Capillary Chromatography - Capillary Column Theory 3

From Poiseules equation,

 

Now,

 

Thus,

 

Rearranging,

 

Taking helium as the carrier gas (g(helium)) = 194 x 10-6 g cm-1 sec-1 room temperature and (Po) = 1.01 x 104 dynes/sq. cm.

 

Then, (3)

 

Employing equations (2) and (3) it is now possible to calculate how the ratio of the two mass transfer coefficients changes with the mobile phase exit velocity (uo) for columns of different length and radii. Two columns were examined, one 30 m long and 100 mm I.D. and the other 15 m long and 300 mm I.D. Each column was examined for solutes having capacity ratios of 1, 5, and 20 (i.e. k=1, 5 and 20). Helium was assumed to be the carrier gas and the diffusivity of the solute in the gas phase (Dm) taken as 0. 4 sq. cm/sec. and that in the stationary phase (Ds), 2.5 x 10-5 sq. cm/sec.. The film thickness (df) was taken in all examples to be a mean value of 0.2 mm. The results obtained are shown as curves relating the log(mass transfer ratio) to the mobile phase exit velocity for each of the four capacity ratio (k') values in figure 15.