The impact of flow randomization in chaotic mixing

Chaotic advection by engineered injection and extraction (EIE) is a promising approach to enhance mixing between dissolved species in laminar flow regimes. However, the effectiveness of the chaotic mixing is often limited by the presence of Kolmogorov–Arnold–Moser (KAM) islands, coherent structures that arise around elliptic points of the flow and act as transport barriers in the otherwise chaotic system. In this work, we randomize the rotated potential mixing (RPM) flow by applying random perturbations to the two flow parameters, rotation angle and time between rotations, over time. This modification makes the flow aperiodic, resulting in a system configuration that may significantly enhance long-term mixing by eliminating all periodic points and preventing the formation of KAM islands. The analysis of the global Lyapunov exponents of the randomized RPM flow confirms that the flow stays globally chaotic despite the applied changes. Although periodic configurations with small KAM islands outperform randomized configurations for short operation times, our approach remains effective, especially if the underlying KAM islands’ structure is unknown. Applying the randomization to only one of the two flow parameters is sufficient to observe mixing enhancement, making our approach relevant for real-world systems with physical or design constraints. Considering these constructional constraints, we optimize the mixing protocol. The evidence that aperiodic chaotic flows can lead to complete mixing also has implications for other engineered and natural systems, in which periodicity is often assumed but rarely encountered in practice.     «

Chaotic advection by engineered injection and extraction (EIE) is a promising approach to enhance mixing between dissolved species in laminar flow regimes. However, the effectiveness of the chaotic mixing is often limited by the presence of Kolmogorov–Arnold–Moser (KAM) islands, coherent structures that arise around elliptic points of the flow and act as transport barriers in the otherwise chaotic system. In this work, we randomize the rotated potential mixing (RPM) flow by applying random pertu...     »