The vertical scale, corresponding to effluent concentration in our situation, does not affect calculation of H or N.
When time is expressed as in Figure 1, the value of s is independent of both the mass of pulse fed (if the effluent curve is Gaussian) and the column diameter. Moreover the mean
residence time equals the time at which the maximum concentration, tmax, occurs. The number of plates is expressed in Equation (5).
The Short-cut Method and the Péclet Number
If effluent curves were always Gaussian, then calculating plate numbers and heights would be a simple process. There would,
of course, be the nagging problem of determining standard deviations from experimental data, and it has been a common practice
to use short-cut methods for this purpose. We discuss a set recommended by the American Society for Testing and Materials.4 Equation (6) from the ASTM is a variant of Equation (5).
If the peak is Gaussian, then the standard deviation is the half-width at 60.7% of peak height and it reduces to Equation
Unfortunately no chromatographic peaks are truly Gaussian, and this is the problem we must deal with next. Figure 2 shows
simulated solute concentrations along a column using L as the distance along the column from inlet.5 It makes evident that solute profiles within a column are functions of percolation velocity, adsorbent particle diameters
and solute diffusivity as expressed via a dimensionless group known as the Péclet number.
Both peaks are left-skewed, but the magnitude of skewness increases with Pé, or inversely with diffusivity. The primary reason for this is intra-particle diffusional transients, and the degree of skewness
depends primarily on a ratio of time constants as in Equation (9).
Anurag S. Rathore, PhD, is a consultant, Biotech CMC Issues, and a member of the faculty in the department of chemical engineering at the Indian Institute of Technology. Rathore is also a member of BioPharm International's Editorial Advisory Board.
Articles by Anurag S. Rathore, PhD
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