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Microfluidic Mixing for Biosensors

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Miniature Fluidic Devices for Rapid Biological Detection

Part of the book series: Integrated Analytical Systems ((ANASYS))

Abstract

Among other factors, the performance of an affinity-based biosensor is dependent on the rate at which analyte is transported to, and captured by, its active sensing surface. The efficiency of analyte delivery can be increased via the use of microfluidics, albeit not without detraction, as microfluidic biosensors are often subjected to severe diffusion limitations when used for the detection of biologically relevant analytes. Such conditions lead to the formation of a boundary layer, void of analyte, which acts to resist the rate at which analyte is captured. It is often proposed to mix the fluid in the sensing chamber, where the exchange of depleted solution with fresh analyte can potentially increase sensor performance. The nature of analyte transport in a mixed channel is complex, however, and simply mixing the contents of a microchannel does not guarantee success. In this chapter, we review developments in the characterization (and prediction of) analyte transport in both mixed and unmixed channels. Our discussion focuses on the conditions under which mixing will (and will not) be beneficial and furthermore, the magnitude of performance increase that can be expected. Special attention is given to flow in the staggered herringbone mixer (SHM): a passive chaotic micromixer often used to enhance the performance of a biosensor. We review relevant experimental works on the topic and compare the results from several studies with the behavior expected from theory. Finally, we note several challenging aspects regarding the detection of circulating tumor cells which, due to their large size, are subject to additional transport mechanisms with respect to smaller analytes.

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Notes

  1. 1.

    The area for signal transduction is often the same as that for biocomponent immobilization, which is assumed herein.

  2. 2.

    As discussed later, the distinction between the two is very important: a reaction-limited biosensor will never benefit from the inclusion of mixing.

  3. 3.

    The rate at which the first step in Eq. (9) proceeds is dependent only on the magnitude of the difference between \(C_s\) and \(C_o\), and hence the presence of \(K_m\) in both the forward and reverse steps.

  4. 4.

    More specifically, the characteristic time for the analyte boundary layer to reach equilibrium is often much smaller than the characteristic time for the analyte to reach equilibrium.

  5. 5.

    Applicable for the geometries here, where a single wall acts to capture analyte. A value of \(\text {Gr} \gg 1\) indicates the boundary layer has not reached the top of the channel.

  6. 6.

    In this region, the rate of analyte capture is proportional to the flow rate, no matter how fast the fluid is stirred.

  7. 7.

    Where the analyte flux in the axial direction can be estimated as \(C_oD/\delta \), and thus \(J\approx C_oDH/\delta L\).

  8. 8.

    Measurement of these values can be accomplished using a variety of methods, the most popular of which the SPR method.

  9. 9.

    The mixing-cup concentration \(c_b\) represents the concentration one would obtain by collecting the microchannel effluent with a small cup.

  10. 10.

    For quasi-steady, diffusion-limited conditions, the limit of detection for a mixed biosensor (\(\text {LOD}_m\)) is related to that of an unmixed biosensor (LOD) of similar dimension as \(\text {LOD}_m = \text {LOD}\cdot E^{-1}\).

  11. 11.

    When flow is reversed, the analyte flux is highest where the grooves meet the channel sidewalls. This arrangement is nonoptimal due to the lower axial velocities near the channel edges.

  12. 12.

    Reprinted from Biosensors and Bioelectronics, 22, Golden J.P., Floyd-Smith T.M., Mott D.R., and Ligler F.S., Target delivery in a microfluidic immunosensor, 2763-2767, 2007, with permission from Elsevier.

  13. 13.

    The scaling laws in Sect. 3.3 predict that there will be an indefinite increase in the maximum sensor enhancement \(E_{max}\) with increases in Pe; however, this scaling law applies only to mixers of length \(L_{opt}\).

  14. 14.

    For unmixed flow in wide channels, the asymptotic local Sherwood number is \(\text {Sh}_\infty \approx 7.5\) [79] and furthermore, the integral in Eq. (21) is multiplied by a factor of 2 into account for the additional reactive surface.

  15. 15.

    From the Einstein–Stokes equation, the diffusivity of an analyte is inversely proportional to the fluid viscosity.

  16. 16.

    This applies for mixing in the sense as shown in Fig. 1, where there is no selective transport specific to the analyte (e.g., (di)electrophoresis, thermophoresis).

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Acknowledgements

The authors would like to acknowledge funding from both the Praemium Academiae of the Academy of Sciences of the Czech Republic as well as the Czech Science Foundation (contract no. P205/12/G118).

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Authors and Affiliations

  1. Institute of Photonics and Electronics, Academy of Sciences of the Czech Republic, Chaberská 57, 18251, Prague, Czech Republic

    N. Scott Lynn Jr.

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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, Minnesota, USA

    Sang-Hyun Oh

  2. Department of Chemical Engineering, Queens University, Kingston, Ontario, Canada

    Carlos Escobedo

  3. Department of Chemistry, University of Victoria, Victoria, British Columbia, Canada

    Alexandre G. Brolo

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Lynn, N.S. (2018). Microfluidic Mixing for Biosensors. In: Oh, SH., Escobedo, C., Brolo, A. (eds) Miniature Fluidic Devices for Rapid Biological Detection. Integrated Analytical Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-64747-0_3

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