Flow velocity optimum

The relationship between column length and particle size is L = NH = Nhdp = 10,000 x 2 x 1.5 x lO cm = 3 cm. Assuming the column has a reduced plate number of 2 at its optimum flow velocity, v = vopt= 1, then a 3 cm column could produce 10,000 plates when packed with 1.5 /.mi particles. 

This equation indicates that the particle size, dp, is the main contributor to the H value. The smaller the particles, the higher the theoretical plate number. The optimum condition is obtained by the relationship between the theoretical plate height and the flow velocity. 

In liquid chromatography, the diffusion rates are slower than that in gas chromatography, and the values of DM and D are very small therefore, the minimum H value is obtained at a low flow rate, as shown by curve E in Figure 5.6. The value of H increases slowly at higher flow rates in liquid chromatography. An experimental result is shown in Figure 5.7. The HETP was minimal at a certain flow rate, and the measured optimum value was less than 10 pm for this column. The optimum flow rate was about 0.9 ml min - corresponding to a linear flow velocity of about 55 mm min -. ... 

It is important to note that, at least for neutral compounds, temperature has only a small effect on efficiency when the column is operated at its optimum flow velocity. Above the optimum velocity, temperature has a beneficial effect on efficiency, whereas below the optimum velocity, increased solute diffusion has a relatively large negative effect on efficiency [32,82,83]. 

Consequently the use of very flne particles, liner than thuiSe presently available with a reasonably good size distribution would pernitt significant improvement in the analysis of high molecular weight solutes which have low diffusion coefficients and for which the optimum reduced velocity, vq. is attained at a very low value of the actual flow velocity, in columns packed with particles having the usual size ... 

The results in Figs. 3 and 4 shows that upon decreasing thd flow velocity below its optimum value, vc, the plate height increases n )derately at first. In difficult cases it it thus possible to achieve high olumn efficiencies with a given chromatographic system even if the upi>er pressure limit of the instrument is not sufficient to operate the column at its maximum efficiency. The price to pay for the high efficiency is ah increase in analysis time. 

There is another way to look at the problem, however. Most analysts would like to have a simple column to solve separation firoblems in general. What colunm length and particle size would be optimum for such a purpose A 30-cm-long column packed well with 10-/Am particles, as now commercially available, can generate a maximum of 10,000 plates for a solute having A = 3 and = 2 x 10 cm /sec at an optimum flow velocity of 0.04 cm/sec v 2). Under these conditions the analysis time is 50 min (3.3 plates/sec) and the pressure is 6 atm with an eluent having 1) = 0.5 cP. The column is suitable to attain difficult separations which require 10 plates, but it is slow. If we raise the pressure to 30 atm, which still is relatively low, (he analysis (line and efficiency afe reduced to 10... 

Many chromatographic systems are run at or above the optimum flow velocity vopt to achieve faster separation. In this case Eq. 12.57 is no longer valid for plate height. However, for purposes of the present discussion, in which we are seeking ways to reduce plate height but not time, we will assume that the first step, velocity optimization, has been taken, and that Eq. 12.57 is applicable. 

The analytical separation was obtained at low flow velocity (0.2 cm/sec) and in the isocratic mode to optimize resolution. Absorbance detectors set at 245 and 280nm respectively, were used in series for effluent monitoring. 215nm detection, though optimum for the cannabinoids, was precluded due to co-elution of en-... 

There are two different philosophies about the optimum channel design for focusing-S-FFF reported in the literature. Whereas Janca et al. utilized channels with trapezoidal or parabolic cross sections [83,308-315], resulting in a variation of the fluid flow velocity across the channel width, Giddings [316] favored the classical rectangular cross section with a parabolic fluid velocity profile. 

Fig. 10.6. Relalion.ship belwecn the theoretical plate height H) and eluent front velocity (u) asing OPLC with forced flow of the mobile phase / = fully on-line OPLC 2 = on-line sample application, off-line detection J = off-line sample application, on line detection 4 = fully off-line OPLC. Optimum of flow velocity can be reached by using fully off-line OPLC. with a set-up for forced flow of the mobile phase. Reproduced by permission from Ref. [80].

An optimum of flow profile has recently been achieved for capillary electrophoresis [76], when the mobile phase migration is done by electroosmosis. It is the situation that has been utilised for electrochromatography. For planar chromatography, the optimum of the linear flow velocity is approximated when the convex shape of a forced-flow profile chiefly counterbalances the concave profile of the advancing meniscus, it is possible to reach optimal efficiency as a function of linear flow velocity [67]. This is demonstrated in Fig. 10.6. At the optimum of efficiency, the microflow profile is nearly linear as the convex and concave forms of laminar flow and the concave form of the advancing meniscus counterbalance each other (Fig. 10.7). 

Fig. 10.7. Optimum of flow velocity reflects the linear shape of the microflow profile.

In this equation the first factor is called the eddy diffusion, the second and third are molecular diffusion, and the last two are called resistance-to-mass-transfer terms. All the terms include the mobile-fluid velocity as a variable that is proportional to the flow rate in some, and inversely proportional in others. The overall relation between plate height and flow velocity of the mobile phase is the statistical resultant of the five terms and is usually depicted in the form of a Van Deemter plot. ° Such a diagram shows that an optimum flow velocity for minimum band spreading exists for a given chromatographic column. 

Band broadening and temperature The five terms of Equation (24-14) can be examined in the context of the influence of temperature on flow rates, retention volumes, and diffusion coefficients to obtain an estimate of the overall influence of temperature on band broadening. Through thermal expansion, temperature also influences such factors as thickness of a liquid film and particle and column diameters, and it may also influence slightly the empirical constants in (24-14). With a liquid mobile phase, flow velocity (with the same inlet and outlet pressures) is strongly dependent on temperature. But with flow velocity u maintained constant the first term of (24-14) becomes smaller as diffusion coefficients increase in the mobile phase. For flow rates near the optimum the first term is approximately inversely proportional to The second and third terms increase in direct proportion to the diffusion coefficients in the mobile and stationary phases D and D, whereas the fourth and fifth... 

When the partition ratio is large, the plate height at the minimum is 1.9r and the velocity 2. DJr. The important conclusion to be reached here is that, the smaller the diameter of the capillary, the smaller the optimum plate height and the higher the optimum flow velocity. This situation means more theoretical plates per unit length and the possibility of shorter analysis time for a given level of separation. 

Figure 16.4 illustrates the dependence of the SLT on the flow velocity. It shows that the SLT increases rapidly with increasing flow velocity above the minimum. This phenomenon explains the sharpness of the production rate optimum reported by Horvath and associates [13,14]. When the flow velocity exceeds the optimum, the SLT broadens, and the volume of pure fractions that can be collected drops rapidly. 

Differentiation of Eq. 16.29 shows that the optimum mobile phase velocity, which is a fimction of the displacer retention factor and concentration, is minimum for Kd = 1, which also corresponds to the optimum displacer conditions for iiiinimiun SLT (see previous section) [11]. This combination of results is obviously imattractive, as it does not correspond to what would have been required for a high production rate. The optimum flow velocity is almost always much lower in displacement chromatography than the optimum velocity imder linear... 

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