(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 Q = 11.6 cm3 s−1 and ω = 1 Hz. (c) Expanded view of the region highlighted by the box at circa. 2000 s and 40 cm on the space-time plot (b), showing the complete width of the VFR and a single FDO band.
((a)–(d)) Space-time plots illustrating modes of pattern formation at rotation rates of ω = 1 Hz and ω = 2.5 Hz and flow rates of Q = 11.6 cm3 min−1 and Q = 13.6 cm3 min−1.
(a) Phase diagram of patterns observed as function of flow and rotation rates. The arrow indicates the transition from lower to higher γRe 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 ω = 1.5 Hz (---), ω = 2 Hz (···), and ω = 2.5 Hz (—).
Digital photographs of the second FDO band from the inlet at Q = 11.6 cm3 min−1 and for increasing rotation rate: ω = 1 Hz (a), ω = 1.5 Hz (b), ω = 2 Hz (c), and ω = 2.5 Hz (d). The dimension of one vortex pair, λ, is indicated in (a). Color figures are available online.
Sketch of two-zone reaction cells (E = outer zone and C = core zone) and processes used in the model.
Phase diagram of chemical patterns with scaled flow rate (1/Da) and scaled inter-cellular exchange rate (1/PeDa) 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/Da = 1 and 1/PeDa = (a) 0 (FDO); (b) 0.5 (CI-FDO); and (c) 0.7 (AI). The grayscale corresponds to concentration of v with white = 0.35.
Simulated space-time plots showing the critical dispersion rate 1/PeDa for the appearance of convective and absolute instabilities at different intra-cellular exchange rates, K e. The scaled flow rate, 1/Da, was 1.
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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