Plug flow profile

The plug flow profile would only be distorted in very narrow bore capillaries with a diameter smaller than the thickness of two double-layers that then overlap. To achieve an undisturbed flow, Knox suggested that the diameter should be 10-40 times larger than 6 [15]. This can easily be achieved in open capillaries. However, once the capillary is packed with a stationary phase, typically small modified silica beads that carry on their own charged functionalities, the distance between adjacent double-layers is only a fraction of the capillary diameter. However, several studies demonstrated that beads with a submicrometer size can be used safely as packings for CEC columns run in dilute buffer solutions [15,35]. 

An advantage of CEC is that the pressure drop across the column is very low so that small particles and longer columns can be used. Also, the electroosmotic flow results in a plug flow profile as opposed to a parabolic or laminar flow derived from a pressure-driven flow (Figure 1). The combination of these advantages leads to highly efficient columns that can be applied to separate components in a mixture. 

Electrodriven separations, such as capillary electrophoresis (CE) and capillary electrochromatography (CEC), are based on the different electrophoretic mobilities in an electric field of the molecules to be separated. They provide a higher separation efficiency then conventional HPLC since the electrophoretic flow (EOF) has a plug-flow profile. Whereas the mobile phase in CE is driven only by the electro-osmotic flow, it is generated in CEC by a combination of EOF and pressure. CEC has a high sample capacity which favours its hyphenation with NMR. 

In the RP CEC of neutral species selectivity is provided primarily by differences in the partition of the analytes between the hydrophobic stationary phase and the more polar mobile phase. There are also contributions from interactions with the silica support, the major one being polar interactions with ionised silanol groups. This is identical to the process in LC, albeit with the advantages of higher efficiencies in CEC resulting from the plug-flow profile. Additional selectivity is introduced in the case of charged species in CEC due to differences in the analytes electromobilities. 

This technique has proven to be a powerful separation technique for the separation of macromolecules, such as antibodies, for two reasons the near flat plug flow profile and the small diffusion constant of the antibodies. These characteristics eliminate band broadening. With both superior separation power and high detection sensitivity, capillary electrophoresis (CE) can separate free Ab and Ag from bound Ab and Ag rapidly and is suitable for immunoassays. CE can combine immunologic recognition with on-line quantitation, microscale... 

For values of n less than 1, this gives a velocity that is flatter than the parabolic profile of new-tonian fluids. As n approaches zero, the velocity profile predicted by this equation approaches a plug flow profile. Figure 10.5 shows the velocity profile generated by Eq. 10.43 for selected values of the power-law index n. It should be noted that the velocity profiles given in Fig. 5 are valid in the hydrodynamically fully developed region where the entrance effect can be neglected. 

Compute the profiles in tubular reactors with axial mixing as a function of total length and compare with the plug flow profile. 

In an ideal tube with plug flow profile, the reaction rate is not constant it varies in the direction of flow. Therefore, a pronounced temperature profile develops along the length of the reactor. Because the mathematical expression for r ff is often complex, the integral in Equation (14-1) must generally be solved numerically. The feed rate a,o can be determined from the known production capacity of the reactor. Thus, Equation 14-1 allows the catalyst mass and therefore the reactor volume to be calculated from the target quantity conversion and the kinetics. This shows the fundamental importance of kinetics in reaction engineering. 

Electroosmotic flow-driven chromatography yields higher separation efficiencies than HPLC because of the use of small particles and reduction of plate heights as a result of the plug-flow profile. 

The dispersion model (diffusion model) explains the deviation of the real flow profile from the ideal plug flow profile due to dispersion analogously to molecular diffusion. For example, in the continuous phase, the axial distribution of the key component is... 

Electroosmotic flow has emerged as a viable alternative transport mechanism to pressure-driven flow in column chromatography. Benefits include a plug-flow profile (reduced transaxial contributions to zone broadening) and a mobile phase velocity that is independent of the column length and particle size. The electroosmotic-driven flow is governed by the dielectric constant of the mobile phase, the zeta potential at the stationary phase/mobile phase interface, and the applied electric field. The efficiency obtainable is limited by double layer overlap or radial dispersion induced by inefficient heat dissipation. 

An entirely different concept in analytical separations is provided by capillary electrophoresis (CE) in which the flow of liquid is generated by electro-osmotic flow (EOF) driven by an external electric field. The major advantage of this approach is the essentiaUy flat plug flow profile that leads to intrinsically more narrow elution peaks than the parabolic flow profiles characteristic of pressure-driven viscous flows. In capillary zone electrophoresis (CZE) separation is achieved by superimposing the different electrophoretic mobihties of the solutes on to the EOF. In electrochromatography the separation is achieved as in packed column HPLC but using an EOF to generate flow of the mobile phase past the stationary phase particles. The importance of these EOF-based techniques is their application to miniaturized devices, lah-on-a-chip or micro total analysis systems. Such devices that can be directly interfaced to a mass spectrometer via an ESI source are currently under intense development. 

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