winding

Low Reynolds Number Flow Thick syrup fills the gap between two cylinders. Turn the inner one a few times and the dye smears into a spiral until it vanishes. Turn it back the same amount — and the blob reappears. With almost no inertia the flow equations are linear and run backwards perfectly; only the slow blur of molecular diffusion is not undone. The journey: Stokes dropped the ρ(∂u/∂t + u·∇u) term (1851), leaving μ∇²u = ∇p — time-symmetric. G. I. Taylor filmed the un-mixing for NCFMF in 1966. Here each dye speck rides the exact circular-Couette profile vḶ(r) = Ar + B/r, so reversing the crank reverses every path.