  Chromatographic processes can be modeled by nonlinear, convection-dominated
partial differential equations, together with nonlinear relations: the
adsorption isotherms. In this paper we consider the nonlinear equilibrium
dispersive (ED) model with adsorption isotherms of Langmuir type. We show that
very efficient, fully conservative, numerical schemes can be designed for this
mode by exploiting the relation between the conserved variables of the model
and the physical concentrations of the multi-component mixtures. We show that
this relation is one to one and admits a smooth global inverse, which cannot be
given explicitly but can be easily computed by using a convenient root finder.
These results provide the necessary ingredients to implement fully conservative
numerical schemes for the model considered.
  Implicit-Explicit (IMEX) techniques can be used in the convection-dominated
regime in order to increase the efficiency of the numerical scheme. We propose
a second order IMEX scheme, combining an explicit
Weighted-Essentially-non-Oscillatory discretization of the convective fluxes
with an implicit treatment of the diffusive term, in order to illustrate the
numerical issues involved in the application of IMEX techniques to this model.
Through a series of numerical experiments, we show that the scheme provides
accurate numerical solutions which capture the sharp discontinuities present in
the chromatographic fronts, with the same stability restrictions as in the
purely hyperbolic case.
