The open flow case

In the blinking vortex-sink chaotic open flow system we have again two qualitatively different regimes, depending on Da, with a transition at the critical value Dac 2.3. As before, for small Da the initial perturbation decays fast towards C = 0. This is, however, not followed by an homogeneous transition to the C = 1 state from the (7 0 unstable configuration. The perturbation is now completely 

In both the open and in the closed flow systems the main qualitative feature that determines the dynamics is the presence or absence of the filaments carrying the reaction products. Consequently, the observed behavior can be explained qualitatively by the reduced lamellar or filament model introduced in Sect. 2.7.1. 

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In the open flow case, the total amount of product within the mixing zone, accumulated on the unstable manifold of the chaotic saddle, can be calculated by recalling the definition of the fractal dimension Df, that states that the number of boxes of linear size w needed to cover the fractal set scales as w Df. Multiplying by the area of these... 

In the open flow case, where now the (7 = 0 state is maintained by the fluid entering through the boundaries, we also find a transition at Dac. Below the transition the perturbation is quickly diluted and the homogeneous state C = 0 is reached. For Da > Dac the growing filament develops until it covers the unstable manifold of the chaotic saddle, producing spatial structures similar to the ones obtained in the autocatalytic case. Figure 7.10 shows the total concentration established in the system as a function of Da. The large Da behavior is similar to the autocatalytic case, but the extinction transition at Dac is discontinuous. 

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