A modeling method based on incomplete mixed cells in counter-current chromatography: Interphase mass transfer ratio

Complex mass transfer processes are highly involved in the performance of counter-current chromatography (CCC), so profound exploration should be conducted to improve the overall performance. To more accurately estimate the interphase mass transfer efficiency in the elution process, this study proposes an incomplete mixed cell model by linking layering-mixing-layering behavior and wave-like mixing. With the model, we proposed a fast estimation algorithm for interphase mass transfer ratio (IMTR), which can independently reflect the magnitude of the interphase mass transfer efficiency. The experimental results show that the IMTR of all samples was relatively small, with an average value of not >10 % under different operating conditions. This indicates that the low column efficiency of CCC may be mainly due to the low efficiency of interphase mass transfer. In addition, by analyzing the influencing factors of IMTR, it is found that IMTR is positively correlated with the number of theoretical plates and the retention of stationary phase (S_f), but negatively correlated with the number of incomplete mixing cells (n). Therefore, in the study of column efficiency optimization, we recommend that the distribution ratio, S_f, and n should remain unchanged in control experiments to ensure that IMTR directly reflects the effect on interphase mass transfer efficiency. This study further completes the evaluation index of the CCC column efficiency, revealing the underlying mechanisms of IMTR on column efficiency and providing a theoretical foundation for future research on high-efficiency CCC.