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Biomicrofluidics / Volume 6 / Issue 1 / REGULAR ARTICLES

Biomicrofluidics 6, 014108 (2012); http://dx.doi.org/10.1063/1.3679950 (9 pages)

Michaelis-Menten kinetics in shear flow: Similarity solutions for multi-step reactions

W. D. Ristenpart1 and H. A. Stone2

1Department of Chemical Engineering and Material Science and Department of Food Science and Technology, University of California at Davis, Davis, California 95616, USA
2Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA

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(Received 19 September 2011; accepted 9 January 2012; published online 31 January 2012)

Models for chemical reaction kinetics typically assume well-mixed conditions, in which chemical compositions change in time but are uniform in space. In contrast, many biological and microfluidic systems of interest involve non-uniform flows where gradients in flow velocity dynamically alter the effective reaction volume. Here, we present a theoretical framework for characterizing multi-step reactions that occur when an enzyme or enzymatic substrate is released from a flat solid surface into a linear shear flow. Similarity solutions are developed for situations where the reactions are sufficiently slow compared to a convective time scale, allowing a regular perturbation approach to be employed. For the specific case of Michaelis-Menten reactions, we establish that the transversally averaged concentration of product scales with the distance x downstream as x5/3. We generalize the analysis to n-step reactions, and we discuss the implications for designing new microfluidic kinetic assays to probe the effect of flow on biochemical processes.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORY
    1. Michaelis-Menten kinetics
    2. Similarity solution
    3. Generalization to n-step reactions
  3. DISCUSSION AND CONCLUSIONS

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KEYWORDS, PACS, and IPC

Keywords

biochemistry, biological fluid dynamics, chemically reactive flow, convection, enzymes, microfluidics, molecular biophysics, perturbation techniques, reaction kinetics, shear flow

PACS

International Patent Classification (IPC)

  • B81B

    Micro-structural devices or systems, e.g. micro-mechanical devices

  • C12

    Biochemistry; Beer; Spirits; Wine; Vinegar; Microbiology; Enzymology; Mutation or genetic engineering

  • F15D

    Fluid dynamics, i.e. methods or means for influencing the flow of gases or liquids

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3679950

PUBLICATION DATA

ISSN

1932-1058 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    R. F. Ismagilov, A. D. Stroock, P. J. A. Kenis, G. Whitesides, and H. A. Stone, Appl. Phys. Lett. 76, 2376 (2000)APPLAB000076000017002376000001.

    J. B. Salmon and A. Ajdari, J. Appl. Phys. 101, 074902 (2007)JAPIAU000101000007074902000001.

    J. B. Salmon, A. Ajdari, P. Tabeling, L. Servant, D. Talaga, and M. Joanicot, Appl. Phys. Lett. 86, 094106 (2005)APPLAB000086000009094106000001.


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