Diffusion Electromigration dispersion

Pee is the electric Peclet number, expressed as the ratio of diffusion time to electromigration time a is the ratio of electroosmosis to electrophoretic mobility /S is the ratio of channel width to characteristic length scale for the initial sample ion concentration distribution and 5 is the ratio of the length scale of the initial BGE and sample ion concentration gradients. Here, d is the channel depth, ss and sb are the initial sample and BGE ion concentration gradients, and Ep is the nominal electric field. The function g x, t) in the advective dispersion term accounts for the axial variation in pressure-driven velocity profile (cf. Figure 38.2). 

The isotachophoretic boundary between two adjacent zones, under constant current condition and in the absence of bulk flow, assumes a constant width governed by the balance of electromigration and dispersion fluxes. For negligible electroosmosis (and negligible Taylor dispersion), the dispersion is determined by diffusion alone. Analytical solution to the concentration of the species in this diffused boundary, for a three-component fully ionized system, has been presented by Saville et al. [90]. The characteristic length-scale, S, of the ITP boundary in this case is given by... 

In the second case, electromigration results in a steady-state migration of the zones where electromigration counteracts dispersion processes at the boundaries (e.g., diffusion). Such a steady state is typical of isotaphoresis migration[17, 18] (see the section 3.2). 

---