Multifold Increases in Turing Pattern Wavelength in the Chlorine Dioxide-Iodine-Malonic Acid Reaction-Diffusion System

Turing patterns in the chlorine dioxide-iodine-malonic acid reaction were modified through additions of sodium halide salt solutions. The range of wavelengths obtained is several times larger than in the previously reported literature. Pattern wavelength was observed to significantly increase with sodium bromide or sodium chloride. A transition to a uniform state was found at high halide concentrations. The observed experimental results are qualitatively well reproduced in numerical simulations with the Lengyel-Epstein model with an additional chemically realistic kinetic term to account for the added halide and an adjustment of the activator diffusion rate to allow for interhalogen formation.

Figure 1

Method of determining wavelength from Fourier transform of CDIMA pattern. Averaged radial power $(\overline{P})$ is determined from the sum of Fourier intensity at a given radius divided by the number of points at that radius. The wavelength determined for this pattern is the reciprocal of the wave number of the peak indicated by the arrow.

Figure 2

Response of Turing patterns in the CDIMA system to addition of NaCl. Light and dark regions correspond to low and high PVA-triiodide complex concentrations, respectively. (a) Images showing response of initial pattern to concentrations of up to 400 mM NaCl. Image size is $5\times 5\mathrm{mm}$. Slices from the black line in the figure are used to construct the space-time plot in (b). (b) Space-time plot [from the diagonal line in (a)] shows how the pattern transitions as the NaCl concentration is increased.

Figure 3

Response of Turing patterns in the CDIMA system to addition of NaBr. Light and dark regions correspond to low and high PVA-triiodide complex concentrations, respectively. (a) Images showing response of initial pattern to concentrations of up to 10 mM NaBr. Image size is $5\times 5\mathrm{mm}$. Slices from the black line in the figure are used to construct the space-time plot in (b). (b) Space-time plot [from the diagonal line in (a)] shows how the pattern transitions as the NaBr concentration is increased.

Figure 4

Wavelengths of Turing patterns in the CDIMA reaction-diffusion system are altered by additions of sodium halides. (a) Semilog plot shows the ratio of wavelengths obtained at a given sodium halide feed concentration $\lambda$ and at the original pattern wavelength ${\lambda }_0$. (b) The Turing patterns corresponding to the largest wavelength patterns shown in the plot are displayed. To compare all on the same scale, these images have been processed with an adaptive threshold filter. Reactor is 25 mm in diameter.

Figure 5

Simulations with Eqs. (1) and (2) with a simultaneous increase in $c$ and $d$. Stable Turing patterns are formed in the model with parameters $d=1$, $a=12$; $s=20$; $c=0$; $b=0.36$ (a) and $b=0.30$ (b). At the times indicated by the arrows, $c$ and $d$ are increased. Image sizes are $75\times 75$ space units. (a) Space-time plot for transitions from a spot pattern with a (c, d) of (0, 1) to (0.02, 4) to (0.03, 6) to (0.12, 20) to (0.16, 30) shown with selected images immediately prior to transitions at $t=5000$, 5100, 5200, 6200 with the last image at 7200 time units. (b) Space-time plot for transitions from a stripe pattern with a (c, d) of (0, 1) to (0.02, 6) to (0.04, 8) to (0.06, 16) to (0.08, 24) shown with selected images immediately prior to transitions at $t=5000$, 5100, 5200, 6200 with the last image at 7200 time units.