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Curves Relating (H) against (u) for Different Coiled Tubes
MOBILE PHASE! 5% ETHYL ACETATE in n-HEXANE
solute: benzyl acetate
However, at high velocities the effective value of the diffusivity of the solute dramatically increases as a result of induced radial flow, eventually reducing the resistance to mass transfer factor to virtually zero. This results in a corresponding dramatic reduction in the value of (H). Finally, at very high velocities, the greatly reduced longitudinal diffusion effect again dominates. At this point, the value of (H) is very small and, in fact, decreases even further as the mobile phase velocity is further increased.
The lew dispersion serpentine tube developed by Katz et ç! (10) was an alternative approach to the coiled tube and was designed to increase secondary flow by actually reversing the direction of flow at each serpentine bend. A diagram of a serpentine tube is shown in figure 3. In fact, the serpentine tubing shown in figure 3 was designed to be an interface
between a liquid chromatograph and an Atomic Adsorption Spectrometer. The serpentine tube is encased in an outer sheath to protect the tube and provide some rigidity.
The Low Dispersion Serpentine Tube
Dimensions : (r), (internal), 0.0127 cm (0.010 in I. D.)
(r), (external), 0.025 cm (0.020 in 0. D.)
(L), length (linear) 42.5 cm.
(1), length (coil) 38.5cm
(s), (serpentine amplitude) 0.05cm.
Graphs of Peak Variance against Flow Rate for Coiled and Serpentine Tubes
Flow Rat* (ml/mln)
A graph relating the variance per unit length of the tube (H) against flow rate is shown in figure 4, for a serpentine tube having the dimensions given in figure 3
The flow rate is employed as the independent variable, an alternative to the more usual linear velocity, as the flow rate is defined by the column with which the low dispersion tubing is to be used. It will be shown in due course that the column flow rate is independently defined by the nature of the separation that is to be achieved by the column. It is seen that a similar curve is obtained for the serpentine tube, as that for the coiled tube, but the the maximum value of (H) is reached at a much lower flow rate than that with the coiled tube. Furthermore, the variance remains more or less constant over a wide range of flow rates that encompass those usually employed in normal LC separations.
Graphs of Peak Variance against Flow Rate for a Straight and
Flow Rat* (ml/mln)
It is now interesting to compare the dispersion characteristics of a straight tube with that of a serpentine tube. The variances of a straight tube and serpentine tube are plotted against flow rate in figure 5. The values of the variance for the straight tube were calculated from the Golay equation It is clearly seen that the dispersion resulting from the serpentine tube is drastically reduced in comparison with the straight tube. According to the graph, the numerical value of the peak variance per unit length for the serpentine tube (.010 in I. D.) is 0.05ö12/ñò and consequently a tube 10 cm
would contribute a variance of 0.5|i 12. in contrast, the dispersion of a straight tube of the same same internal diameter and only one centimeter in linear length would be 5.5|i I2, which is an order of magnitude larger.
Low dispersion connecting tubes are still not in common use in LC equipment today although, at least one manufacturer provides serpentine tubing as a standard column/detector connection in a combined sample valve /column/detector system. Low dispersion tubing has a another feature that, in fact, could be anticipated from its principle of operation. The secondary flow, that results from its serpentine form, also greatly improves its thermal conducting properties and thus, serpentine tubes can be used as highly efficient heat exchangers. As a consequence, another instrument manufacturer utilizes serpentine tubing as a heat exchanger between a thermostating medium and the Inlet tube carrying mobile phase to the column. It was found that only a few centimeters of serpentine tubing were necessary to achieve complete thermal equilibrium between the thermostating medium and the mobile phase.
Dispersion in column frits was originally thought to be large and thus, made a significant contribution to the overall extra column variance. It was not until the introduction of low-dispersion unions that it was found that most of the dispersion that was thought to occur in the frits, actually occurred in the unions that contained the frits. Scott and Simpson (11) measured the dispersion that occurred in some commercially available column frits and demonstrated that their contribution to dispersion to be insignificant compared with other sources of extra column dispersion.
Dispersion In the Detecting Cell
Dispersion that takes place in detector cells can make a large contribution to the overall extra column dispersion of a chromatographic system. This is because the detecting cell must have a significant volume (which in some cases may be quite large) in order that the detector may have adequate sensitivity. The dispersion that takes place in a detector cell also results from the parabolic velocity profile that occurs in all tubular fluid conduits However, due to the fact that the aspect ratio of the cell (length/radius) is relatively small the simple Golay equation does not accurately describe the dispersion that takes place. Atwood and Golay, (12), examined the dispersion that takes place in tubes of small aspect ratios. If (n) is the number of