Modeling a Low-Re Passive Microfluidic Mixer for Bioprinting Applications*

Mixing at microfluidic scales is challenging due to the dominance of diffusion in laminar flows. Of the microfluidic solutions that have been designed and studied to increase mixing within microfluidic mixers, passive mixers provide advantages such as reliability, manufacturability, and straightforward integration into pressure-driven systems. In particular, two-layer crossing-channel micromixers (TLCCMs) induce chaotic advection at low Reynolds numbers (Re), resulting in high mixing efficiencies when compared with other passive mixer designs. Previous work has characterized this class of micromixer down to Reynolds numbers on the order of 0.01, but applications such as bioprinting often deal with lower Re ranges due to the high viscosities of bio-inks. In this work, we model and evaluate a TLCCM at these lower Re ranges using finite volume numerical methods. We determine mixing efficiency over a range of low-Re flows, for a series of TLCCM geometries, and as a function of the number of consecutive mixing units. The results from these models will broaden the current design space for TLCCMs and serve as a foundation for the eventual implementation of the microfluidic mixer into a bioprinting system.