Particle effective

FluidiZed-Bed Combustion. Fluidized-bed combustors are able to bum coal particles effectively in the range of 1.5 mm to 6 mm in size, which are floating in place in an expanded bed (40). Coal and limestone for SO2 capture can be fed to the combustion zone, and ash can be removed from it, by pneumatic transfer. Very Htfle precombustion processing is needed to prepare either the coal or the sorbent for entry into the furnace (41). 

Flere C is the volume concentration of j-phase particles is the mass concentration of the analyte in the j-phase particles w is the x-ray fluorescence radiation yield t. is the mass absorption coefficient of the analyte for the primar y radiation d. is the j-phase particle effective size r fs... 

The most important conclusions of their work were that the inter-particle effects are reasonably small for the particular recycle reactor design, and that kinetic constants determined in the recycle reactor were trustworthy. 

Small-Particle Effects and Structural Considerations for Electrocatalysis Kinoshita, K. 14... 

The second step has bo include the miLti-particle effects, and the total aiergy as a function of all gecraetrical oonfigurations of the particles has to be evaluated. 

Kinoshita, K., Small-particle effects and structural considerations for electrocatalysis, in Modem Aspects of Electrochemistry, 1. O M. Bockris, Eds., Vol. 14, Kluwer, New York, 1982, p. 557. 

Tan, C. S., and Smith, J. M. Catalyst particle effectiveness with unsymmetrical boundary conditions. Chem. Eng. Sci. 35,1601-1609 (1980). 

As will be shown in Section 3, inelastic X-ray scattering experiments can help to decide which theoretical approach is appropriate. One must keep in mind that this static correction is far from an appropriate description of electron correlations. A more accurate way is to account for dynamical screening by writing %(q, co) in terms of the one-particle Greens function G(p, e) corrected for many-particle effects by a... 

An alternative description of nonspherical particles is often represented by the sphericity factor (tfi), which is the number that, when multiplied by the diameter of a sphere with the same volume as the particle (ds), gives the particle effective diameter (dp) ... 

Intraparticle Mass Transfer. One way biofilm growth alters bioreactor performance is by changing the effectiveness factor, defined as the actual substrate conversion divided by the maximum possible conversion in the volume occupied by the particle without mass transfer limitation. An optimal biofilm thickness exists for a given particle, above or below which the particle effectiveness factor and reactor productivity decrease. As the particle size increases, the maximum effectiveness factor possible decreases (Andrews and Przezdziecki, 1986). If sufficient kinetic and physical data are available, the optimal biofilm thickness for optimal effectiveness can be determined through various models for a given particle size (Andrews, 1988 Ruggeri et al., 1994), and biofilm erosion can be controlled to maintain this thickness. The determination of the effectiveness factor for various sized particles with changing biofilm thickness is well-described in the literature (Fan, 1989 Andrews, 1988)... 

Case B. Suppose, more realistically, that the catalyst undergoes a known, experimentally determined, rate of attrition as a function of particle size (Zenz, 1971 Zenz Kelleher, 1980). The particle loss rate from the cyclone system will now approach and finally equal the rate of production of 0 to 10 micron particles by attrition from all the larger sizes. To maintain reactor inventory, this loss rate will be replaced, at an equal rate, with fresh catalyst. Since the rate of attrition of any size particle depends on its concentration in the stream subjected to the attrition (as finer particles effectively cushion the coarser), and since the loss is replaced with fresh catalyst (containing the coarsest), the bed size distribution will reach a steady state between 10 and 150 microns in which the mean size, as well as all sizes smaller than the largest, will now be decreased from what would have prevailed under conditions of zero attrition. 

For some soft particles effective anchoring may require covalent grafting of the incompatible PS blocks to the core polymer. 

For this purpose, we introduce the particle effectiveness factor tj, the ratio of the observed rate of reaction for the particle as a whole to the intrinsic rate at the surface conditions, cAj and Ts. In terms of a reactant A,... 

We consider the effects of cA and Tseparately, deferring the latter to Section 8.5.5. In focusing on the particle effectiveness factor, we also ignore the effect of any difference in concentration between bulk gas and exterior surface (cAg and cAs.) in Section 8.5.6, we introduce the overall effectiveness factor to take this into account. 

For a flat-plate porous particle of diffusion-path length L (and infinite extent in other directions), and with only one face permeable to diffusing reactant gas A, obtain an expression for tj, the particle effectiveness factor defined by equation 8.5-5, based on the following... 

The definition of the particle effectiveness factor 77 involves the intrinsic rate of reaction, ( rA)int> for reaction A - products, at the exterior surface conditions of gas-phase concentration (cAs) and temperature (Ts). Thus, from equation 8.55,... 

The particle effectiveness factor 17 defined by equation 8.5-5 takes into account concentration and temperature gradients within the particle, but neglects any gradients from bulk fluid to the exterior surface of the particle. The overall effectiveness factor y)0 takes both into account, and is defined by reference to bulk gas conditions (cA, Tg) rather than conditions at the exterior of the particle (cAj, Ts) ... 

The starting points for the continuity and energy equations are again 21.5-1 and 21.5-6 (adiabatic operation), respectively, but the rate quantity7 (—rA) must be properly interpreted. In 21.5-1 and 21.5-6, the implication is that the rate is the intrinsic surface reaction rate, ( rA)int. For a heterogeneous model, we interpret it as an overall observed rate, (—rA)obs, incorporating the transport effects responsible for the gradients in concentration and temperature. As developed in Section 8.5, these effects are lumped into a particle effectiveness factor, 77, or an overall effectiveness factor, r]0. Thus, equations 21.5-1 and 21.5-6 are rewritten as... 

The calculation of the induced electron density may be done in the context of the Kohn-Sham approach to density functional theory, because the response of a KS system to a change in the one particle effective potential (r) corresponds to that of a system of non-interacting electrons. 

To calculate the release through diffusion of an entrapped residue, Barraclough et al. (2005) considered the size of organic matter particles (effective radius 10" to 10 cm) and the effective diffusion coefficient of small organic molecules in a sorbing medium (D 10 cm s )- The time for 50% of the material in a sphere to diffuse out is given by... 

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