Efficient mixing at low Reynolds numbers using polymer additives

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Abstract
Mixing in fluids is a rapidly developing area in fluid mechanics, being an important industrial and environmental problem. The mixing of liquids at low Reynolds numbers is usually quite weak in simple flows, and it requires special devices to be efficient. Recently, the problem of mixing was solved analytically for a simple case of random flow, known as the Batchelor regime. Here we demonstrate experimentally that very viscous liquids containing a small amount of high-molecular-weight polymers can be mixed quite efficiently at very low Reynolds numbers, for a simple flow in a curved channel. A polymer concentration of only 0.001% suffices. The presence of the polymers leads to an elastic instability and to irregular flow, with velocity spectra corresponding to the Batchelor regime. Our detailed observations of the mixing in this regime enable us to confirm several important theoretical predictions: the probability distributions of the concentration exhibit exponential tails, moments of the distribution decay exponentially along the flow, and the spatial correlation function of concentration decays logarithmically.
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