Key parameters controlling the development of constant-pattern isotachic trains of two rare earth elements in ligand-assisted displacement chromatography

In this study, an efficient rate model and simulations of LAD were developed and verified with experimental data for non-ideal systems. Verified simulations were used to understand the mechanisms of separations and the transition from the transient state to the constant-pattern state. The key dimensionless factors affecting the transition for binary non-ideal systems were identified. Dimensionless groups were developed to reduce the number of variables. Simulations were used to find the transition points fromthe transient state to the constant-pattern state, which indicates the minimum dimensionless column lengths in the multi-parameter space. Strategic combination of the key dimensionless groups allows the minimum dimensionless column lengths to correlate with the combined groups in a two-dimensional diagram (or a map). The correlation curve divides the multi-dimensional space into the transient region and the constant-pattern region. The correlation was further verified with five sets of experiments. It can be used to find, without process simulations or experiments, the minimum column lengths for developing constant-pattern isotachic trains for non-ideal systems, which is useful for designing efficient ligand-assisted displacement chromatography at any scale.