Plate height nonequilibrium

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. 

We imagine molecules hopping erratically between mobile and stationary phases. The hops represent random steps forward and backward with respect to the zone center. Equation 9.12 shows that plate height H for such a process is proportional to transfer or equilibration time teqi in agreement with our conclusions based on nonequilibrium considerations. 

Recall that the plate height corresponding to an effective diffusion process is given by Eq. 5.38, H = 2DTIW. The nonequilibrium contribution to H is obtained by replacing the total diffusion coefficient DT by the nonequilibrium contribution Dn and, of course, general displacement velocity W by zone velocity Rv. Thus with the help of Eq. 10.38, we get... 

The last two equations show that the nonequilibrium plate height (corresponding to the rate of outward diffusion of the zone) is directly propor-... 

Calculate the plate height contributed by sorption-desorption mass transfer (nonequilibrium) through a uniform liquid layer (configuration factor q = 2/3) of thickness 1.0 x 10 3 cm coated on the inside of an open tubular (capillary) column. The gas velocity v is 10 cm/s. The solute retention ratio is 0.10 and its diffusion coefficient Ds through the stationary liquid is 1.0 x 10 5 cm2/s. 

Figure 12.4. Plate height versus flow velocity plot for negligible stationary phase nonequilibrium effects (bottom curve) and for dominant stationary phase effects (top).

Generalized Nonequilibrium Theory of Plate Height in Large Scale Gas Chromatography, J. C. Giddings, J. Gas Chromatogr., 1, 38 (1963). 

With the proper technique [5], such plots are linear and the y intercept is equivalent to Hp. Alternatively, Hp can be obtained by subtracting the nonequilibrium bandbroadening contribution to plate height (Hj ) from the experimentally measured value. Methods for calculating... 

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 ... 

In Eq. 15, R[ accounts for the zone broadening caused by the longitudinal diffusion and is expressed by 2D/ R). This effect can be neglected at usual FFF operating conditions. The second term, is the nonequilibrium effect on the plate height. 

One of the methods to evaluate the nonequilibrium effect is the comparison of the apparent polydispersity converted from the plate height due to that effect. For this purpose, the ratio ([Pg.297]

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... 

The value of N calculated from one peak in a chromatogram should be the same for each of the other peaks. Another way to characterize the efficiency of a column is to calculate the quantity N/L, called H, the height equivalent per equivalent plate (L is the length of the column). N and H will depend on the number of equilibrium stages in the process, as we have seen above in our discussion of CCD. The actual band widths observed are always larger than ideal because of the nonequilibrium but reproducible processes accompanying mass transfer, such as diffusion of various sorts. 

Except for the short introductory Section 1.3. to this point the entire analysis of separation processes has been equilibrium based. Effects of nonequilibrium operation have been lunped into either a stage efficiency f Sections 4.11.10.2.12.5. and 13.51 or to the height equivalent of a theoretical plate (HETP Sections 10.9 and 10.111. We must move beyond an equilibrium analysis if we want to be able to predict values of the stage efficiency and the HETP fChapter 161. to study membrane separators fChapter 171. or to study sorption separations fChapter 181. For all of these situations, we must look at the mass transfer occurring in the separator. This chapter presents the fundamentals of diffusion and mass transfer in sufficient detail so that the analysis in the remaining chapters is understandable. Additional information on mass transfer is presented as needed in Chapters 16 to 18. If you have already studied mass transfer and diffusion, most, but probably not all, of this chapter will be a review, and you will not have to spend much time studying the material. 

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