The General Rate Model of Chromatography

The study of the lumped kinetic models shows that, as long as the equilibration kinetics is not very slow and the column efficiency exceeds 25 theoretical plates (a condition that is satisfied in all the cases of practical importance), the band profile is a Gaussian distribution. We can thus identify all independent sources of band broadening, calculate their individual contributions to the variance of the Gaussian distribution, and relate the column HTTP to the sum of these variances. The method is simple and efficient. It has been used successfully for over 40 years [29]. We may want a more rigorous approach. 

The mass balance equation in the mobile phase is written 

The term dq/dt in Eq. 6.58 is the rate of adsorption averaged over the particle. For a spherical particle it is given by dq/dt = 3/(RpMf) where Mp is the mass flux of solute from the bulk solution to the external surface of the particle. 

The boimdary condition at the outer surface of the particle is given by 

The differential mass balance of the solute inside the pores of an adsorbent particle is given by another partial differential equation  

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The general rate model of chromatography is the most complex of all the models used in this field. In this model, it is assumed that the mobile phase percolates through the interstitial volume between stationary phase particles, diffusion takes place from this stream into the particles and inside the pores of the stationary phase particles, where the mobile phase is stagnant, and adsorption-desorption takes place between the stagnant mobile phase within the pores and the adsorbent surface. 

This set of equations (Eqs. 2.25 to 2.35) constitutes the general rate model of chromatography. 

Numerical Solution of The General Rate Model of Chromatography. 754... 

This set of equations constitutes the general rate model of chromatography. 

Many authors have described procedures for the calculation of numerical solutions of the general rate model of chromatography with a variety of initial and boundary conditions corresponding to practically all the modes of chromatography (with the notable exception of system peaks). Orthogonal collocation on finite elements seems to be the most popular approach for these calculations. 

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