(168d) Computational Study of Convection-Diffusion Mixing in a Microchannel Mixer

The growing research effort in micro mixing devices in recent years has led better understanding and design of more efficient microchannel mixers. Such micro mixers have been widely used in chemical and biochemical applications. Due to the limit in sizes, flows in these devices are dominantly laminar flows and efficient mixing is to create chaotic flows. At such small scales, molecular diffusion is often a key factor in mixing mechanism. It is well know that all numerical schemes introduce false diffusion in CFD solutions. This fact has hindered better understanding of mixing in microchannel mixers using CFD. In this presentation, we present a method to quantitatively measure the effect of numerically introduced false diffusion in a CFD solution of a passive scalar distribution. With this method, we can estimate the mesh size required to characterize molecular diffusion with a given diffusivity. The method is used to analyze mixing in a topologic microchannel mixer. The predicted mixing structures in the mixer are found in good qualitative agreement with experimental results for the calculated effective molecular diffusivity. The numerical analysis of false diffusion reveals a range of molecular diffusivity that the convective-diffusive mixing in the mixer can be studied with CFD without significant effect of false diffusion. This range covers many practical viscous solutions including many bio and protein solutions. The main mixing mechanism in the mixer at creeping flow range is the baker's transformation. At higher Re, secondary flow is created and the mixing mechanism becomes result of the competition of kinematic baker's transformation and the dynamic secondary flow. It is found that the most efficient mixing is the baker's transformation alone for Re < 10. This is in agreement with the theoretical findings but first confirmed in a practical mixer. Diffusion in this mixer is important even at a molecular diffusivity smaller than 10-11 m2/s, a typical value for bio solutions. In just a few elements, diffusion broadening will smear the boundary of striations and striation doubling of the baker's transformation ceases.