In chapter I, the transient convective mass transfer in three dimensional rectangular channels in the presence of a transverse field is analyzed to include the time dependence of the convection and dispersion coefficients. The methodology of generalized dispersion theory is used to predict the breakthrough curves. The functions, $f_0$ and $f_1$, are determined by introducing a two-dimensional Strum-Liouville operator and this approach is used conveniently to generate a structurally neat analytical solution.
In the practical field-flow fractionation (FFF) systems, the elution time of the constituents is not long enough for the value of the asymptotic dispersion coefficient to be used to predict the breakthrough curves. It is suggested that the side wall effects on the axial dispersion can not be neglected and a dispersion equation with time dependent coefficients is appropriately describable of the practical FFF systems.
The approximate flow average concentration is obtained by using the resultant equation of the generalized dispersion theory. It is found that the large transverse Peclet number brings about the large difference between the breakthrough curves expressed in the flow average concentration and in the area average concentration used customarily in the past. Since the flow average concentration is measurable in real FFF system, the breakthrough curves should be expressed in that concentration when a comparison of theoretical predictions with experimental data is made.
The generalized dispersion theory generates the useful solution of the convective diffusion equation in the area average concentration, but technical difficulties limit the implied construction in nonarea averages. This problem is avoided by separating the construction of the solution of the convective diffusion equation from the construction of dispersion approximations thereto. The general procedure of De Gance and John is followed to evaluate the dispersion approximations of arbitrary order in the area average and the flow average concentration. It also follows that the second-order dispersion approximation is constructed for the two-dimensional dispersion in rectangular FFF channels. The full time dependence of the first three dispersion coefficients is investigated. In
chapter II, a new separation technique utilizing a slowly rotating annular open column with a transversely applied field is described. In this technique, the concept of a FFF is superimposed on the concept of a continuous annular chromatograph. In contrast to FFF using a rectangular channels, this rotating annular field-flow chromatograph (RAFFC) has no side wall effects on the solute dispersion. It has no peak broadening due to the lateral flow, even though the broadening is observed in a continuous free-film electrophoresis because of an electroosmotic flow. The resolution in the RAFFC with a continuous feed is not affected by the axial convective dispersion, which is a primary factor for the dispersion in FFF.
A mathematical model is used to describe the concentration profiles at the exit of a RAFFC. Dispersion approximations have been constructed on the basis of the flow average concentration and the area average concentration by applying the Hermite moment method instead of the generalized dispersion theory.
The effects of rotation rate, eluent velocity, column size and field strength are predicted to show how they affects the performance of the RAFFC system.
