Dispersion reduction in pressure-driven flow through microetched channels

Fluid is often moved about microetched channels in lab-on-a-chip applications using electrokinetic flows (electrophoresis or electroosmosis) rather than pressure-driven flows because the latter result in large Taylor dispersion. However, small pressure gradients may arise unintentionally in such systems due to a mismatch in electroosmotic flow rates or hydrostatic pressure differentials along the microetched channel. Under laminar flow conditions, Doshi et al. (Chem. Eng. Sci. 1978, 33, 795-804) have shown that for a channel with rectangular cross-section of width W and depth d, longitudinal diffusivities can attain values as large as approximately 8 K0 for small values of the aspect ratio d/W, where K0 is the value of the longitudinal diffusivity obtained by ignoring all variations across the channel. Microchannels in lab-on-a-chip geometries are often not rectangular in cross-section. Isotropic etching techniques, for example, lead to channels with quarter-circular ends. In this paper we examine the effect of this geometry on the magnitude of longitudinal dispersivity for pressure-driven flows and also investigate modifications to this design which may minimize such dispersion. Optimal channel profiles are shown to lead to dispersivities approaching K0, the theoretical minimum, for small values of d/W.