Eddy diffusion, zone broadening

Equations 2.61 and 2.65 account for the effect of ordinary and eddy diffusion in the zone broadening process. Now we need to express nonequilibrium effects which are concerned with the time the solute molecules spend in the two phases. Let us define a few more terms in order to set up some mathematical relation ships ... 

FIGURE 16 Schematic representation of the origins of zone-broadening behavior and mass transfer effects of a polypeptide or protein due to Brownian motion, eddy diffusion, mobile phase mass transfer, stagnant fluid mass transfer, and stationary-phase interaction transfer as the polypeptide or protein migrated through a column packed with porous particles of an interactive HPLC sorbent. 

Peak broadening is a result of ordinary diffusion, eddy diffusion (due to flow along longer or shorter paths in packed columns), and local non-equilibrium. The eddy diffusion is absent in capillary columns. The zone spreading due to the ordinary diffusion od can be expressed by the formula ... 

Resolution and separations in SEC are described by the van Deemter equation (Eq. 14.7). The main contributions to zone broadening, in order of importance, are as follows. The first factor involves the kinetics of partitioning between the mobile phase and the gel there is a limited rate at which equilibrium can be established, and this rate depends on the solute s diffusion coefficient. Second, differences in the lengths of different stream paths in the packed bed of irregularly shaped particles result in eddy diffusion with an ideally packed column, this is not a significant problem, but in practice, eddy diffusion may be significant. Finally, longitudinal... 

The van Deemter rate theory identified three major factors that cause band or zone broadening during the chromatographic process the eddy diffusion or the multi-path effect (A-term), longitudinal diffusion or molecular diffusion of the analyte molecules (B-term), and resistance to mass transfer in the stationary phase (C-term). The broadening of a zone was expressed in terms of the plate height, H, and was described as a function of the average linear velocity of the mobile phase, u. 

Skoog and West describe three causes of zone broadening eddy diffusion, longitudinal diffusion, and nonequilibrium mass transfer [1], The Van Deemter equation was developed to relate the flow rate and plate height ... 

Obviously, the aim is for a chromatographic separation in which peak width is narrow relative to the time of elution (wi/Vr is minimized), i.e., the number of theoretical plates is maximized. There are three main factors that give rise to band broadening (1) multiple path effect (eddy diffusion), (2) axial (longitudinal) diffusion, and (3) mass transfer—slow transfer/equilibration between mobile and stationary zones. 

The terms 1/A,- and HC iV describe the effect of the eddy diffusion and nonequilibrium in the mobile phase, respectively. The contribution to zone broadening due to the eddy diffusion is dominating at high flow rates. The importance of both these terms is related with the particle size distribution (PSD) and with the homogeneity of the column packing or, in other words, with the relative differences in the flow... 

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