Band dispersion, electrophoresis

Currently, analytical approaches are still the most preferred tools for model reduction in microfluidic research community. While it is impossible to enumerate all of them in this chapter, we will discuss one particular technique - the Method of Moments, which has been systematically investigated for species dispersion modeling [9, 10]. The Method of Moments was originally proposed to study Taylor dispersion in a circular tube under hydrodynamic flow. Later it was successfully applied to investigate the analyte band dispersion in microfluidic chips (in particular electrophoresis chip). Essentially, the Method of Moments is employed to reduce the transient convection-diffusion equation that contains non-uniform transverse species velocity into a system of simple PDEs governing the spatial moments of the species concentration. Such moments are capable of describing typical characteristics of the species band (such as transverse mass distribution, skew, and variance). 

A last variant we mention is capillary zone electrophoresis (Gordon et al. 1988). It employs an electroosmotically driven flow in a capillary, arising from an electric field applied parallel to the capillary, which is charged when in contact with an aqueous solution (Section 6.5). The flow has a nearly flat velocity profile (Fig. 6.5.1), thereby minimizing broadening due to Taylor dispersion of the electrophoretically separated solute bands. 

In electrophoresis, band broadening is mainly caused by longitudinal diffusion. The peak dispersion, o, is directly proportional to the diffusion coefficient, D, of the analyte and its migration time, t ... 

Philpot (1940) obtained such a result in terms of t = Ljvz. The number of different charged species which can therefore be separated in a ffee-flow electrophoresis device is limited by solute dispersion in the x-direction, amongst other things. The peak-to-peak distance between two species may be estimated from equation (7.3.7). A more exact solution, which includes the effect of dispersion in the z-direction, has been provided by Reis etal. (1974) for a parabolic velocity profile Vziy) in the y-direction effectively, the Philpot (1940) model underestimates x-directional band broadening substantially. The base width of the profile described by equation (7.3.9) depends on t at z values less than L, the base width will be smaller. Note, however, the separation of Figure 7.3.1 is essentially at steady state. The time coordinate used here allows a specification of position along the z-axis. 

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