Moving Walls Accelerate Mixing

Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario, the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice, several authors have found that the no-slip boundary condition at the walls of a vessel can slow down mixing considerably, turning an exponential decay into a power law. This slowdown affects the whole mixing region, and not just the vicinity of the wall. The reason is that when the ergodic mixing region extends to the wall, a separatrix connects to it. The approach to the wall along that separatrix is polynomial in time and dominates the long-time decay. However, if the walls are moving then closed orbits are created, separated from the bulk by a homoclinic orbit connected to a hyperbolic fixed point. The long-time approach to the fixed point is exponential, so we recover an overall exponential decay, albeit with a thin unmixed region near the wall.