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^* = U_s d_s² / 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^* 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^* and mixing rates, and found that (mixing rate × d_s² / D) becomes a function of only Pe^*. Thus, slug mixing can be designed using the new dimensionless number, (mixing rate × d_s² / D), and 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^* includes effects of D, l, d_s, and U_s, effects of initial arrangements of reactants inside a slug and slug cross-sectional shapes are not considered. Thus, the relations between (mixing rate × d_s² / D) and Pe^* (referred as Pe^* correlation) are quantitatively determined to cover the effects of these parameters. Furthermore, we used the Pe^* correlation to show theoretically that channel contraction is an effective microfluidic operation to enhance mixing in slugs.