Migration and elution equations in gradient liquid chromatography.

What is known in the literature as the fundamental equation for gradient elution (FEGE) was previously proven only for conventional gradient LC - uniform (the same at any distance from the inlet) static (fixed in time) solvent velocity (um) in a column of uniform and static internal structure, cross-section and thermodynamic properties. A published alternative to the FEGE - the general migration equation - is valid for any column-based linear chromatography (GC, LC, SFC etc.). It allows one to theoretically or numerically predict a solute migration time to any location along the column. Starting from that general equation, several migration equations in gradient LC under different operational conditions including non-uniform non-static um, Neue-Kuss retention model and others have been developed in this report. It has been shown that the conditions of validity of the FEGE can be expanded to include non-uniform um. On the other hand, the FEGE is not valid for other unconventional operations of LC including gradient LC with dynamic (changing in time) um. This implies that FEGE cannot be applied to, e.g., gradient LC operating at constant pressure where, due to the change in solvent composition, the solvent viscosity changes causing the change in um with time. Applications of newly developed equations to other unconventional operations of gradient LC were also considered. Several new time parameters of the mobile phase flow were identified, interpreted, and evaluated.