HPLC Column Cross-Sectional Area and Scaling

Here is a simple formula to use when scaling up or down Internal Column Diameter to maintain retention values (under constant linear velocity). Flow rate must be adjusted to account for any changes made to the column's cross-sectional area. We usually refer to these types of changes as the "Scaling Factor". To determine the scaling factor, we need to know the internal column diameters of the two columns we are scaling from (actually, we need to know the radius, but once we have the diameter, we simply divide the diameter by 2 to obtain the radius). *In this discussion, changes in cross-sectional area are the only parameters we are concerned with as column length does not affect scaling.

• Scaling Factor = (S);
• Column #1 Radius =  (R1);
• Column #2 Radius =  (R2).

     S = R2² / R1²

Example #1: 250 x 4.60 mm column scaled down to a 250 x 2.10 mm column. 

          Answer = 0.208. 

• If the original flow rate was 1.000 mL/min, the the scaled down flow rate would be 0.208 of the original or 0.208 mL/min for the 2.10 mm ID column. *For practical use and application, we often use either 200 ul/min or 210 ul/min to simplify the value.

Example #2: 250 x 4.60 mm column scaled up to a 250 x 10.00 mm ID semi-prep column.

          Answer  = 4.726. 

• If the original flow rate used was 1.000 mL/min with the 4.60 mm ID column, then we would increase the flow rate to 4.726 mL/min on the 10.00 mm ID column to maintain the same relative velocity (and relative retention). *For practical use and application, we often use 5 mL/min to simplify (round off) the value. 

Notes:

1. Flow rate optimization should always be carried out by running a standard at different flow rates and plotting the plate height (N) vs the flow rate. Test flow rates that are slightly below the predicted linear velocity and up to 2 times higher than that rate to find and optimize the flow rate for your sample (it must be determined through experimentation for your specific method). 
    
2. HPLC Columns packed with sub 2 micron supports may have optimum flow rates 2 to 5 times more than the predicted std linear flow rate so actual testing is critical to determining the most efficient flow rate. I recommend optimizing the flow rate used with analysis methods which use any particles which are 2.5 microns or smaller in diameter.