Abstract
A discontinuous change in sequential velocity fields is known to generate laminar flow mixing through the mechanism of streamline crossing. However, previous research has suggested that a small degree of continuous transition between velocity fields may not necessarily be detrimental. This study therefore used a modified blinking vortex system with varying degree of continuous transition to assess the precise effect that this continuous transition has on mixing performance. This system was studied for the parameters: blinking period, vortex spacing, and the fraction of time spent in transition. Continuous Eulerian indicators were computed to investigate their correspondence with Lagrangian-based metrics, such as Intensity of Segregation, under such conditions. The results showed that up to 30% transition time yielded improvements in mixing, most notably when vortex spacing was large, and this was consistent across different time periods. The mixing prediction by the Eulerian indicators, particularly mobility, showed good agreement with actual mixing quality, albeit not perfectly, suggesting room for refinement in these metrics. Overall, the findings imply that mixing systems, such as continuous pipe flow-based devices, which are designed assuming a discontinuous change in velocity fields, might benefit from the presence of a small degree of continuous transition between discrete states.
Highlights
Since Aref’s [1] introduction of the blinking vortex system, discontinuous change in velocity fields, embedding streamline crossing, has been known to be an effective route to laminar flow mixing by chaotic advection
Mixing performance was evaluated for three parameters—continuous transition time, vortex spacing, and blinking period—which interact with one another, thereby providing different results with a different set of the parameters
Mixing analysis was conducted with continuous transition varying either μ or ν to observe their interactions and mainly focused on phenomena occurring between the fixed vortices where the essential effect of the continuously moving vortex appears to be focused
Summary
Since Aref’s [1] introduction of the blinking vortex system, discontinuous change in velocity fields, embedding streamline crossing, has been known to be an effective route to laminar flow mixing by chaotic advection This discontinuous property has been studied in other systems such as a partitioned pipe mixer [2,3,4,5], a twisted pipe [6,7], a mixer using helical geometry [8,9,10], etc. The fluids are mixed by axially superimposed streamlines and by the baker’s transform, which squeezes/stretches fluid material elements and cuts and stacks them to create additional layers of the different fluids [11] This device was studied further by bifurcation analysis [3], as a generalised partitioned pipe mixer [4], and as a partitioned pipe mixer with a barrier embedded, under different rotation protocols [5]. Jen et al [7] tested twisted microchannels in T-shaped mixers from the assumption that
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