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Tham khảo tài liệu 'understanding non-equilibrium thermodynamics - springer 2008 episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 168 6 Instabilities and Pattern Formation Fig. 6.14 Spatial structure in Belousov-Zhabotinsky reaction leopard tail or biological morphogenesis has been a subject of surprise and interrogation for several generations of scientists. The question soon arises about the mechanism behind them. In 1952 Turing proposed an answer based on the coupling between chemical reactions and diffusion. As an example of a Turing structure let us still consider the Brusselator but we suppose now that the chemical reaction takes place in a unstirred thin layer or a usual vessel so that spatial non-homogeneities are allowed. The basic relations are the kinetic equations 6.67 and 6.68 to which are added the diffusion terms DxV2X and Dy V -y respectively it is assumed that the diffusion coefficients Dx and Dy are constant. By repeating the analysis of Sect. 6.5.1 it is shown that the stationary homogeneous state becomes unstable for a concentration B larger than the critical value Bc k kk A2 k ljL Dx Dy j 0.1-2- 6 at the condition that the diffusion coefficients are unequal if Dx Dy diffusion will not generate an instability l is a characteristic length. Nonhomogeneities will begin to grow and stationary spatial patterns will emerge in two-dimensional configurations. A rather successful reaction for observing Turing s patterns is the CIMA chlorite-iodide-malonic acid redox reaction which was proposed as an alternative to BZ reaction. The oscillatory and space-forming behaviours in CIMA are made apparent through the presence of coloured spots with a hexagonal symmetry. By changing the concentrations new patterns consisting of parallel narrow stripes are formed instead of the spots see Fig. 6.15 . Although it is intuitively believed that diffusion tends to homogenize the concentrations we have seen that when coupled with an autocatalytic 6.6 Miscellaneous Examples of Pattern Formation 169 Fig. 6.15 Examples of Turing two-dimensional structures from Vidal et al. 1994 reaction under far from
