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A maximum entropy approach to optimal mixing in a pulsed source–sink flow
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View: Figures


Image of FIG. 1.
FIG. 1.

(a) Domain geometry and source-sink locations, with and . The source locations are indicated by and labeled and the sink locations by and . Source and sink are operated together as a pair, as are and . In the model flow each source and sink is a point located at the center of its symbol. (b) Sample streamlines generated by steady operation of source-sink pair 1. (c) Trajectory of a particle leaving at for . Circles show the locations of the particle after each pulse. This particle is extracted through during the fifth pulse and reinjected through during the sixth pulse.

Image of FIG. 2.
FIG. 2.

Poincaré sections for the pulsed source-sink flow when pair 1 is operated first in the period. If pair 2 is instead operated first, or if particle positions are recorded on the half-period, the Poincaré sections are reflected about a horizontal axis. Panels are labeled according to the value of . Initial particle locations vary between panels and are chosen to highlight island structure.

Image of FIG. 3.
FIG. 3.

(a) , the fraction of the domain area covered by the chaotic sea; (b) , the maximum Lyapunov exponent for the flow; and (c) , the maximum Lyapunov exponent for the map. Each value was obtained by following multiple initial points in the chaotic sea for or more periods.

Image of FIG. 4.
FIG. 4.

KS entropy for (a) with fluid relocation, (b) with fluid relocation, and (c) without fluid relocation, where is a dimensionless delay time between pulses. (d) The mixing rate, , from the experiments in Ref. 3 with .

Image of FIG. 5.
FIG. 5.

Portion of the Poincaré section for formed by following six particles in the bottom half of the domain for 750 periods.


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Scitation: A maximum entropy approach to optimal mixing in a pulsed source–sink flow