Note on the problem of considering the presence of wall in the modeling of chromatographic columns

The development of modern chromatography, in addition to improving and creating new experimental techniques, also includes the progress of precise and robust mathematical models and fast and reliable numerical methods enabling their solution. Accurate mathematical models combined with effective numerical techniques enable prediction of the behavior of chromatographic columns in various operating conditions. In a series of recent works Qamar et al. proposed a number of effective numerical solutions that provide profiles of concentrations and outlet temperatures also in non-isothermal conditions, requiring the application of a heat transport model in the chromatographic system modeling. However, to simplify the solutions, the authors did not take into account the presence of an important object for heat transport, which is the column wall. In our work a mathematical model of the column taking into account the presence of wall is proposed. The model is solved for a number of selected typical cases of chromatography for a variable conditions of: column diameter, solute inlet concentration, column wall material and thermal effects of the adsorption process. Based on the obtained results, the column operating conditions were indicated in which the neglecting of the column wall presence is acceptable (analytical conditions) and column wall presence in the model cannot be omitted.