Analysis of the Ideal Model for a Single Component in Preparative Gradient Elution Chromatography

The analytical solutions of the ideal model of chromatography for a single component were studied by using the
method of characteristics for solving partial differential
equations. By assuming that the mobile-phase gradient
entering the column is not affected by any sorption of
mobile-phase solvents on the column, we demonstrated
that the stationary-phase concentration of the component
is kept constant along the characteristic curve irrespective
of the isotherm and gradient profile used. By using this
property and assuming a Langmiur isotherm, we also
calculated the band profiles for single linear, stepwise,
and ladderlike gradients, respectively. These band profiles
were compared with those computed by using the finite-difference method. The results were found to be in good
agreement.