I have a question related with the determination of the mass transfer coefficient for the transport-dispersive model in chromatography.
According to what I read in the book of Guiochon (Fundamentals of Preparative and Nonlinear Chromatography), for the solid linear driving force model, one has:
dq/dt = km*(q* - q)
and km is related to the film and pore mass transfer resistances through:
F/(k0*km) = dp/(6*kf) + dp^2/(60*Dp)
where F is the phase ratio, k0 the retention factor for linear conditions, dp the particle diameter and Dp the pore diffusion coefficient of the molecule. This equation was obtained equaling the plate equation for the transport-dispersive model to the general rate model.
However, in the book "Preparative Chromatography" edited by Henner Schmidt-Traub:
dq/dt = k,eff * 3/rp * (q*-q)
and the effective mass transfer coefficient is given by:
1/k,eff = rp/(5*ep*Dp) + 1/k_film
where rp is the particle radius, ep the particle porosity and k_film the external mass transfer coefficient.
There is an important difference here, since one is depending on the retention factor k0 and the other not. Do you know why this difference?
I think it depends on the granularity you want to capture in your model. The equation from Guiochon's book you referred compares the lumped mass-transfer kinetics with an equivalent expression from general rate model for linear chromatography. As GRM captures molecule retention even within the pore structure, naturally it appears in the lumped form. The other equation you mentioned ignores these details and considers the transport phenomena as the main rate limiting factor.
At the end of the day, it depends on how accurately you want to predict the elution profiles and whether it's worth it. As one of the main purpose is to employ these models in optimization studies, one tries to keep it simple while sacrificing the details. That's why the simplistic ED model is so popular. That's what my take on this would be!
- Badges
- Science method