Unmixing a mixture

In the comments to the post of weird fluids, Jared A mentioned seeing a demonstration in which a fluid was first stirred so that two colors became mixed and then, when the direction of stirring was reversed, the liquid became ‘unmixed’ so to speak.

Intrigued, I looked into it and found this video that demonstrates something similar to what he had likely seen.

How is this possible? It illustrates an interesting point about reversibility and irreversibility in the laws of physics. At the microscopic level, the laws of physics are reversible so that reversing the cause will reverse the effect. But when many particles are involved, as is the case with fluids at the macroscopic level, the interactions between the molecules become so complex that you cannot reverse the motions of all the constituent particles and so unmixing is not possible in any practical sense although theoretically not forbidden.

But under certain conditions, such as by constraining fluid of a certain viscosity between two cylinders so that you have close to a two-dimensional fluid, normal chaotic perturbations can be minimized and unmixing achieved. This was first demonstrated as far back as in 1966.

In the journal Nature, Troy Shinbrot discusses a 2005 paper titled Chaos and threshold for irreversibility in sheared suspensions that studies the phenomenon in some detail to determine the conditions under which this occurs.

Incidentally, one has to be always careful with such videos and look for signs that the effect was not obtained by simply running the video backwards, as done by the Mythbusters guys ‘solving’ Rubik’s cube blindfolded and with their feet. There are people who can actually do this, but the Mythbusters were pulling our legs.


  1. says

    That is rather odd, but it makes some intuitive sense under the understanding that certain types of fluids don’t mix significantly under ordinary conditions. Perhaps the most obvious example is most oils and water, where you can stir the two together as much as you like and they will still ultimately separate. This dye-like substance refusing to mix due to viscosity and a relative pressure equilibrium as opposed to distinct densities and intermolecular forces makes for a more impressive demonstration — if only because we’ve all seen the other many times before.

  2. Jared A says

    Yes, that is the effect I was talking about! Actually, the version I saw was much smaller and there was only one type of dye, but even so it is jaw-dropping when you see it in person.

    Fluid dynamics is never something I learned, but I guess there’s something about the two cylinder topology that minimizes eddy currents perpendicular to the torus (maybe related to the hairy ball theorem?). Thus, you have control over the primary convection mode, and can make it go back and forth at will.

    In a standard setup n there are chaotic eddy currents so that it looks enough like diffusion (which is irreversible, isn’t it?) to the human eye that we forget that that diffusion is a much, much slower process. With this idea in mind, you get tricked into thinking entropy is being reversed, but really that’s not what’s going on at all!

  3. Jared A says

    If I recall correctly, this works regardless of the miscibility of the dye and the medium. So actually it is not “refusing to mix”. In general viscosity is not correlated with miscibility.

  4. eigenperson says

    The reason the fluid can be “unmixed” is that it was never mixed.

    When the inner cylinder is rotated, the fluid near it moves faster than the fluid further away, in a roughly linear fashion. As a result, the drops are distorted into streaks, with the inner portions of the streaks moving farther around the cylinder than the outer portions. However, at no point do the streaks actually mix with each other.

    As the cylinder is rotated further, the streaks become spirals — but they are non-intersecting spirals. At no point do the different dyes ever come into contact with each other.

  5. Jared A says

    True, that’s what I was trying to say about the trick your mind plays on you. In my original comment I tried to use the word “stirred” instead of mixed to avoid this confusion, but I may have “mixed it up”.

  6. eigenperson says

    Hmm, I hadn’t seen your earlier post.

    There are actually two dimensionless quantities that need to be low for this to work. The first is the Taylor number (in the interest of not trying to figure out how to write greek letters I’ll just recommend Wikipedia for the formulae) and the second is the Reynolds number.

    The Taylor number is specific to fluid flow between coaxial cylinders. If the Taylor number is above a critical value the flow is no longer circumferential (vortices would develop), but could potentially remain steady. Unfortunately, I don’t think this flow regime would be reversible (at least not without a lot of care) because it might be too sensitive to the speed at which the cylinder is rotated. I’m not sure.

    The Reynolds number is not specific to this apparatus. If the Reynolds number is above a critical value (in reality there is a transition range), turbulence develops and the entire thing becomes chaotic and irreversible. (The critical Reynolds number depends on the setup and I am not sure what the critical Reynolds number is for this system.)

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