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On-chip capillary electrophoresis was first developed in the early 1990's [1] and remains an important separation technique for microfluidic systems today. The motivation to shrink separation systems comes from their increased portability, reduced consumption of expensive reagents, and more feasible parallel analysis of separations. Since the separation efficiency increases with the separation length, serpentine channels have become a preferred design topology because of their high channel density. However, introducing turns into the separation channel creates additional sources of variance from the new electric field structure and geometric path length differences.
These additional sources of dispersion have been previously modeled in [2,3,4,5]. The problem with each of these models is that they are based on the assumption of a linear electric field structure in a single-turn, which excludes many higher-order effects. This work shows a new model of the high Peclet variance for entire serpentine channels using the full structure of the electric fields described by complete solutions to Laplace's equation. This model is based on closed-form algebraic expressions for rapid computation and possible use in gradient-based optimization. It is a functional model type, as described in [6], for serpentine channels of an arbitrary number of turns. The new variance description can be used in a component-based model for lab-on-a-chip systems that consist of an injector, serpentine separation channel, and detector, which is a common separation system topology [7].
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