Pressure-driven transport of fluid and solute samples is often desirable in microfluidic devices, particularly where sufficient electroosmotic flow rates cannot be realized or the use of an electric field is restricted. Unfortunately, this mode of actuation also leads to hydrodynamic dispersion due to the inherent fluid shear in the system. While such dispersivity is known to scale with the square of the Peclet number based on the narrower dimension of the conduit (often the channel depth), the proportionality constant can vary significantly depending on its actual cross section. In this article, we review previous studies to understand the effect of commonly microfabricated channel cross sections on the Taylor-Aris dispersion of solute slugs in simple pressure-driven flow systems. We also analyze some recently proposed optimum designs which can reduce the contribution to this band broadening arising from the presence of the channel sidewalls. Finally, new simulation results have been presented in the last section of this paper which describe solutal spreading due to bowing of microchannels that can occur from stresses developed during their fabrication or operation under high-pressure conditions.
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.
Solute dispersion in open-channel liquid chromatography is often dominated by transverse diffusion limitations in the mobile phase (Martin, M.; Guiochon, G. Anal. Chem. 1984, 56, 614-620) convecting the solute species. While such dispersion is known to scale with the square of the Peclet number based on the narrower dimension of the conduit, the proportionality constant may significantly vary with the aspect ratio of the channel geometry. In this article, we investigate the effect of channel sidewalls on axial dispersion in electrokinetically and pressure-driven chromatographic systems. The analysis presented here clearly identifies the contribution from flow, wall retention, and the interaction between the two to the overall slug dispersion in the mobile phase for any arbitrary channel geometry. The particular geometries that have been investigated in this work, however, are the rectangular and the isotropically etched profiles often employed in microanalysis systems. Further, the effectiveness of simple double-etched profiles proposed elsewhere (Dutta, D.; Leighton, D. T. Anal. Chem. 2001, 73, 504-513) to diminish the effect of channel sidewalls on Taylor-Aris dispersion has also been examined. Analysis shows that dispersion arising due to shear and wall retention, as well as the interaction between the two, may be significantly reduced in large aspect ratio microchannels for optimized channel geometries.
Curved channel geometries introduced on microchip separation devices to achieve greater separation distances often lead to large analyte dispersion, degrading the performance of these systems. While such electrokinetic dispersion may be minimized by reducing the channel width around the curved region, alternative strategies involving larger channel curvatures may be promising as well, depending on the application. For example, Culbertson et al. (Anal. Chem. 2000, 72, 5814-5819) recently demonstrated the effectiveness of gentle spiral geometries in carrying out separations of small molecules. For moderate and large Peclet number systems, however, larger spiral geometries are necessary to diminish electrokinetic dispersion of solute slugs which may not conform to the needs of the microchip format. In this work, we investigate a modified spiral geometry with a wavy wall along the inner track of the channel. Analysis shows that such width profiling may significantly improve the performance of the spiral geometry, making the design effective for larger Peclet number or smaller radii systems. Numerical simulations performed to optimize these modified spirals suggest equating transit times along the inner and the outer track of the channel as a useful design criterion for minimizing electrokinetic dispersion. An analytical model has been formulated to derive the optimal channel parameters based on this criteria which compares well with the simulation results.
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