Numerical solution of the complete mass balance equation in chromatography

A new approach to simulate the movement of bands through a chromatographic column is presented. Similar to the Craig distribution model, the mass balance equation is divided into two equations describing two successive processes. The first equation includes two effects: solute diffusion in the mobile phase and migration of the solute band with the mobile phase. The second equation deals with the distribution of the solute between phases, i.e., the adsorption isotherm. The partial differential equations are integrated numerically over time and space using two methods. The first approach is a finite difference method. In the second approach, the propagation operator is expanded in a Chebyshev series, where large time steps can be used. The rate of adsorption and desorption is determined by the size of the time increment. By varying the size of the time step, it is possible to study kinetic effects. The influences of sample size, injection width, rate of mass transfer, and mobile phase velocity on the elution profile were studied. Simulations using the modified Craig approach with either of the two numerical procedures showed that the solutes behaved in the chromatographically expected manner. Moreover, with linear adsorption isotherms, direct relationships between HETP, as well as retention times, and experimental parameters could be established.