Infinitely fast reactions in micromixers

Efficient mixing to promote chemical reactions is extremely desirable in lab-on-a-chip 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 include the effects of chemical reaction terms to describe the infinitely fast reaction between two species. Analytical 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.