Behavior of the BZ system when the solution thickness is in the range 1.5–2.0 mm. (a) Big waves develop from the border of the reactor towards the center. (b) Rippled waves travel and make visible the underlying mosaic patterns generated by the Marangoni instabilities.
Behavior of the BZ system when the solution thickness is above3.0 mm. (a) ex = 0.025 mol , (b) ex = 0.050 mol , and (c) ex = 0.100 mol .
(a) Waves rippling and breaking into segments at ex = 0.025 mol . (b) Stack of four consecutive snapshots with a lag time of 5 s. (c) Space-time plot for the wave fragment indicated by the arrow in panel b. (d) Stack of all snapshots revealing the underneath convective structures.
(a) Waves propagating across the convective patterns at ex = 0.05 mol . (b) Space-time plot of the reactor portion along the arrow depicted in panel a.
Anti-phase convective patterns. Time between snapshots 2 s. Frame size = .
Sketch of the vertical slab considered in our model. Target waves are moving along x direction. The resulting local accumulations of the oxidised form of the catalyst trigger density gradients since the oxidized state of the solution () is denser than the reduced state (). Also, traveling waves () locally increase the surface tension of the solution at the air-solution interface with respect to reduced regions (), generating surface flows.
Stack of four snapshots describing the chemical wave dynamics when it experiences only surface flows (Ra = 0, Ma = –50). The waves, reported at intervals of 4 Model Time Units (M.T.U.), propagate from the left to the right of the spatial domain. Blue regions identify the reduced substrate where the oxidized fronts (red color) travel.
Propagating waves when Marangoni and buoyancy effect are coupled (Ma = −50, Ra = −2). Snapshots, taken at time intervals of 4 time units illustrate four salient moments featuring the superficial break of the chemical front.
Space-time plots describing the transition from deformed to segmented waves as the excitability of the system is increased, with Ma 2 and Ra 2 set to −50 and −2, respectively. Panels a and c report the spatiotemporal dynamics of the superficial concentration and the velocity field for the low excitable system . These are compared to the more excitable case , sketched in panels b (surface concentration) and d (surface function).
Resonance probability reported as a function of the chemical wavelength scaled over the horizontal spatial length (panel a) and the excitability (panel b). Both analysis show a sharp transition from deformed to segmented patterns as .
(a)–(d) Waves propagation at the surface of an open top vertical reactor when excitability is ex = 0.050 mol . Snapshots are taken every 10 s, frame area is . The arrow highlights the presence of a convective roll. (e) Space-time plot showing the dynamical behavior of thewaves along the horizontal black line depicted in panel (d). Total time is530 s.
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