Walking column

In this section, we will discuss two techniques that are used to obtain the resolution of a long column or a large column bank using only one or two columns. They are applied to separate a small number of compounds, usually two, that elute very closely to each other (low selectivity). One technique is called recycling the other technique is known as the walking column. 

Various mathematical concepts and techniques have been used to derive the functions that describe the different types of dispersion and to simplify further development of the rate theory two of these procedures will be discussed in some detail. The two processes are, firstly, the Random Walk Concept [1] which was introduced to the rate theory by Giddings [2] and, secondly, the mathematics of diffusion which is both critical in the study of dispersion due to longitudinal diffusion and that due to solute mass transfer between the two phases. The random walk model allows the relatively simple derivation of the variance contributions from two of the dispersion processes that occur in the column and, so, this model will be the first to be discussed. 

Equation (1) can be used in a general way to determine the variance resulting from the different dispersion processes that occur in an LC column. However, although the application of equation (1) to physical chemical processes may be simple, there is often a problem in identifying the average step and, sometimes, the total number of steps associated with the particular process being considered. To illustrate the use of the Random Walk model, equation (1) will be first applied to the problem of radial dispersion that occurs when a sample is placed on a packed LC column in the manner of Horne et al. [3]. 

This example of the use of the Random Walk model illustrates the procedure that must be followed to relate the variance of a random process to the step width and step frequency. The model will also be used to derive an expression for other dispersion processes that take place in a column. 

Equation (14), although derived from the approximate random walk theory, is rigorously correct and applies to heterogeneous surfaces containing wide variations in properties and to perfectly uniform surfaces. It can also be used as the starting point for the random walk treatment of diffusion controlled mass transfer similar to that which takes place in the stationary phase in GC and LC columns. 

The MSDS from the chemical manufacturer identifies hazards for entry in the spreadsheet in columns 8 and 10. This is performed for all chemicals that are associated with the process, if the analysis is hmited to a process, or for a plant. The spreadsheet may be filled out variously according to convenience and effectiveness. It is practically impossible to get all needed information from documentation alone. A plant walk-through is advised for viewing operating conditions as they exist, for interviewing operators about the risk concerns that they have, and about the operability of safety and mitigation systems. These results are entered into the spreadsheet. 

The hrst joke is a three-men joke. In table 1.2, thejoke itself is in the left-hand column, the moves are in the center column, and the sentences that accomplish the moves are in the right-hand column. Thejoke is told in six moves (or steps) thejoke setup actions 1,2, and 3 the punch-line setup and the punch-line delivery. The second joke is a variation of a guy-walks-into-a-bar joke (table 1.3). (We could not resist this joke because it pokes fun at incorrect punctuation.) The joke is told in seven moves thejoke setup, a four-step action/reaction sequence between the guy (panda) and the bartender, the punch-line setup, and the punchline delivery. In both examples, the sequencing of moves plays an important role in achieving the purpose of the jokes if the moves were sequenced differently (e.g., if the punch line were given hrst), the jokes would no longer be successful. Thus, the appropriate moves not only must be present but also must be presented in the correct order. 

To develop an HETP equation it is necessary to first identify the dispersion processes that occur in a column and then determine the variance that will result from each process per unit length of column. The sum of all these variances will be (H), the Height of the Theoretical Plate or the total variance per unit column length. There are a number of methods used to arrive at an expression for the variance resulting from each dispersion process and these can be obtained from the various references provided. However, as an example, the Random-Walk Model introduced by Giddings (5) will be employed here to illustrate the procedure.The theory of the Random-Walk processes itself can be found in any appropriate textbook on probability (6) and will not be given here but the consequential equation will be used. 

Sally puts up her hand. Stop I get the picture. She pauses as you both walk over to the window and watch the swollen sun collapse into a notch between the columns of the Capitol building. Beautiful The winter sun burns the columns to a golden brown, and torpid yellow-tinted clouds hang over the alabaster reflections. Soon it will be dark, and you should head home. 

We will look at the three variables that may cause zone spreading, that is, ordinary diffusion, eddy diffusion, and local nonequilibrium. Our approach to this discussion will be from the random walk theory, since the progress of solute molecules through a column may be viewed as a random process. 

This is a rather complete expression for the mobile phase random walk, giving, as desired, Hc as a function of dp9 Dm9 and u. While the w, and A, constants are unspecified, they should be the same for equally well packed columns, for all mobile phases (gases and liquids), and for all solutes. The universality of this equation will be put to good use in the following chapter. 

Several approximate forms of Eq. 12.1 can be used for packed columns. Over a limited low-velocity range where diffusion controls the mobile phase random walk, the terms containing drop out and Eq. 12.1 reduces to... 

Two basic components of plate height in packed columns are Hf and HD, given by Eqs. 11.23 and 11.28, respectively. When these two terms are equal—which occurs at the specific velocity v c = AICm—we are at the transition point between a flow-controlled and diffusion-controlled random walk. (This transition, as it turns out, occurs near the minimum of each of the plate height curves shown in Figure 12.2.) The velocity u is a fundamental parameter characterizing every packed column system. Its value can be expressed by (see Eqs. 11.23 and 11.28)... 

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