Numerical study on mixing in a chaotic serpentine mixer using a mapping method

We introduce a chaotic serpentine mixer (CSM), which is motivated by the three-dimensional serpentine channel [Liu et al., 2000, J. Microelectromech. Syst. 9, pp. 190-197], and demonstrate a systematic way of utilizing the mapping method [Singh et al., 2008, Microfluid Nanofluid 5, pp. 313-325] to find out an optimal set of design variables for the new mixer. The new mixer shows globally chaotic mixing even in the Stokes flow regime, while maintaining the benefits of the original design. One geometrical period of the mixer consists of two functional units, inducing two flow portraits with crossing streamlines. Each half period of the mixer consists of an "L-shaped" bend and a bypass channel. The two flow portraits may be either co-rotational or counter-rotational. As a preliminary study, first of all, mixing in the original serpentine channel has been analyzed to demonstrate the flow characteristics and to find out a critical Reynolds number showing chaotic mixing above the limit. The working principle of the newly proposed mixer is explained by the manifold of the deforming interface between two fluids. To optimize the mixer, we choose three key design variables: the sense of rotation of the two flows, the aspect ratio of the rectangular channel, and the lateral location of the bypass channel. Then, simulations for all possible combinations of the variables are carried out. At proper combinations of the variables, almost global chaotic mixing is observed in the creeping flow regime. The design windows, provided as a result of the parameter study, can be used to determine a proper set of the design variables to fit with a specific application. The deforming interface of the two fluids shows that, even in a poor mixer in Stokes flow regime, as the Reynolds number increases, more efficient mixing is resulted in due to the enhanced cross-sectional vertical motion and back flows near the bends.