Some Further Definitions

Before proceeding to Chapter 3. some terms and equations commonly used in reaction engineering need to be defined. We also consider the special case of the plug-fiow design equation when the volumetric flow rate is constant. 

The space time, i, is obtained by dividing reactor volume by the volumetric flow rate entering the reactor  

For example, if the volumetric flow rate were 0.01 m-Vs. it would take the upstream volume shown by the dashed lines a time t 

In the absence of dispersion, which is discussed in Chapter 14, the space time is equal to the mean residence time in the reactor, This time is the average time the molecules spend in the reactor. A range of typical processing times in terms of the space time (residence time) for industrial reactors is shown in Table 2-4. 

Reactor Type Meatt Residence Time Range Production Capacity 

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For the understanding of the Act there are some further definitions to be noted ... 

The definitions for a tree and a spanning tree were given at the beginning of this section. Let us give some further definitions. 

The total molar concentration of active sites per imit mass of catalyst is equal to the number of active sites per imit mass divided by Avogadro s number and will be labeled C, (mol/g-cat.) The molar coneentration of vacant sites, C , is the number of vacant sites per imit mass of eatalyst divided by Avogadro s number. In the absence of catalyst deactivation we assume that the total concentration of active sites remains constant. Some further definitions include ... 

Some further definitions standard states and standard values... 

There are many unique polymerization processes which share a conunon heritage with emulsion polymerization, but which often are unrecognized as such. It is the purpose of this review to describe some of these emulsion polymerization-like processes and their products. Some further definition is in order unconventional emulsion polymerizations can be described as those processes whereby the product is a polymer latex that physically resembles latex from emulsion polymerization and cannot be grouped into any other recognized form of heterogeneous polymerization. In many cases the reasons why a process is not recognized as an emulsion polymerization is that the polymerization is not via a free-radical process. This review (hscusses four distinct types of polymerization processes, all of which have examples that produce latex particles and in many ways can be described as unconventional emulsion polymerizations. These are free-radical polymerization, ionic polymerization, transition metal catalyzed polymerization and enzyme-catalyzed polymerization. The precise systems discussed in this review are described in Table 23.1. 

If you have used brainstorming to identify some existing management systems, the resulting list may be lengthy. One way to consider these systems is to subject them to further definition, drawing distinctions such as the following ... 

Although this definition might need some further specification, it is satisfactory to start the design of the project. The first task in such a project is to obtain a sufficient amount of raw material with the desired properties. The amount of material needed is dictated by the following parts of the projects ... 

For the definition of ruggedness, which refers to inter-laboratory situations, some further (unknown) effects uAk must be added to Eq. (7.30) ... 

In this chapter we introduce some basic definitions for graphs, maps, and polyhedra. We present here the basic notions. Further definitions will be introduced later when needed. The reader can consult the following books for more detailed information [Gru67], [Cox73], [Mun71], [Cro97]. 

To proceed further, we have to know how to handle the products of creation and annihilation operators. It is Wick s theorem which tells us how to deal with the products of these operators. Before presenting Wick s theorem we have to introduce some necessary definitions and relations. The creation and annihilation operators satisfy the anticommutation relation... 

Two further definitions are needed here only to help understand some items referred to later. 

All these definitions will reduce to the standard definitions in the case when A and B are subspaces of a bigger linear space C having a binary product with hermitean symmetry, so that x y = y x = = . In this case, the two binary products are identical, and some further simplifications are possible. 

A review of some of the features of these diagrams in terms of the Phase Rule is enlightening (Findlay 1951). A system composed of two different solid forms of a substance will have one component and two solid phases. In the absence of a further definition of the system there will be one degree of freedom. In Fig. 2.7 this is either the temperature or the pressure along the I<->II line. Choosing either variable fixes a point and defines the system. However, suppose that we are interested in the situation when the two phases are in equilibrium with the liquid or the vapour. Each one of those is an additional phase, making three in total and, by virtue of the Phase Rule, rendering the system invariant. Invariance results in a triple point for each case, defined by the intersection of the I<->II curve with the I<->v. and n<->v. curves on the one hand and the intersection of the I<->II curve with the I<->1. and II<->1. curves on the other hand. 

Some fundamental definitions are now introduced to simplify further discussion. Assume incident energy is approaching a body. This incident energy can be transmitted,... 

After some further manipulation, using known properties of the modified Bessel functions and putting in the definition of a, we can write this as... 

We also note that radiated tests usually only bother to measure the E-field — since the H-field is then automatically known, being proportional to the E-field. Of course, the near-field and far-held definitions assume a point source. Therefore, especially in the case of the 3 m test, some further validation to prove that we really do have only far-fields may become necessary. 

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