Intermittent flow in yield-stress fluids slows down chaotic mixing.

We present experimental results of chaotic mixing of Newtonian fluids and yield-stress fluids using a rod-stirring protocol with a rotating vessel. We show how the mixing of yield-stress fluids by chaotic advection is reduced compared to the mixing of Newtonian fluids and explain our results, bringing to light the relevant mechanisms: the presence of fluid that only flows intermittently, a phenomenon enhanced by the yield stress, and the importance of the peripheral region. This finding is confirmed via numerical simulations. Anomalously slow mixing is observed when the synchronization of different stirring elements leads to the repetition of slow stretching for the same fluid particles.

Rotation shields chaotic mixing regions from no-slip walls.

We report on the decay of a passive scalar in chaotic mixing protocols where the wall of the vessel is rotated, or a net drift of fluid elements near the wall is induced at each period. As a result the fluid domain is divided into a central isolated chaotic region and a peripheral regular region. Scalar patterns obtained in experiments and simulations converge to a strange eigenmode and follow an exponential decay. This contrasts with previous experiments [Gouillart, Phys. Rev. Lett. 99, 114501 (2007)] with a chaotic region spanning the whole domain, where fixed walls constrained mixing to follow a slower algebraic decay. Using a linear analysis of the flow close to the wall, as well as numerical simulations of Lagrangian trajectories, we study the influence of the rotation velocity of the wall on the size of the chaotic region, the approach to its bounding separatrix, and the decay rate of the scalar.

Slow decay of concentration variance due to no-slip walls in chaotic mixing.

Chaotic mixing in a closed vessel is studied experimentally and numerically in different two-dimensional (2D) flow configurations. For a purely hyperbolic phase space, it is well known that concentration fluctuations converge to an eigenmode of the advection-diffusion operator and decay exponentially with time. We illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern. We show for different physical viscous flows that, in the case of a fully chaotic Poincaré section, parabolic periodic points at the walls lead to slower (algebraic) decay. A persistent pattern, the backbone of which is the unstable manifold of parabolic points, can be observed. However, slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain, and hence delays the formation of an eigenmode until it is no longer experimentally observable. Inspired by the baker's map, we introduce a 1D model with a parabolic point that gives a good account of the slow decay observed in experiments. We derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no-slip wall.

Walls inhibit chaotic mixing.

We report on experiments of chaotic mixing in a closed vessel, in which a highly viscous fluid is stirred by a moving rod. We analyze quantitatively how the concentration field of a low-diffusivity dye relaxes towards homogeneity, and we observe a slow algebraic decay of the inhomogeneity, at odds with the exponential decay predicted by most previous studies. Visual observations reveal the dominant role of the vessel wall, which strongly influences the concentration field in the entire domain and causes the anomalous scaling. A simplified 1D model supports our experimental results. Quantitative analysis of the concentration pattern leads to scalings for the distributions and the variance of the concentration field consistent with experimental and numerical results.