The Monte Carlo Model of Nonlinear Chromatography

Dondi et al. developed a stochastic approach to nonlinear chromatography based on the Monte Carlo method [69]. The Monte Carlo method consists in simulating the migration of an ensemble of molecules through the chromatographic column that contains a finite number of adsorption sites. The random sequence of adsorption-desorption events is modeled at the molecular level with the stochastic terms and concepts discussed in Chapter 6, Section 6.5. 

The linear chromatographic process is modeled as a composite Poisson process a chain of exponentially distributed fly times, followed by exponentially distributed adsorption times are generated. When adsorbed, the molecule is stationary the mean adsorption time is t . When desorbed, the molecule travels with the velocity of the mobile phase the mean fly time—residence time between a desorption and the subsequent adsorption—in the mobile phase is t. The elution time of the molecule is recorded when it reaches the end of the colxunn after n adsorption-desorption events on the average. The distribution of the single molecule elution times gives the band profile. 

Two types of events are possible adsorption and desorption. To characterize 

Nonlinearity is taken into accormt by generating the adsorption time as a function of local coverage. For instance, in the case of Langmuir kinetics, the site coverage factor is either 1 or 0, depending on whether the site is free or already occupied. The molecule will stop and adsorb only if the site is free. 

Cavazzini et at. showed that the above Monte Carlo model of nonlinear chromatography is equivalent to the Thomas kinetic model of second order Langmuir kinetics [70]. The solution of the Thomas model for a Dirac impulse injection is given by Eq. 14.65. When the chromatographic process is modeled at the molecular level with the stochastic model, the Thomas model becomes [70]  

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