Key parameters controlling the development of constant-pattern isotachic trains of two rare earth elements in...

Ligand-assisted displacement chromatography (LAD) has been developed for separating rare earth elements since the 1950's. Isotachic displacement trains, which are similar to those in conventional displacement chromatography, were reported previously. However, there has been no general theory delineating the conditions required to form constant-pattern displacement trains for non-ideal systems (or systems with significant mass transfer resistance). The constant-pattern state is critical for obtaining pure products with high yield and high productivity. Without theoretical guidance, all the previous studies found the constant-pattern state by experimental trial and error, which was time consuming and costly. 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.