Modelling the simultaneous adsorption of two competing species

In this paper, we develop a mathematically consistent analytical framework to describe the simultaneous adsorption of two competing species in a packed column, accounting for adsorption, desorption and competitive replacement. Starting from previous work on the capture of a single species, we extend the analysis to a two-component system in which a stronger adsorbate can displace a weaker one while both compete for adsorption sites. The model yields simple closed-form expressions for the breakthrough curves in two distinct regions: a downstream region governed by single-species behaviour and an upstream competition region controlled by a replacement mechanism. For the specific class of systems studied — one-way competitive displacement with Langmuir kinetics on a single site type — the two-component model requires only a single additional fitting parameter beyond the single-component data. The analytical solutions are validated against numerical simulations of the full governing equations. Further validation against experimental data for several adsorbate–adsorbent systems demonstrates that the model captures key phenomena such as roll-up and breakthrough with high accuracy. The mathematical model provides a simple tool for interpreting experimental data and so predicting column performance and guiding the design of adsorption systems under realistic two component conditions.