Dependence of Turing pattern wavelength on diffusion rate

The relation between the diffusion coefficient of reactants and the wavelength of Turing patterns is examined in experiments on the chlorite–iodide–malonic acid (CIMA) reaction in gel media. The diffusion coefficients in polyacrylamide and agarose gels are varied by varying the gel densities. The diffusion coefficient D of NaCl is found to vary from 0.5×10−5 to 1.8×10−5 cm2/s for the gel conditions considered. The CIMA reactants are assumed to have diffusion coefficients that are directly proportional to that of NaCl. The wavelength λ of the observed hexagonal patterns (0.13–0.28 mm) varies in accord with the predicted relation for Turing patterns, λ∼D1/2. Moreover, the predicted relationship to a characteristic period of oscillation τ, λ=(2πτD)1/2, is supported by measurements of τ just beyond a Hopf bifurcation in a stirred flow reactor.