Pressure-driven plug flow

An important advantage of the use of EOF to pump liquids in a micro-channel network is that the velocity over the microchannel cross section is constant, in contrast to pressure-driven (Poisseuille) flow, which exhibits a parabolic velocity profile. EOF-based microreactors therefore are nearly ideal plug-flow reactors, with corresponding narrow residence time distribution, which improves reaction selectivity. 

Fig. 9.7.1 Visualization of (a) pressure-driven Poiseuille flow (parabolic) in a 100 )xm ID fused silica capillary and (b) electrokinetically-driven plug flow in a 75 pm ID capillary. Numbers denote time in milliseconds between micrographs in both sequences. See text for details.

Figure 5 Transport of analytes in LC and CE pressure driven flow profile in liquid chromatography (1) electroosmotic flow driven plug flow in capillary electrophoresis (2).

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. 

Figure 9.2 Pressure-driven (a) and electrodriven (b) flow profiles. Laminar flow in pressure-driven systems results in a bullet-shaped profile, wliile the profile of electroosmotic flow is plug-shaped, wliich reduces band broadening.

Convection is mass transfer that is driven by a spatial gradient in pressure. This section presents two simple models for convective mass transfer the stirred tank model (Section II.A) and the plug flow model (Section n.B). In these models, the pressure gradient appears implicitly as a spatially invariant fluid velocity or volumetric flow rate. However, in more complex problems, it is sometimes necessary to develop an explicit relationship between fluid velocity and pressure gradients. Section II.C describes the methods that are used to develop these relationships. 

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. 

CEC has recently become an alternative to HPLC. A capillary is filled or its internal wall covered with a porous sorbent. The free volume remaining in the capillary is filled with an electrolyte. High voltage (on the order of ten kV) is applied across the length of the capillary. Sample plugs are introduced at one end. Sample components are carried to the other end due to electro-osmosis and - in the case of ions - also electrophoresis. In CEC the more important effect is electro-osmosis, which is essentially a flow mechanism of the electrolyte solution without the need for applied pressure. The separation of the sample components occurs mainly due to phase distribution between the stationary phase and the flowing electrolyte. Thus CEC is very similar to HPLC in a packed capillary except that the flow is not pressure driven and that ionic analytes undergo electrophoresis additionally to phase separation. 

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. 

Ideally, a sample is introduced into a chromatograph as a perfect plug. In practice, this is not the case, and diffusion occurs because of the injector. For narrow-bore and microbore applications, injectors capable of introducing the required sample volumes are commercially available and optimized to reduce dispersion. This is not the case for capillary LC, and homemade injection systems include the sample tube technique, in-column injection, stopped-flow injection, pressure pulse-driven stopped-flow injection (PSI), groove injection, split injection, heart-cut injection, and the moving injection technique (MIT). Of the injection techniques, only the split injector, MIT and PSI approaches can introduce subnanoliter sample volumes accu-... 

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