The experimental video below shows a classic fluid dynamics experiment designed to demonstrate two competing forces in action – viscous force and inertial force. The motion of fluid governed by viscous forces and inertial forces can be characterized by a non-dimensional number, the Reynolds number that is defined as the ratio of inertial to viscous forces. For highly laminar flows, corresponding to very small Reynolds numbers, i.e., values much less than 1, viscous effects dominate inertial effects. Under such a limit there is little or no small scale mixing, for example by turbulence, and flows that appear mixed can sometimes be reversed and unmixed. This is case in the following video:
Video demonstrating laminar flow filmed at the University of New Mexico – Physics Department
The video shows fluid in the annulus between two cylinders in which the inner cylinder is slowly rotated. Then the velocity of the inner cylinder is reversed. The Reynolds number within the apparatus is much lesser than one, and because of this reversal, the flow also reverses (slightly imperfectly) the apparent mixing of the dyed fluid.
Numerical animations below show one and three droplets, respectively, to demonstrate this approximate reversibility phenomenon in FLOW-3D.
Animation showing partial reversal of a single drop of fluid
Animation highlighting partial reversal of 3 droplets that get visually mixed and then un-mixed at the end of simulation
Corn syrup properties are used in the simulation because of corn syrup’s high viscosity compared to other fluids like water. The inner wall is set to have a tangential velocity magnitude of 0.05 m/s while the outer wall is fixed to imitate the motion of the experiment in the numerical simulation. The direction of tangential velocity is switched from positive to negative over a span of 1 second after 500 seconds, and is thereafter maintained at -0.05 m/s for another 500 seconds. The video on the right shows apparent mixing of the three droplets, but they are nearly reversed back to their original locations and shapes following the reversal of the flow illustrating a property of highly laminar flow.
No process in the nature is absolutely reversible. This process is not completely reversible in our simulations because of unavoidable numerical dissipation. In the real world some energy is dissipated in the form of viscous heating as layers of the fluids slide against each other. These losses are reflected in the final state of the dyes that are not completely reversed to their original location and shape.