Species continuity equations specific forms

With some significant simplifying assumptions, the species-continuity equation can be put into a form that is analogous to the thermal-energy equation. Specifically, consider that there is no gas-phase chemistry and that a single species, A, is dilute in an inert carrier gas, B. In this case, considering Eq. 3.128, Eq. 6.24 reduces to... 

Several colloidal systems, that are of practical importance, contain spherically symmetric particles the size of which changes continuously. Polydisperse fluid mixtures can be described by a continuous probability density of one or more particle attributes, such as particle size. Thus, they may be viewed as containing an infinite number of components. It has been several decades since the introduction of polydispersity as a model for molecular mixtures [73], but only recently has it received widespread attention [74-82]. Initially, work was concentrated on nearly monodisperse mixtures and the polydispersity was accounted for by the construction of perturbation expansions with a pure, monodispersive, component as the reference fluid [77,80]. Subsequently, Kofke and Glandt [79] have obtained the equation of state using a theory based on the distinction of particular species in a polydispersive mixture, not by their intermolecular potentials but by a specific form of the distribution of their chemical potentials. Quite recently, Lado [81,82] has generalized the usual OZ equation to the case of a polydispersive mixture. Recently, the latter theory has been also extended to the case of polydisperse quenched-annealed mixtures [83,84]. As this approach has not been reviewed previously, we shall consider it in some detail. 

There is a nonzero mass source in the continuity equation, Sm, arising from the summation of all species equations. A general form of this source term is given in Table 1. Use has been made of the assumption that summation of interspecies diffusion within the gas phase is equal to zero. Specifically, one has... 

The thermodynamics of irreversible processes begins with three basic microscopic transport equations for overall mass (i.e., the equation of continuity), species mass, and linear momentum, and develops a microscopic equation of change for specific entropy. The most important aspects of this development are the terms that represent the rate of generation of entropy and the linear transport laws that result from the fact that entropy generation conforms to a positive-definite quadratic form. The multicomponent mixture contains N components that participate in R independent chemical reactions. Without invoking any approximations, the three basic transport equations are summarized below. 

For each of the chemical species participating in the mechanism, a mass balance equation must be written. The appropriate form of the mass balance for the specific type of reactor at hand must be used. Two of the most common types of reactors used in industry are the CSTR (continuous stirred tank reactor) and the tubular reactor. The corresponding mathematical models for their idealized forms, based on transport phenomena equations and available in any standard chemical reactor text [17, 18], are the ideal CSTR and the ideal model for the plug flow tubular reactor (PFR). The ideal CSTR model is given by Equation 12.1 ... 

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