System-oriented dispersion models of general-shaped electrophoresis microchannels

This paper presents a system-oriented model for analyzing the dispersion of electrophoretic transport of charged analyte molecules in a general-shaped microchannel, which is represented as a system of serially connected elemental channels of simple geometry. Parameterized analytical models that hold for analyte bands of virtually arbitrary initial shape are derived to describe analyte dispersion, including both the skew and broadening of the band, in elemental channels. These models are then integrated to describe dispersion in the general-shaped channel using appropriate parameters to represent interfaces of adjacent elements. This lumped-parameter system model offers orders-of-magnitude improvement in computational efficiency over full numerical simulations, and is verified by results from experiments and numerical simulations. The model is used to perform a systematic parametric study of serpentine channels consisting of a pair of complementary turn microchannels, and the results indicate that dispersion in a particular turn can contribute to either an increase or decrease of the overall band broadening. The efficiency and accuracy of the system model is further demonstrated by its application to general-shaped channels that occur in practice, including a serpentine channel with multiple complementary turns and a multi-turn spiral-shaped channel. The results indicate that our model is an accurate and efficient simulation tool useful for designing optimal electrophoretic separation microchips.