Infinitely fast reactions in micromixers

Efficient mixing to promote chemical reactions is ex-tremely desirable in lab-on-a-chip devices, but is dif-ficult to achieve in the typical low Reynolds-number flows. Numerical simulation of the high Peclet-number case common in microfluidics is computationally chal-lenging, and asymptotic solutions have proved useful in understanding the interplay between convection and dif-fusion 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 in-clude the effects of chemical reaction terms to describe the infinitely fast reaction between two species. Ana-lytical results identify two important timescales for the yield of the product species: an initial Rhines-Young shear-enhanced mixing time, and a long-time approach of the yield to its final value. The latter regime is crucial for high-efficiency microreactors, and is associated with persistent structures in the mixer flow field