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Low Dispersion Connecting Tubes
It is obvious that the ideal situation where the sample valve and the detector sensor cell is coupled directly to the column is virtually impossible in practice and thus, a connecting system that provided little or no dispersion would be highly desirable. The dispersion in simple open tubes results from the parabolic velocity profile that exists in such tubes causing the solute contained in the mobile phase close to the wall to move very slowly and that at the center to move at the maximum velocity. This effect causes the band dispersion that is described by the Golay equation, in order to reduce this dispersion, the parabolic velocity profile of the fluid flowing through the tube must be disrupted to allow rapid radial mixing. The parabolic velocity profile can be disturbed, and secondary flow introduced, into the tube, by deforming its regular geometry.
The dispersion in geometrically deformed tubes (squeezed, twisted and coiled ) has been extensively studied by Halasz (6, 7 and 8), and the effect of radial convection (secondary flow) on the dispersion introduced in tightly
coiled tubes has been examined both theoretically and experimentally by Tijssen (9). The effect of secondary flow produced by employing serpentine shaped tubes has also been examined by Katz and Scott (10). It was found that the dispersion characteristics of serpentine tubing were far superior to those of coiled tubes. Furthermore, the dispersion that takes place in serpentine tubing is practically independent of the mobile phase linear velocity and consequently, such tubes can be used over a wide range of flow rates. The authors first examined the effect of secondary flow on band dispersion that took place in tubes of different radius coiled to different diameters. The theory of Tijssen (9), was successfully employed to qualitatively describe the relationship between the variance per unit length,
(H), and the mobile phase velocity.
For the sake of simplicity, the equations that Tijssen derived for radial dispersion in coiled tube are given in terms of conventional chromatographic terminology. At relatively low linear velocities (but not low relative to the optimum velocity for the tube) Tijssen derived the equation,
where (j) is a constant over a given velocity range, and the other symbols have the meaning previously ascribed to them
It is seen that the band variance is directly proportional to the square of the tube radius and the relationship is very similar to that derived by Golay (5) for a straight tube.
At high linear velocities, Tijssen deduced that,
where (b), is a constant for a given mobile phase and (f), is the ratio of the tube radius to the coil radius, and was given
the term the coii aspect ratio.
It can be seen from equation (8) that, at the higher linear mobile phase velocities, the value of (H) depends on (Dm) taken to the power of 0.14 and inversely dependent on the coil aspect ratio and the linear velocity. According to equations (7) and (8) at low velocities the band dispersion increases with (u), whereas at high velocities the band dispersion decreases with (u). It follows that a plot of (H) against (u) should exhibit a maximum at a certain value of (H). By combining equations (7) and (8), an equation can be obtained (5), that predicts the value of (u) at which (H) is a maximum, and is given by,
where (c) is a constant for a given solute and given mobile phase
The above equations were employed to investigate the effect of tube radius and coil aspect ratio on the onset of radial mixing in coiled tubes. The dimensions of the coiled tubes examined are given in Table 1 and the curves relating (H) and (u) in figure 2.
Table 1 Physical Dimensions of Coiled Tubes Examined
Tube (r)cm. (L)cm. r(coil)cm. (f) L(coil)cm.
1 0.019 365.8 0.5 0.038 18.5
2 0.020 365.0 0085 0.235 65 8
3 0.0127 998.0 0.0765 0.166 128.0
4 0.0127 337.5 0.0498 0 0255 73.7
It can be seen that at low linear velocities where radial mixing is still poor, the values of (H) increases as (u) increases. Furthermore, the dispersion in coiled tubes (I) and (2) of larger radii, is greater than that in tubes (3) and
(4) which had smaller radii. At high linear velocities, were radial mixing commences, the values of (H) decrease as (u) increases. As the the range of linear velocities is approached where radial mixing dominates the solute dispersion becomes independent of the linear velocity (u). It is also seen the maximum value of (H) for any particular coil occurs at different values of
(u) depending on the combined values of r and (ø). In general, it would seem that a high coil aspect ratio reduces both the maximum value of (H) and the value of (u) at which it occurs.
It Is interesting to note that, although the straight tube theory of Golay is not applied to coiled tubes, his equation can be employed to qualitatively explain the shape of the curves given in figure 2. At low values of the mobile phase velocity the effect of longitudinal diffusion dominates, but as the velocity tends to approach the optimum, the resistance to mass transfer term begins to increase and the value of (H) also rapidly increases.