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strictions/expansion units where ≈ 2 × enhancement was found [30]. This enhancement is an open problem currently being investigated [31], but is thought to be due to the modula- tion of width enhancing diffusion [31] due to convective cross flow movement (e.g. periodic movement perpendicular to the main flow direction) [46]. 

We note that Lam et al. Ref. [32] create instabilities by driving viscoelastic fluids through abrupt 8:1 constrictions using a syringe pump, and therefore have a mechanically driven device similar to our device. They observe enhancement of mixing in their liquids over deionized water at equal flow rates, demonstrating that absolute mixing increase can be obtained over low viscosity Newtonian liquids. However, they use dis-similiar fluids of differ- ent viscosity, shear-thinning, and elastic properties making interpreting their results difficult as flow focusing, shear-thinning [33], and viscous thread folding [34] or other coflowing ef- fects are physical mechanisms that all may play important roles in addition to viscoelastic instabilities in promoting the mixing they observe. 

We have shown that viscoelastic instabilities alone will not lead to rapid mixing, in contrast to earlier studies [5, 14, 17] that found up to orders of magnitude improvement in mixing for mechanically driven channel flow. However, significant shear stretching is 

