Nonequilibrium zone spreading

The effective diffusion coefficient for nonequilibrium zone spreading, obtained by equating the last term of Eq. 10.36 to Eq. 10.37, is... 

The apparent dispersion coefficient in Equation 10.8 describes the zone spreading observed in linear chromatography. This phenomenon is mainly governed by axial dispersion in the mobile phase and by nonequilibrium effects (i.e., the consequence of a finite rate of mass transfer kinetics). The band spreading observed in preparative chromatography is far more extensive than it is in linear chromatography. It is predominantly caused by the consequences of the nonlinear thermodynamics, i.e., the concentration dependence of the velocity associated to each concentration. When the mass transfer kinetics is fast, the influence of the apparent axial dispersion is small or moderate and results in a mere correction to the band profile predicted by thermodynamics alone. 

We will look at the three variables that may cause zone spreading, that is, ordinary diffusion, eddy diffusion, and local nonequilibrium. Our approach to this discussion will be from the random walk theory, since the progress of solute molecules through a column may be viewed as a random process. 

Clearly, departures from equilibrium—along with the resultant zone spreading—will decrease as means are found to speed up equilibrium between velocity states. One measure of equilibration time is the time defined in Section 9.4 as teq, equivalent to the transfer or exchange time between fast- and slow-velocity states. Time teq must always be minimized this conclusion is seen to follow from either random-walk theory or nonequilibrium theory. These two theories simply represent alternate conceptual approaches to the same band-broadening phenomenon. Thus the plate height from Eqs. 9.12 and 9.17 may be considered to represent simultaneously both nonequilibrium processes and random-walk effects. 

The above phenomena have been incorporated into a theoretical approach which explicitly associates zone spreading with flow velocity and the rates of various equilibration processes. This is the generalized nonequilibrium theory developed by the author [5]. While the theoretical details are too lengthy to develop here, some semi-quantitative reasoning can be used to understand the nature of nonequilibrium-induced zone spreading and the parameters that control it. 

In the pores of the particles the mobile phase is stagnant, so that the contribution to zone spreading due to nonequilibrium in this portion of the mobile phase differs from that due to nonequilibrium in the flowing mobile phase. In the case that the particles are of spherical shape it holds [21] that... 

Several dispersive processes contribute to zone broadening longitudinal diffusion, nonequilibrium and relaxation processes, spreading due to the external parts of the whole separation system, such as the injector, detector, connecting capillaries, and so forth. It has theoretically been found [2] that the resulting efficiency of the FFF, characterized by the height equivalent to a theoretical plate, can very accurately be described by... 

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