Numerical Study of Scalar Mixing in Curved Channels at Low Reynolds Numbers S. P. Vanka, G. Luo, and C. M. Winkler Dept. of Mechanical and Industrial Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801 DOI 10.1002/aic.10196 Published online in Wiley InterScience (www.interscience.wiley.com). A computational study has been performed to determine the rates of mixing in a curved square duct at low Reynolds numbers of interest to microfluidic applications. Two flow streams with inlet scalar concentrations of zero and unity in the two halves of a duct perpendicular to the plane of curvature were allowed to mix by convection and diffusion. Concentration distributions and unmixedness coefficients are presented for several Rey- nolds and Schmidt numbers and are compared with values for a straight channel of equivalent length. It is seen that for large Schmidt number fluids, mixing is considerably enhanced at moderately low Reynolds numbers (Re  10), but is not enhanced at Reynolds numbers of the order of 0.1. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2359 –2368, 2004 Keywords: scalar mixing, curved channels Introduction Rapid mixing of two (or several) streams is essential to many microfluidic devices currently under development (Brody et al., 1996; Gravesen et al., 1993; Jensen, 2001). In these devices, two (or many) streams of fluid enter a chamber (or a channel), mix, and may undergo a chemical reaction. The fluids to be mixed are usually liquids with small diffusion coefficients (Schmidt numbers of the order of 1000 or greater). Also the characteristic dimension of these channels can be of the order of a few hundreds of microns. For the chosen volumetric rates of the flow, the Reynolds numbers encountered are very small, ranging anywhere from 0.1 to 50. Because of such low Rey- nolds numbers and high Schmidt numbers, mixing in these devices is slow, dictated primarily by the laminar diffusion coefficient. The molecular diffusion-based mixing time can be expressed as time  L 2  (1) where L is a characteristic length scale of the mixer (commonly a channel width) and  is the scalar diffusivity. For systems that have dimensions on the order of tens of microns, the molecular diffusion-based mixing time is on the order of sec- onds. For other mixers with dimensions on the order of hun- dreds of microns, molecular diffusion-based time for complete mixing can be tens of seconds. These diffusion times are large and thus several innovative methods (Branebjerg et al., 1996; Deshmukh et al., 2000; Evans et al. 1997; Lee et al., 2000, 2001; Liu et al., 2000; Miyake et al., 1993; Volpert et al., 1999; Yi and Bau, 2000; Yi et al., 2000) have been proposed in the past to enhance mixing over the purely diffusive limit. The numerous mixer designs previously proposed can be classified in two main categories: active and passive. Active mixers use features such as moving walls, bubbles, or pulsed pressure gradients and pulsed flows to enhance mixing. Evans et al. (1997) developed a mixer based on chaotic advection principles (Aref, 1984; Jones et al. 1989). It consisted of two antisymmetric source/sink combinations that were pulsed at a certain frequency. A mixing chamber was filled with two fluid layers one on top of the other. The source and sink dipole was then pulsed for 18 cycles, which resulted in one fluid penetrat- ing and mixing with the other. The flow unsteadiness was generated using bubble pumps. Deshmukh et al. (2000) used alternate pulsing of two streams in a straight channel to mix the two fluids. The pulsing was achieved by alternately generating Correspondence concerning this article should be addressed to S. P. Vanka at spvank@uiuc.edu. © 2004 American Institute of Chemical Engineers AIChE Journal 2359 October 2004 Vol. 50, No. 10