Dispersion by pressure-driven flow in serpentine microfluidic channels

Microfluidic hydrodynamic chromatography performed in serpentine microchannels etched on chips is analyzed in the limiting case of chips containing a large number of periodically arrayed turns. Comparison is made between these results and those for a straight channel of the same length as the curvilinear channel, all other things being equal. Explicitly, generalized Taylor-Aris dispersion (macrotransport) theory for spatially periodic systems is adapted to compute the chip-scale solute velocity (U) over bar* and dispersivity (D) over bar* for effectively point-size, physicochemically inert Brownian particles entrained in a low Reynolds number, pressure-driven solvent flow occurring within the curvilinear interstices of such serpentine devices. Attention is focused upon relatively thin channels of uniform cross section, enabling the various transport fields pertinent to the problem to be expressed as regular perturbation expansions with respect to a small dimensionless parameter E, representing the ratio of channel half-width to curvilinear channel length per turn. The generic leading-order results obtained for (U) over bar* and (D) over bar*, valid for any sufficiently "thin" channel, formally demonstrate that the serpentine geometry results simply reproduce those for a straight channel, when account is taken of the channel's "tortuosity," namely the square of the ratio of curvilinear serpentine length to rectilinear straight channel length-a conclusion shown to accord with intuition.