Mixing Concepts, Theory, Fundamentals

The action of the impeller design produces flow of the fluid, head on the fluid, or shear in the fluid, all to varying degrees depending on the specific design. A general identification of these characteristics for several types of impellers is given by [27]. (Note Use consistent dimensions). 

Applied Process Design for Chemical and Petrochemical Plants 

The quantity of flow is defined as the amount of fluid that moves axially or radially away from the impeller at the surface or periphery of rotation. This flow quantity is never actually measured, but its relative relation to head characterizes the particular system. The flow rate, Q, is usually available from the manufacturer for a given impeller [21]. 

This is probably the most important dimensionless group used to represent the actual flow during mixing in a vessel. Flow Number, Nq (or pumping number)  

Nq is strongly dependent on the flow regime, Reynolds Number, NRe, and installation geometry of the impeller. The flow from an impeller is only that produced by the impeller and does not include the entrained flow, which can be a major part of the total motion flow from the impeller. The entrained flow refers to fluid set in motion by the turbulence of the impeller output stream [27]. To compare different impellers, it is important to define the type of flows being considered. 

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To circumvent the above problems with mass action schemes, it is necessary to use a more general thermodynamic formalism based on parameters known as interaction coefficients, also called Donnan coefficients in some contexts (Record et al, 1998). This approach is completely general it requires no assumptions about the types of interactions the ions may make with the RNA or the kinds of environments the ions may occupy. Although interaction parameters are a fundamental concept in thermodynamics and have been widely applied to biophysical problems, the literature on this topic can be difficult to access for anyone not already familiar with the formalism, and the application of interaction coefficients to the mixed monovalent-divalent cation solutions commonly used for RNA studies has received only limited attention (Grilley et al, 2006 Misra and Draper, 1999). For these reasons, the following theory section sets out the main concepts of the preferential interaction formalism in some detail, and outlines derivations of formulas relevant to monovalent ion-RNA interactions. Section 3 presents example analyses of experimental data, and extends the preferential interaction formalism to solutions of mixed salts (i.e., KC1 and MgCl2). The section includes discussions of potential sources of error and practical considerations in data analysis for experiments with both mono- and divalent ions. 

The geometric perspective of a system is an important aspect of AR theory, for it allows us to utilize the fundamental concepts of concentration vectors, mixing, and convex hulls. In Chapter 3, we will return to the BTX beaker experiment and use the graphical concepts described in this chapter to improve the maximum toluene concentration (larger than that obtained in Chapter 1). 

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