Variance of a zone migrating in a non-uniform time-invariant linear medium

Abstract

A general model describing the evolution (expansion and contraction) of a zone migrating in a non-uniform (coordinate-dependent) chromatographic medium was developed. Equations for the spatial and temporal rates of change of variance of a zone were derived starting from the basic principle of mass balance in convective diffusion in a one-dimensional non-uniform medium. Also, the distinction between local and average values of many important quantities describing the evolution of a zone in a non-uniform medium such as velocity of a zone, plate height, chromatographic efficiency and was re-examined. It was shown that under certain conditions covering all practically important cases the chromatographic efficiency of a non-uniform medium cannot exceed that of a corresponding uniform medium. The study also produced unexpected results. It became apparent that a gradient of diffusivity affected the velocity of migration of an analyte in a column, and part of dispersion-related zone broadening could be recovered. It also became apparent that previous approaches for dealing with non-uniformity depended on unknown implicit conditions. Typically, these conditions were not satisfied in the cases considered. For example, many classical results deemed to be exact values must be viewed only as approximations. Hence, the known pressure correction factor for plate height in capillary gas chromatography with ideal gases is only an approximation to a still unknown correct value.