Dense-particle phase

Some researchers have noted that this approach tends to underestimate the lean phase convection since solid particles dispersed in the up-flowing gas would cause enhancement of the lean phase convective heat transfer coefficient. Lints (1992) suggest that this enhancement can be partially taken into account by increasing the gas thermal conductivity by a factor of 1.1. It should also be noted that in accordance with Eq. (3), the lean phase heat transfer coefficient (h,) should only be applied to that fraction of the wall surface, or fraction of time at a given spot on the wall, which is not submerged in the dense/particle phase. This approach, therefore, requires an additional determination of the parameter fh to be discussed below. 

Convective Heat Transfer. Most researchers concur that for bubbling fluidized beds, the gaseous convection is significantly enhanced by the presence of sohd particles (Ozkaynak and Chen, 1980 Kunii and Levenspiel, 1991). Models often have focused on the dense/particle phase contribution, or on the total convective contribution,... 

Many different models and correlations have been proposed for the prediction of the heat transfer coefficient at vertical surfaces in FFBs. At time of this writing, no single correlation or model has won general acceptance. The following discussion presents a summary of some potentially useful approaches. It is helpful to consider the total heat transfer coefficient as eomposed of convective contributions from the lean-gas phase and the dense-particle phase plus thermal radiation, as defined by Eqs. (15) and (16). All eorrela-tions based on ambient temperature data, where thermal radiation is negligible, should be considered to represent only the convective heat transfer coefficient hr. 

Figure 14.4 contains solutions to eqn (14.28) for a typical group B air-fluidized system it shows bubble void fractions ej for all values of dense phase void fraction e. There is a lot of information in this diagram, but only one solution is of relevance from a strictly practical point of view the jump at the minimum fluidization condition, ei = e f = 0.4, to a virtually completely void bubble, 2 1 (In fact this value computes to over 0.999.) This result provides a truly theoretical justification for the long established two-phase theory of gas fluidization for moderately sized powders, which postulates a dense particle phase that remains at the minimum bubbling condition for all fluid fluxes in excess of 17 /, with the remaining gas forming completely void bubbles (Toomey and Johnstone, 1952)... 

Nonaqueous phase Hquids (NAPLs) present special problems for soil and ground water cleanup. Contaminant transport through ground water depends in part on the water solubiHty of the compound. Because NAPLs cling to subsurface particles and are slow to dissolve in ground water, they hinder cleanups and prolong cleanup times. Dense nonaqueous phase Hquids (DNAPLs) migrate downward in the aquifer and can coUect in pools or pockets of the substmcture. Examples of DNAPLs are the common solvents tetrachloroethylene (PCE) and trichloroethylene (TCE) which were used extensively at many faciHties before the extent of subsurface contamination problems was realized. 

Kobayashi et al. [91] recently synthesized a phase that is comprised of thiol-modified gold-coated polystyrene particles. An increase in the selectivity of the anthracene-phenanthrene pair was observed on the Cis-Au particle when compared with a traditional monomeric Cis phase with a surface coverage of 3.0 p,mol/m. This isomer pair is not the ideal choice for the determination of shape selectivity however, this synthetic technique should in general lead to dense, ordered phases that are anticipated to yield relatively highly shape-selective chromatographic separations. 

The Eulerian continuum approach, based on a continuum assumption of phases, provides a field description of the dynamics of each phase. The Lagrangian trajectory approach, from the study of motions of individual particles, is able to yield historical trajectories of the particles. The kinetic theory modeling for interparticle collisions, extended from the kinetic theory of gases, can be applied to dense suspension systems where the transport in the particle phase is dominated by interparticle collisions. The Ergun equation provides important flow relationships, which are useful not only for packed bed systems, but also for some situations in fluidized bed systems. 

For the Eulerian continuum modeling discussed in this chapter, it is assumed that the basic form of the Navier-Stokes equation can be applied to all phases. For some dense suspension cases, the particle phase may behave as a non-Newtonian fluid. In these cases, a simple extension of the Navier-Stokes equation may not be appropriate. 

Considerations about fluid beds with small particles of high density to improve the capture of large macromolecules at high speed have been extensively described.78 80 This technology has been described for the capture of monoclonal antibodies from crude feedstocks containing cells using dense solid phases. In a first example, soluble antibodies from mammalian... 

The general features of this phase diagram have been well confirmed by experiments, especially those of Nakajima and of Miller and their co-workers. The emergence of a concentrated, well-ordered anisotropic phase when % exceeds a small positive value (that depends on the axial ratio x) is readily understood as the consequence of interactions that are effectively attractive between the rodlike particles. The dense anisotropic phase may be regarded as the prototype of a quasi-crystalline state with uniaxial order only. Comprehension of the three-dimensional order characteristic of the crystalline state is, of course, beyond the scope of the model, which does not... 

Constraint dynamics is just what it appears to be the equations of motion of the molecules are altered so that their motions are constrained to follow trajectories modified to mclude a constraint or constraints such as constant (total) kinetic energy or constant pressure, where the pressure in a dense adsorbed phase is given by the virial theorem. In statistical mechanics where large numbers of particles are involved, constraints are added by using the method of undetermined multipliers. (This approach to constrained dynamics was presented many years ago for mechanical systems by Gauss.) Suppose one has a constraint g(R, V)=0 that depends upon all the coordinates R=rj,r2...rN and velocities V=Vi,V2,...vn of all N particles in the system. By differentiation with respect to time, this constraint can be rewritten as l dV/dt -i- s = 0 where I and s are functions of R and V only. Gauss principle states that the constrained equations of motion can be written as ... 

The cyclone, or inertial separation method, is a common industrial approach for segregating a dispersed phase from a continuous medium based upon the difference in density between the phases. The concept takes advantage of the velocity lag which occurs for dense particles with respect to a lower density medium when both phases are subject to an accelerating flow field, such as within a rotating vortex. The larger the acceleration, the smaller the particle which fails to follow the continuous phase streamlines and will migrate to the outer wall of the cyclone for collection. 

Ding and Gidaspow [16], for example, derived a two-phase flow model starting with the Boltzmann equation for the distribution function of particles and incorporated fluid-particle interactions into the macroscopic equations. The governing equations were derived using the classical concepts of kinetic theory. However, to determine the constitutive equations they used the ad hoc distribution functions proposed by Savage and Jeffery [65]. The resulting macroscopic equations contain both kinetic - and collisional pressures but only the collisional deviatoric stresses. The model is thus primarily intended for dense particle flows. 

Boelle A, Balzer G, Simonin O (1995) Second order prediction of the particle phase stress tensor of inelastic spheres in simple shear dense suspensions. Gas-Solid Flows, ASME FED 228 9-18... 

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