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Chemical patterns in translating vortices: Inter- and intra-cellular mixing effects
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10.1063/1.4807619
/content/aip/journal/chaos/23/2/10.1063/1.4807619
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/2/10.1063/1.4807619
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(a) Schematic diagram of the VFR with translating vortices. The box in the centre of the right-hand annulus of the VFR indicates the region selected for averaging and plotting the space-time plots. (b) Space-time plot of FDO patterns at  = 11.6 cm s and  = 1 Hz. (c) Expanded view of the region highlighted by the box at . 2000 s and 40 cm on the space-time plot (b), showing the complete width of the VFR and a single FDO band.

Image of FIG. 2.
FIG. 2.

((a)–(d)) Space-time plots illustrating modes of pattern formation at rotation rates of  = 1 Hz and  = 2.5 Hz and flow rates of  = 11.6 cm min and  = 13.6 cm min.

Image of FIG. 3.
FIG. 3.

(a) Phase diagram of patterns observed as function of flow and rotation rates. The arrow indicates the transition from lower to higher γ values and the dashed lines separate the regions of different behavior. (b) Plot of the average distance between stable FDO bands against flow rate for  = 1.5 Hz (---),  = 2 Hz (), and  = 2.5 Hz (—).

Image of FIG. 4.
FIG. 4.

Digital photographs of the second FDO band from the inlet at Q = 11.6 cm min and for increasing rotation rate:  = 1 Hz (a),  = 1.5 Hz (b),  = 2 Hz (c), and  = 2.5 Hz (d). The dimension of one vortex pair, , is indicated in (a). Color figures are available online.

Image of FIG. 5.
FIG. 5.

Sketch of two-zone reaction cells (E = outer zone and C = core zone) and processes used in the model.

Image of FIG. 6.
FIG. 6.

Phase diagram of chemical patterns with scaled flow rate (1/) and scaled inter-cellular exchange rate (1/) when there is no mass transfer between E and C. Red circle = FDOs, left-pointing triangle = CI-FDO, and right-pointing triangle = AI. The space-time plots (50 cells × 250) show pattern formation when 1/ = 1 and 1/ = (a) 0 (FDO); (b) 0.5 (CI-FDO); and (c) 0.7 (AI). The grayscale corresponds to concentration of with white = 0.35.

Image of FIG. 7.
FIG. 7.

Simulated space-time plots showing the critical dispersion rate 1/ for the appearance of convective and absolute instabilities at different intra-cellular exchange rates, . The scaled flow rate, 1/, was 1.

Image of FIG. 8.
FIG. 8.

Simulated space-time plots showing the effect of increasing flow rate and inter-cellular exchange rate on the patterns at two different intra-cellular exchange rates.

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/content/aip/journal/chaos/23/2/10.1063/1.4807619
2013-05-23
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Chemical patterns in translating vortices: Inter- and intra-cellular mixing effects
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/2/10.1063/1.4807619
10.1063/1.4807619
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