Design of microfluidic slug mixing based on the correlation between a dimensionless mixing rate and a modified Peclet number

A method to design mixing in microfluidic slugs using a modified Peclet number, Pe*=Usds2/lD, has been reported by the authors, but it was limited to mixing at constant diffusivity D. This paper reports an improved method to quantitatively determine the effect of D   on a relation between Pe*Pe* and mixing rates. Computational fluid dynamics (CFD) simulations were used for the investigation. We introduce D   into the mixing rate term in the relation between Pe*Pe* and mixing rates, and found that (mixing rate×ds2/D) becomes a function of only Pe*Pe*. Thus, slug mixing can be designed using the new dimensionless number, (mixing rate×ds2/D), and Pe*Pe*. This allows us to use mixing rate data at any value of D to estimate mixing rates at another value of D  . Though Pe*Pe* includes effects of D, l  , dsds, and UsUs, effects of initial arrangements of reactants inside a slug and slug cross-sectional shapes are not considered. Thus, the relations between (mixing rate×ds2/D) and Pe*Pe* (referred as Pe*Pe* correlation) are quantitatively determined to cover the effects of these parameters. Furthermore, we used the Pe*Pe* correlation to show theoretically that channel contraction is an effective microfluidic operation to enhance mixing in slugs.