DISSIPATIVE STRUCTURES IN A REACTION-DIFFUSION SYSTEM

KIM SH; YEO SC

Korean Journal of Chemical Engineering, Vol.7, No.3, 188-197, July, 1990

A transient analysis of reaction-diffusion equations associated with the model reaction of Prigogine and Lefever(Brusselator model), has been performed. For low system lengths and for fixed boundary conditions, steady state solutions with the low amplitude are unstable. For zero flux boundary conditions the multiplicity of symmetric solutions with the same wave number may exist and the majority of them are unstable. The diffusion of initial components induces relaxation oscillations the spatial profiles result in single or multiple propagating fronts. High system lengths for both zero flux and periodic boundary conditions, may give rise to a multipeak incoherent wave pattern. For periodic boundary conditions the multiplicity of waves has been observed. Numerical simulation of two-dimensional spatial structures reveals the existence of certain similarities between the one- and two-dimensional cases.

[References]

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[1] Herschkowitz-Kaufman M, Bull. Math. Biol., 37, 589 (1975)

[2] Ortoleva P, Ross J, J. Chem. Phys., 60, 5090 (1974)

[3] Nicolas G, Erneux T, Herschkowitz-Kaufman M, Adv. Chem. Phys., 38, 263 (1978)

[4] Nicolis G, Prigogine I, Self Organization in Non-Equilibrium Systems, John Wiley, New York (1977)

[5] Nicolis G, Prigogine I, J. Chem. Phys., 46, 3542 (1967)

[6] Kubicek M, Ryzler V, Marek M, Biophys. Chem., 8, 235 (1978)

[7] Prigogine I, Lefever R, J. Chem. Phys., 48, 1695 (1968)

[8] Kim SH, Yang J, Korean J. Chem. Eng., 6, 165 (1989)

[9] Evans DJ, Mathematics and Computers in Simulation XXI, 270 (1979)

[10] Hlavacek V, Janssen R, Van Rompay P, Z. Naturforsch., 37A, 39 (1982)

[11] Hlavacek V, Kubicek M, Chem. Eng. Sci., 26, 1737 (1971)

[12] Pismen LM, Phys. Rev., A, 23, 334 (1981)

[13] Vafek O, Pospisil P, Marek M, Scientific Papers of the Prague Institute of Chemical Technology, K14, 179 (1979)

[14] Herschkowitz-Kaufman M, Nicolis G, J. Chem. Phys., 56, 1890 (1972)

[15] Ortoleva P, Ross J, J. Chem. Phys., 63, 3398 (1975)

[16] Brown KJ, Eilbeck JC, Bull. Math. Biol., 44, 87 (1982)