Walls Inhibit Chaotic Mixing

TL;DR

This study investigates how walls affect chaotic mixing in viscous fluids, revealing that walls cause slow algebraic decay of concentration inhomogeneity, contrasting with previous exponential decay predictions.

Contribution

The paper demonstrates experimentally and theoretically that vessel walls significantly influence mixing dynamics, leading to anomalous decay scaling in chaotic mixing of viscous fluids.

Findings

Walls cause slow algebraic decay of concentration inhomogeneity.

A simplified 1D model supports experimental observations.

Concentration distribution scalings match experimental and numerical results.

Abstract

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.