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Chaotic mixing

by Jop - published on , updated on

Emmanuelle Gouillart, Pierre Jop, Franck Pigeonneau, Jalila Boujlel (postdoc 2013-2014), Dawn Wendell (postdoc 2011-2012)

Chaotic mixing of viscous fluids

Very viscous fluids are not easily mixed together: trying to homogenize intimately honey and sugar syrup, for instance, requires much effort! One of the reasons for this challenge is that turbulence is inexistent for such viscous flows, and the very regular velocity field doesn’t display important spatial fluctuations over a wide range of scales, that mix very efficiently in turbulent flows.

The best strategy for mixing efficiently viscous fluids is to use flows that create chaotic, that is complicated, Lagrangian trajectories. In such flows, neighboring fluid particles separate exponentially with time, hence they visit rapidly different regions of the fluid - a requirement for efficient mixing. This phenomenon is known since the 80’s as chaotic advection. Flows promoting chaotic advection allows visualization of the beautifully elongated structures of chaos directly in dye spreading experiment (see picture below). Besides all industrial processes benefiting from a better understanding of mixing, this aesthetic facet might explain partly all the enthusiasm generated by chaotic advection since 20 years!

Our work on chaotic mixing stems mostly from the following question : " How fast can you mix ? ", that is, what are the temporal dynamics of homogenizing the concentration field of a diffusive species inside a viscous fluid stirred by chaotic advection ? Needless to say, this question is of central importance for industrial processes, where one would like to predict the time needed to achieve a given quality of mixing.

Mixing of non-Newtonian fluids

Many industrial applications involve the mixing of highly viscous fluids with non-Newtonian behavior. For the same reasons explained above, the only process efficient to mix these fluids is chaotic advection. However, this mixing is far from being mastered.

Here, we focus on the chaotic mixing of viscoplastic fluids (also called yield stress fluids). The high shear localization and / or the appearance of dead zones in the mixing of these fluids may affect the velocity of the mixing by slowing the transport between the different regions of the fluid. We then seek to understand the physical mechanisms involved in this mixing and determine how the rheological properties of the fluid change the mixing characteristics.

We study this problem carrying out experiments and numerical simulations. Experimentally, we study the mixing of a transparent yield stress fluid with a blob of dye in a mixing protocol inspired by the figure-eight stirring with a rotating vessel.

Impact of the radius of the rods of agitation

We observe the effects of the yield stress in the characteristic shape of the mixing area and in the mixing rate when varying the absolute velocity of the system and the radius of the rods of agitation.

Impact of the number of period of rotation of the rods per period of rotation of the vessel

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