•UV-CD dual detector setup was used to provide more informative data for the use of inverse method.•Ibuprofen adsorption on Chiralcel OD column exhibits non-Langmuirian features.•TD model parameters and true inlet profiles were pre-determined.•Binary quadratic model and Moreau model with inflection points were investigated and the former gave better fits.•Quadratic model parameters were stepwisely determined by fitting elution profiles of both S- and racemic ibuprofens.Competitive adsorption isotherm of ibuprofen enantiomers on Chiralcel OD stationary phase at 298 K was determined by the application of inverse method. Transport dispersive (TD) chromatography model was used to describe mass balances of the enatiomers. Axial dispersion and mass transfer coefficients were estimated from a series of linear pulse experiments. It was found that the overloaded elution profile of total concentration of racemic ibuprofen cannot be satisfactorily fitted by substituting bi-Langmuir model, the most widely used isotherm model for enantiomers, into TD model and tuning the isotherm parameters. UV–CD dual detector setup was then applied to obtain the individual overloaded elution profiles of both enantiomers. The more informative experimental data revealed non-Langmuirian adsorption behavior of ibuprofen enantiomers on chiralcel OD stationary phase. Two analytical binary isotherm models, both accounting for adsorbate–adsorbate interactions and having the feature of inflection points, were then evaluated. A comparison between quadratic model and Moreau model showed that the former gives better fitting results. The six parameters involved in quadratic model were determined stepwisely. Three of them were first obtained by fitting overloaded elution profiles of S-ibuprofen. The other three were then acquired by fitting overloaded elution profiles of both enantiomers recorded by UV–CD dual detector for racemic ibuprofen. A further attempt was also made at reducing the number of quadratic model parameters.