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Infinitely fast reactions in micromixers

J.P. Gleeson
University College Cork, Ireland, IE

Keywords:
mixing, reaction yield, mathematical modelling

Abstract:
Efficient mixing to promote chemical reactions is extremely desirable in lab-on-a-chip microfluidic devices, but is difficult to achieve in the typical low Reynolds-number flows. Numerical simulation of the high Peclet-number case common in microfluidics is computationally challenging, and asymptotic solutions have proved useful in understanding the interplay between convection and diffusion in particular devices.
 
Most mixing studies to date have examined non-interacting species, so that the total concentration of each is conserved. In this paper we move to the next level, and include the effects of chemical reaction terms to describe the (infinitely fast) reaction between two species. The goal is to accurately predict the total yield y(t) of the product species over time. We introduce a general mathematical modelling framework and highlight the important similarities and differences between earlier work on measures of mixing efficiency and the experimentally measurable quantity y(t). In particular, analytical and numerical results identify two important timescales in the evolution of y(t): an initial Rhines-Young shear-enhanced mixing time, and a long-time approach of y(t) to its final value. The latter regime is crucial for high-efficiency microreactors, and we identify the source of the long-time scaling.

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