Eulerian indicators for predicting and optimizing mixing quality

Many different methods exist for measuring, quantifying and predicting the quality of a mixture resulting from a fluid mixing device. In general, these rely on Lagrangian information from the system, as they involve the evolution of individual trajectories. In this paper, we propose tools that are formulated using only Eulerian information, and yet can predict the Lagrangian mixing properties of a mixing device. The proposed Eulerian indicators are motivated by the recent linked twist map (LTM) formulation of fluid mixing. We describe their features and application in the context of four different fluid flows: the blinking vortex flow and the partitioned pipe mixer (two paradigm flows from the early studies of chaotic mixing), a model of a channel flow containing 'separatrices' in the cross-sectional flow (which is a common flow feature in a large number of micromixers), and a flow generated by pulsed source–sink pairs (which has been used as a model for mixing in DNA microarrays).