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We exploited the viscoelasticity of biocompatible dilute polymeric solutions, namely, dilute poly͑ethylene oxide͒ solutions, to significantly enhance mixing in microfluidic devices at a very small Reynolds number, i.e., ReϷ 0.023, but large Peclet and elasticity numbers. With an abrupt contraction microgeometry ͑8:1 contraction ratio͒, two different dilute poly͑ethylene oxide͒ solutions were successfully mixed with a short flow length at a relatively fast mixing time of Ͻ10 s. Microparticle image velocimetry was employed in our investigations to characterize the flow fields. The increase in velocity fluctuation with an increase in flow rate and Deborah number indicates the increase in viscoelastic flow instability. Mixing efficiency was characterized by fluorescent concentration measurements. Our results showed that enhanced mixing can be achieved through viscoelastic flow instability under situations where molecular-diffusion and inertia effects are negligible. This approach bypasses the laminar flow limitation, usually associated with a low Reynolds number, which is not conducive to mixing.

The response amplitude and the non-dimensional frequency of flexible cylinder vortex-induced vibrations from laboratory and field experiments show significant trends with increasing Reynolds number from 103 to 2 * 105. The analysis uses complex data from experiments with wide variations in the physical parameters of the system, including length-to-diameter ratios from 82 to 4236, tension dominated natural frequencies and bending stiffness dominated natural frequencies, sub-critical and critical Reynolds numbers, different damping coefficients, standing wave and traveling wave vibrations, mode numbers from 1 – 25th, and different mass ratios.