Concrete is commonly used, but other materials may also be appropriate. This containment zone may include the ground floor of a process structure or a portion (one or more bays) of a structure. Local containment may also be used on upper levels of a structure or in a building around specific equipment with identified potential for spills or releases. 

Continuous flow reactors allow a new way of catalyst preparation. The fluidic pathways can be used for the transport of impregnation liquid or solid particles if means are supplied to localize the catalysts at defined positions inside the reactor. One possibility is the flow impregnation of wash-coated micro structures with catalyst solutions [38],... 

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