The Minimum Column Length

The expression for the optimum column length is given by equation (30) in chapter 12 and is as follows. 

It is seen that the length (L) will increase as (l/(a-l)2) and, as (Hmin) increases linearly with the particle diameter, which also increases as the reciprocal of (a-l). 

The column length will actually increase as (l/(a-l)3). This means that the column length is extremely sensitive to the separation ratio of the critical pair and explains 

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It should be pointed out that equations (14) and (15) do not give an expression for the minimum column lengths, as the optimum particle diameter has yet to be identified. 

Thus, the minimum column length (L) will be given by... 

Lmin) is the minimum column length, and (e) is the fraction of the column occupied by the mobile phase. 

The minimum column length increases as the value of (a) is reduced and, at the... 

The minimum column length was calculated for a series of separation ratios using equation (19) and the results obtained are shown in Figure 14. 

Figure 14. Graph of the Log of the Minimum Column Length against the Separation Ratio of the Critical Pair...

It is seen that the minimum column length ranges from 100 meters to 2 or 3 mm. It should be pointed out at this time that the theory may not predict data accurately when the column lengths become less than a few centimeters. It is now of interest to calculate the corresponding analysis times. 

The equation is important in column design, for example, to achieve a given separation in the minimum column length and analysis time. Resolution is a function of the square root of N so large changes in N are required to have a marked effect. Efficiency may be improved by increasing column length but... 

Thus, the separation ratio that will be obtained for the solute pair can be calculated for any temperature. This equation will be used in chapter 5 to calculate the minimum column length necessary to complete the separation in the minimum time. 

D16. A column packed with gas-phase activated carbon is initially filled with clean air. At t = 0 a feed gas containing y = 0.0005 wt frac toluene in air is started. This feed continues until t = 10.0 hours at which time a feed that is y = 0.0015 wt frac toluene is introduced and continued throughout the remainder of the operation. The superficial velocity is always 15.0 cm/s. Find the minimum column length required to have a single shock wave exit the column. 

The minimum column length increases as the value of (a) is reduced and, at the same time, the optimum velocity also falls.This has a double effect on the analysis time and it can be shown that the analysis time increases as (l/(a-l)4). It is seen that, as the analysis time is a function of ((a-1)4), the range of analysis times is... 

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