Errors involved in the existing B-term expressions for the longitudinal diffusion in fully porous chromatographic media

• Published in: Journal of Chromatography A Vol. 1188; no. 2; pp. 171 - 188
• Main Authors: Desmet, G., Broeckhoven, K., De Smet, J., Deridder, S., Baron, G.V., Gzil, P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 2008; Amsterdam; New York: Elsevier
• Subjects: Composite media; Computational fluid dynamics; Effective medium theory; Obstruction factor; Peak parking; Pillar array column; Surface diffusion; Composite media; Computational fluid dynamics; Effective medium theory; Surface diffusion; Peak parking; Pillar array column; Obstruction factor
• ISSN: 0021-9673
• DOI: 10.1016/j.chroma.2008.02.018

Numerically solving the effective diffusion in a simplified representation of a chromatographic bed, it was found that the B-term expressions that have up to now been used in the literature, and which can all be reduced to either D eff = ( γ m D m + k′ γ s D s)/(1 + k′) or D eff = ( γ me D m + k″ D part)/(1 + k″), can no longer be considered to be unconditionally valid. This could be demonstrated by showing that the simulated diffusion data are in agreement with the mathematically sound effective medium theory (EMT), whereas the B-term expressions used up to now in literature are in conflict with the EMT, a theory that is widely accepted in all other fields of science. It is also shown that the use of the existing B-term expressions can lead to very large measurement errors (up to a 100% and more) for the determination of the stationary phase diffusion coefficient γ s D s from peak parking experiments. The representation of the B-term diffusion should in the future hence be based on the D eff expressions that can be derived from the EMT. These are physically sound and are also more accurate than the classical B-term expressions used up to now.