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

W. D. Ristenpart, Howard A. Stone

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Article number014108
Issue number1
StatePublished - Mar 2 2012

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Fluid Flow and Transfer Processes
  • Biomedical Engineering
  • General Materials Science
  • Colloid and Surface Chemistry


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