Lateness of mixing

PF, to model the effect of earliness or lateness of mixing, depending on the sequence, on the performance of a single-vessel reactor. The following two examples explore the consequences of such series arrangements-first, for the RTD of an equivalent single vessel, and second, for the fractional conversion. The results are obtained by methods already described, and are not presented in detail. 

The performance results for the two configurations are the same for first-order, or linear, process, even though the earliness and lateness of mixing differ. 

The third case, n = 1, is the easiest to understand. The earliness or lateness of mixing has no effect when the relationship between —rp, and Ca is linear. The slope of the —rp, vmisus Ca curve does not depend on Ca. It does not matter whether mixing occurs at high Ca or atlow Ca. 

For a first-order system, earliness or lateness of mixing does not affect reactor performance, for a given residence time distribution. Therefore, when the residence time distribution is known, the exact performance of a system of first-order reactions can be calculated from the macrofluid model. 

For first-order reactions, performance depends only on the residence time distribution. The scale of miring and the earliness or lateness of mixing do not affect either the conversion or the product distribution, if... 

Arrington C A, Morse M D and Doverstal M 1995 Spectroscopy of mixed early-late transition metal diatomics ScNi, YPd, and ZrCo J. Chem. Rhys. 102 1895... 

The use of mixed gel technology has become widespread since the late 1980s. If the column is well designed it should not he necessary to supplement resolution in certain areas of the operating range (particularly the extremes) hy the addition of individual pore size columns. This practice is not necessary or recommended for PLgel mixed gel columns, although it is a common practice for other commercial products. 

Time-Dependent Density Functional theory (TDDFT) has been considered with increasing interest since the late 1970 s and many papers have been published on the subject. The treatments presented by Runge and Gross (36) and Gross and Kohn (37) are widely cited in the discussion of the evolution of pure states. The evolution of mixed states has been considered extensively by Rajagopal et al. (38), but that treatment differs in many aspects from the form given here. 

Research into cluster catalysis has been driven by both intrinsic interest and utilitarian potential. Catalysis involving "very mixed -metal clusters is of particular interest as many established heterogeneously catalyzed processes couple mid and late transition metals (e.g., hydrodesulfurization and petroleum reforming). Attempts to model catalytic transformations arc summarized in Section II.F.I., while the use of "very mixed -metal clusters as homogeneous and heterogeneous catalysis precursors are discussed in Sections I1.F.2. and I1.F.3., respectively. The general area of mixed-metal cluster catalysis has been summarized in excellent reviews by Braunstein and Rose while the tabulated results are intended to be comprehensive in scope, the discussion below focuses on the more recent results. 

The state of mixing generally controls tire mass transfer. In a liquid-liquid system, for example, the reaction rate is based on the mass transfer which depends on the interface area of the two liquid layers. This area is dramatically changed by a change in the mixing rate. If, for example, the agitator is started late, the increase in mass transfer area will lead to a rapid increase in the conversion rate and hence in the heat production rate. 

Mixed-valence chemistry was reviewed in the late 1960 s both by Robin and Day (4) and by Hush (5). Their work provided the beginnings of a theoretical background for understanding the properties of mixed-valence compounds including the low energy absorption bands which have been termed Intervalence Transfer (IT) or Metal-Metal Charge Transfer (MMCT) bands. 

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