banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Chemical patterns in translating vortices: Inter- and intra-cellular mixing effects
Rent this article for
View: 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.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Chemical patterns in translating vortices: Inter- and intra-cellular mixing effects