Assessment and numerical search for minimal Taylor–Aris dispersion in micro-machined channels of nearly rectangular cross-section

• Ultra-fast numerical method to determine Taylor–Aris dispersion coefficient.
• Assessment of dispersion of a variety of quasi-rectangular cross-sectional channel shapes.
• Impact of real world etching imperfections on dispersion in optimized cross sections.

A mathematical procedure using the Matlab® PDE toolbox to calculate the numerical constant appearing in the general Taylor–Aris expression for the dispersion in a laminar flow through open-tubular conduits with a variety of quasi-rectangular cross-sectional shapes is described. The procedure has been applied to assess the effect of some of the most frequently occurring etching imperfections (linear or curved tapering of the inter-pillar distance along the depth coordinate, occurrence of local notches) in etched pillar array columns. In addition, covering a broad range of possible geometries, a number of new shapes and optimal geometries to minimize the dispersion in open-tubular microchannels and pillar array columns have been proposed. Making a full shape-sensitivity study, it was also found that, whereas the proposed designs can theoretically reduce the dispersion up to a factor of 8, relatively small deviations from this ideal shape can however again dramatically increase the dispersion. Designers should therefore be very careful before implementing an optimized shape and should first aim at solving the etching imperfection problems.