Hydrodynamic dispersion in shallow microchannels: the effect of cross-sectional shape

We highlight the fact that hydrodynamic dispersion in shallow microchannels is in most cases controlled by the width of the cross section rather than by the much thinner height of the channel. We identify the relevant time scales that separate the various regimes involved. Using the lubrication approximation, we provide simple formulas that permit a quantitative evaluation of dispersion for most shallow cross-sectional shapes in the "long-time" Taylor regime, which is effectively diffusive. Because of its relevance for microfluidic systems, we also provide results for the short-time "ballistic regime" (for specific initial conditions). The special cases of parabolic and quasi-rectangular shapes are considered due to their frequent use in microsystems.