Today's KNOWLEDGE Share : Reversible Fluid Mixing

Today's KNOWLEDGE Share

Reversible Fluid Mixing

What it shows:

Ink is squirted into a fluid and mixed in until it disappears. By precisely undoing the motions in the reverse direction, the ink becomes unmixed! The demonstration seems to defy #thermodynamics in that it appears that entropy decreases, but in actuality the reversible mixing is made possible by ensuring that the mixing/unmixing is done without turbulence.

The space between two transparent and concentric cylinders is filled with a viscous fluid (glycerine or Karo™ syrup). One or more lines of colored fluid are also injected into this fluid reservoir, parallel to the axis of the cylinder(s). When the inside cylinder is slowly rotated (by means of a crank) with respect to the outside cylinder, the lines of colored fluid become mixed with the rest of the fluid. Several revolutions renders the mixture completely clear and "mixed". If one now reverses the direction of #rotation, the colored fluid lines reappear by "#unmixing" after the same number of rotations in the opposite sense.

The design and operation of the apparatus ensures laminar flow. Diffusion processes are, of course, much much slower than the time scale of the demonstration. As one cylinder is rotated w.r.t. the other, one can simply think of layers of fluid being displaced without involving #turbulence, the boundary layer next to the inner rotating cylinder being displaced the most and the layer adjacent to the outside cylinder the least. #Counterrotation slips these layers back into place.

Setting it up:

The fluid should be of high viscosity. We have used glycerine or corn syrup. The apparatus capacity is 2.2 to 2.3 liters; thus about 5 bottles of Light Corn Syrup should suffice. It will be necessary to add some kind of preservative 1 to the corn syrup if you plan to leave it in the apparatus for extended periods. Mold does not grow in the glycerine, but glycerine costs about $50/gallon.

The #ink should have similar #viscosity to the fluid you use. A few drops of food coloring mixed into about 10 ml of fluid works well. A #verticalline" of colored fluid is squirted into the apparatus by means of a hypodermic syringe fitted with a large needle and long stainless-steel extension tube. Alternatively, a 5 ml volumetric pipette fitted with a pipette rubber squeeze-bulb also works well. After the demonstration, the dye can be thoroughly mixed (by a few dozen turns) so that the syrup (or glycerine) can be used again. This will give you many uses before you have to discard it.

References:

J.P. Heller, Am J Phys 28, 348-353 (1960). "An Unmixing Demonstration"

This reference provides the mathematical description (Navier-Stokes equations) of the mixing transformation in the geometry of the Couette viscometer, which is a similar geometry to our apparatus.

R. Brewer and E. Hahn, Scientific American, Dec 1984

Source:https://sciencedemonstrations.fas.harvard.edu

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