The Optimum Column Length

The equation for the column length is give in chapter 13, equation (14) and is reproduced as follows. 

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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. 

Substituting the optimum value for the particle diameter from equation (18) in equation (13) the optimum column length can be obtained, 

Equation (19) shows that the optimum column length is inversely proportional to the third power of the function (ot-1) and thus, will increase very rapidly with the difficulty of the separation It is also seen that the length is inversely proportional to the square root of the available inlet pressure and, consequently, has a similar sensitivity to pressure as the optimum column radius. 

A graph relating optimum column length to the separation ratio of the critical pair for inlet pressures of 2000, 4000, and 6000 p.s.i. is shown in figure (2). 

Graph of Log. Optimum Column Length against Separation Ratio 

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It follows that knowing the optimum particle diameter, the optimum column length can also be identified. It must be emphasized that this optimizing procedure... 

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

It should be pointed out that equation (13) does not the optimum column length as the optimum particle identified. 

It is seen from figure 2 that, operating at an inlet pressure of only l p.s.i, the optimum column length varies from about 15 meters for the separation of solute pairs having a separation ratio of 1.01 to only 2cm for solutes having a separation ratio of 1.12, At the other extreme of pressure 1000 p.s.i., the column length varies from about 65 cm for a separation ratio of... 

Employing Equation (3) and the data given in table 1, the optimum column length was calculated for the preparative separation of a solute where the separation ratio of the critical pair ranged from 1.01 to 1.50, again at inlet pressures of 1,10,100,1,000 and 10,000 p.s.i. The results obtained are shown in figure 2... 

It is seen from figure 2 that the optimum column length ranges from over 500 meters to a fraction of a millimeter. It is also obvious that there must be further limitations placed on the design of the column to ensure its practical use. A preparative column less than 5 cm in length would be very difficult to pack as would a preparative column that had a length greater... 

The optimum column length, 2/ The optimum column radius. 

In summary, increasing the selected particle size requires an increased column length with no change in linear velocity to have sufficient plates for the separation. Since the required plate count decreases, the cycle time increases and the cost/g increases. The use of the optimum d /L provides a simple way to relate the selected particle size to the optimum column length. 

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