Faceted design of channels for low-dispersion electrokinetic flows in microfluidic systems

A novel methodology for designing microfluidic channels for low-dispersion, electrokinetic flows is presented. The technique relies on trigonometric relations that apply for ideal electrokinetic flows, allowing faceted channels to be designed using common drafting software and a hand calculator. Flows are rotated and stretched along the abrupt interface between adjacent regions having differing specific permeability--a quantity with dimensions of length that we introduce to derive the governing equations. Two-interface systems are used to eliminate hydrodynamic rotation of bands injected into channels. Regions bounded by interfaces form faceted flow "prisms" with uniform velocity fields that can be combined with other prisms to obtain a wide range of turning angles and expansion ratios. Lengths of faceted prisms can be varied arbitrarily, simplifying chip layout and allowing the ability to reduce unwanted effects such as transverse diffusion and Joule heating for a given faceted prism. Designs are demonstrated using two-dimensional numerical solutions of the Laplace equation.