Band spreading in two-dimensional microchannel turns for electrokinetic species transport

Analytical and numerical methods are employed to investigate species transport by electrophoretic or electroosmotic motion in the curved geometry of a two-dimensional turn. Closed-form analytical solutions describing the turn-induced diffusive and dispersive spreading of a species band are presented for both the low and high Peclet number limits. We find that the spreading due to dispersion is proportional to the product of the turn included angle and the Peclet number at low Peclet numbers. It is proportional to the square of the included angle and independent of the Peclet number when the Peclet number is large. A composite solution applicable to all Peclet numbers is constructed from these limiting behaviors. Numerical solutions for species transport in a turn are also presented over a wide range of the included angle and the mean turn radius. On the basis of comparisons between the analytical and numerical results, we find that the analytical solutions provide very good estimates of both dispersive and diffusive spreading provided that the mean turn radius exceeds the channel width. These new solutions also agree well with data from a previous study. Optimum conditions minimizing total spreading in a turn are presented and discussed.