Moving walls accelerate mixing

TL;DR

Moving walls in viscous fluid mixing systems can transform slow, power-law decay of concentration profiles into faster, exponential decay by introducing closed orbits and hyperbolic fixed points, thus enhancing mixing efficiency.

Contribution

This paper demonstrates that moving or rotating walls can significantly accelerate mixing by changing the boundary conditions and the structure of the flow.

Findings

Moving walls create closed orbits that improve mixing.

Exponential decay of concentration is restored with moving walls.

Unmixed regions near the wall are minimized by wall motion.

Abstract

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 chaotic 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 moved or rotated, closed orbits appear, separated from the central mixing region by a hyperbolic fixed point with a homoclinic orbit. The long-time approach to the fixed point is exponential, so an overall exponential decay is recovered, albeit with a thin unmixed region near the wall.