Correlation of Mixing Efficiency and Entropy Generation Rate in a Square Cross Section Tee Junction Micromixer

Abstract

The potential applications of micromixers continues to expand in the bio-sciences area. In particular, passive micromixers that may be used as part of point-of-care (POC) diagnostic testing devices are becoming commonplace and have application in developed, developing, and relatively undeveloped locales. Characterizing and improving mixing efficiency in these devices is an ongoing research effort. Micromixers are used in some lab-on-chip (LOC) devices where it is often necessary to combine two or more fluids into a mixed solution for testing or delivery. The simplest micromixer incorporates a tee junction to combine two fluid species in anti-parallel branches, with the mixed fluid leaving in a branch perpendicular to the incoming branches. Micromixers rely on two modes of mixing: chaotic advection and molecular diffusion. In micro-mixers flow is typically laminar, making chaotic advection occur only via induced secondary flows. Hence, micromixers, unless carefully designed, rely almost exclusively on molecular diffusion of fluid species. A well designed micromixer should exhibit significant chaotic advection; which is also a sign of large strain rates and large entropy generation rates. This paper describes the development of an analytical relationship for the entropy generation rate and the mixing efficiency as function of the outgoing branch Reynolds number. Though there has been extensive research on tee junctions, entropy generation, and the mixing efficiencies of a wide variety of micromixers, a functional relationship for the mixing efficiency and the entropy generation rate has not been established. We hypothesize a positive correlation between the mixing index and the entropy generation rate. The worked described here establishes a method and provides the results for such a relationship. A basic tee junction with square cross sections has been analyzed using computational fluid dynamics to determine the entropy generation rate and outgoing mixing efficiencies for Reynolds numbers ranging from 25–75. The mixing efficiency is determined at a location in the outgoing branch where the effects of molecular diffusive mixing is minimized and chaotic advective mixing is the focus. The entropy generation rate has been determined for the indicated range of Reynolds number and decomposed into its viscous and diffusive entropy terms. The functional relationships that have been developed are applicable for micromixer design and serve as a reference for more complex passive micromixer designs.