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Efficient mixing at low Reynolds numbers using polymer additives

Abstract

Mixing in fluids is a rapidly developing area in fluid mechanics1,2,3, 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 regime4,5,6,7,8. 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 instability9 and to irregular flow10, with velocity spectra corresponding to the Batchelor regime4,5,6,7,8. 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 tails6,8, moments of the distribution decay exponentially along the flow8, and the spatial correlation function of concentration decays logarithmically.

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Figure 1: Experimental set-up and two snapshots of the flow.
Figure 2: Power, P, of fluctuations of velocity in the middle of the channel at N = 12 as a function of frequency, f.
Figure 3: Plots of probability density function (PDF) of the concentration of the fluorescent dye at different positions.
Figure 4: Dependence of M1 (circles) and M2 (squares) on the position, N, along the channel.
Figure 5: Correlation coefficients for the concentration as functions of the distance Δx across the channel (semilogarithmic coordinates).

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Acknowledgements

We thank G. Falkovich for theoretical guidance and discussions. The work was partially supported by the Minerva Center for Nonlinear Physics of Complex Systems, by a Research Grant from the Henry Gutwirth Fund and by an Israel Science Foundation grant.

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Correspondence to Victor Steinberg.

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Groisman, A., Steinberg, V. Efficient mixing at low Reynolds numbers using polymer additives. Nature 410, 905–908 (2001). https://doi.org/10.1038/35073524

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