Distribution of striation thicknesses in reacting lamellar systems

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Abstract
We study analytically the evolution in the structure of a reacting, nonhomogeneous system. Under incomplete mixing, the reactants often display arrays of alternating striations, whose width and structure change during the course of the reaction. The problem can be modeled using results from the theory of zero-level crossings for stationary Gaussian processes. This allows us to obtain analytical expressions for the distribution of striation thicknesses. At large times this distribution turns out to be universal, depending only on the dimensionless width ζ=x/ √8Dt . We support our findings by direct numerical simulations of the reacting system.