Theory of separation stages

In separation processes, a common problem is a mixture of a certain composition to be separated into two fractions, where after separation each fraction is of the required composition. If the separation is carried out in a countercurrent flow column, the 

Using the notation given for cocurrent flow, a mass balance for the whole separation column (balance area I in Fig. 1-52) for the component to be transferred is 

BAI Balance area I (total separation column) BAII Balance area II (a column section) 

BL Balance line EC Equilibrium curve y Loading of phase II X Loading of phase I 

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If trays are used as internals in a column, the theory of separation stages is particularly important for the determination of the actual column height (see Chapter 2.5.6.1). 

The theory of separation stages is also valid for packed columns. Since single stages cannot be distinguished, an evaluation number n, or its reciprocal value HETP or HETS is introduced... 

In absorption and extraction processes, the assumption of phase equilibrium of the phases leaving the stage is less valid than in rectification processes. The exact calculation for a counterflow column using the theory of separation stages is generally carried out for rectification processes. The following discussion of a system of nonlinear equations, based on the column model, is particularly valid for rectification, but this may be applied to all other counterflow processes. Before the equation system can be formulated the variables used to describe the state of the counterflow system must be expressed. According to the column model in Fig. 1-60 they are... 

The separation techniques described here are those of most interest to analytical chemistry. The background and theory of separation by the single-stage processes of precipitation and electrodeposition are discussed in Chapters 7 and 14. In this chapter some general introduction to separations is presented along with a brief background for several separation processes. 

An exact method for calculating the minimum number of separating stages has been developed by Harbert [182], who refers the volatilities of the individual components to the vapour pressure of the most volatile constituent. An excellent article bj Bruijn [183] deals with the theory of multicomponent distillation at a minimum reflux ratio. The thermodynamic foundation of multicomponent rectifications has been treated systematically by Wagner in a series of publications [183a]. Starting from the physical properties of mixtures the various steps in distillation practice are described in an exemplary manner. The description is supplemented by a great number of references. 

Kinetics and Mechanisms. Early researchers misunderstood the fast reaction rates and high molecular weights of emulsion polymerization (11). In 1945 the first recognized quaHtative theory of emulsion polymerization was presented (12). This mechanism for classic emulsion preparation was quantified (13) and the polymerization separated into three stages. 

Plate height is the constant of proportionality between the variance, cr2, of the band and the distance it has traveled, x. The name came from the theory of distillation in which separation could be performed in discrete stages called plates. Plate height is also called the height equivalent to a theoretical plate. Plate height is approximately the length of column required for one equilibration of solute between mobile and stationary phases. We explore this concept further in Box 23-2. The smaller the plate height, the narrower the bandwidth. 

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