Other Forms of Chemical Transport Models

OTHER FORMS OF CHEMICAL TRANSPORT MODELS 1215 23.5.2 Pressure-Based Coordinate System... 

Typically, an electrochemical simulation models the transport of the reactant from the bulk to the electrode surface, the transfer of electrons at the electrode/solution interface and the transport of the product away from the electrode. Depending on the complexity of the electrochemical process, the simulation may account for the rate of electron transfer kinetics, the possibility and rate of preceding or following chemical reactions, the possibility and rate of adsorption processes and even combinations of different forms of mass transport (planar or spherical diffnsion, convection and migration). In other words, the simulation performs a series of actions which mimic the sequence of events thought to occur in the electrode reaction. 

Of all of the methods reviewed thus far in this book, only DNS and the linear-eddy model require no closure for the molecular-diffusion term or the chemical source term in the scalar transport equation. However, we have seen that both methods are computationally expensive for three-dimensional inhomogeneous flows of practical interest. For all of the other methods, closures are needed for either scalar mixing or the chemical source term. For example, classical micromixing models treat chemical reactions exactly, but the fluid dynamics are overly simplified. The extension to multi-scalar presumed PDFs comes the closest to providing a flexible model for inhomogeneous turbulent reacting flows. Nevertheless, the presumed form of the joint scalar PDF in terms of a finite collection of delta functions may be inadequate for complex chemistry. The next step - computing the shape of the joint scalar PDF from its transport equation - comprises transported PDF methods and is discussed in detail in the next chapter. Some of the properties of transported PDF methods are listed here. 

Fluid-fluid reactions are reactions that occur between two reactants where each of them is in a different phase. The two phases can be either gas and liquid or two immiscible liquids. In either case, one reactant is transferred to the interface between the phases and absorbed in the other phase, where the chemical reaction takes place. The reaction and the transport of the reactant are usually described by the two-film model, shown schematically in Figure 1.6. Consider reactant A is in phase I, reactant B is in phase II, and the reaction occurs in phase II. The overall rate of the reaction depends on the following factors (i) the rate at which reactant A is transferred to the interface, (ii) the solubihty of reactant A in phase II, (iii) the diffusion rate of the reactant A in phase II, (iv) the reaction rate, and (v) the diffusion rate of reactant B in phase II. Different situations may develop, depending on the relative magnitude of these factors, and on the form of the rate expression of the chemical reaction. To discern the effect of reactant transport and the reaction rate, a reaction modulus is usually used. Commonly, the transport flux of reactant A in phase II is described in two ways (i) by a diffusion equation (Pick s law) and/or (ii) a mass-transfer coefficient (transport through a film resistance) [7,9]. The dimensionless modulus is called the Hatta number (sometimes it is also referred to as the Damkohler number), and it is defined by... 

In practical terms, an indoor air quality model should provide a reasonable description of the mass balance of the test chamber experiments, trying to address factors such as material emissions, airflows into and out of the chamber and chemical/physical decay or other removal and/or transformation processes of the VOCs. VOC concentrations are increased by emissions within the defined volume of the chamber and by infiltration from external air to the chamber. Similarly, concentrations are decreased by transport via exiting chamber air, by removal to chemical and physical sinks within the chamber air, or by transformation of a VOC to other chemical forms. A general mass balance equation concerning the concentration of a VOC in a test chamber can be written in the form of one or more differential equations representing the rate of accumulation and the VOC gain and loss. This concept for a VOC concentration C (mass units/ m ) in a chamber of volume V (m ) is translated into the following differential equation ... 

Polymerization reactors are a specific kind of chemical reactors in which polymerization reactions take place therefore, in principle, they can be analyzed following the same general rules applicable to any other chemical reactor. The basic components of a mathematical model for a chemical reactor are a reactor model and rate expressions for the chemical species that participate in the reactions. If the system is homogeneous (only one phase), these two basic components are pretty much what is needed on the other hand, for heterogeneous systems formed by several phases (emulsion or suspension polymerizations, systems with gaseous monomers, slurry reactors or fluidized bed reactors with solid catalysts, etc.), additional transport and/or thermodynamic models may be necessary to build a realistic mathematical representation of the system. In this section, to illustrate the basic principles and components needed, we restrict ourselves to the simplest case, that of homogeneous reactors in other sections, additional components and more complex cases are discussed. 

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