The reversibility of laminar mixing often comes as a surprise to observers accustomed to the experience of being unable to separate two fluids after they’ve been combined. As you can see above, however, inserting dye into a highly viscous liquid and then mixing it by turning the inner of two concentric cylinders can be undone simply by turning the cylinder backwards. This works because of the highly viscous nature of Stokes flow: the Reynolds number is much less than 1, meaning that viscosity’s effects dominate. In this situation, fluid motion is caused only by molecular diffusion and by momentum diffusion. The former is random but slow, and the latter is exactly reversible. Reversing the rotation of the fluid undoes the momentum diffusion and any distortion remaining is due to molecular diffusion of the dye.
Reversing a Flow
