Open Tubular Conduits

The dispersion that takes place in an open tube, as discussed in chapter 8, results from the parabolic velocity profile that occurs under conditions of Newtonian flow (i.e., when the velocity is significantly below that which produces turbulence). Under condition of Newtonian flow, the distribution of fluid velocity across the tube 

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The effect is much less when the fluid is a gas, where the solute diffusivity is high and the solute tends to diffuse rapidly across the tube and partially compensate for the nonlinear velocity profile. However, when the fluid is a liquid, the diffusivity is five orders of magnitude less and the dispersion proportionally larger. 

If u Dm/r, which will be true for all conditions except if open tubular columns are 

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Having established that a finite volume of sample causes peak dispersion and that it is highly desirable to limit that dispersion to a level that does not impair the performance of the column, the maximum sample volume that can be tolerated can be evaluated by employing the principle of the summation of variances. Let a volume (Vi) be injected onto a column. This sample volume (Vi) will be dispersed on the front of the column in the form of a rectangular distribution. The eluted peak will have an overall variance that consists of that produced by the column and other parts of the mobile phase conduit system plus that due to the dispersion from the finite sample volume. For convenience, the dispersion contributed by parts of the mobile phase system, other than the column (except for that from the finite sample volume), will be considered negligible. In most well-designed chromatographic systems, this will be true, particularly for well-packed GC and LC columns. However, for open tubular columns in GC, and possibly microbore columns in LC, where peak volumes can be extremely small, this may not necessarily be true, and other extra-column dispersion sources may need to be taken into account. It is now possible to apply the principle of the summation of variances to the effect of sample volume. 

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