An Explicit Form of the Equation of Motion of the Interface in Bicontinuous Phases.

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  • Tomita Hiroyuki
    Department of Fundamental Sciences, Faculty of Integrated Human Studies Kyoto University, Kyoto 606–8501, Japan

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  • Explicit Form of the Equation of Motion of the Interface in Bicontinuous Phases

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The explicit form of the interface equation of motion derived assuming a minimal surface is shown to be applicable to more general bicontinuous interfaces that appear in the late stage of the spinodal decomposition of binary mixtures. The derivation is based on a formal solution of the simple-layer integral equation for the Dirichlet problem of the Laplace equation with an arbitrary boundary surface. It is shown that the assumption of a minimal surface used in the previous linear theory is not necessary, but the bicontinuous nature of the interface is the essential condition required for us to rederive the explicit form of the equivalent simple layer. The derived curvature flow equation has a phenomenological cutoff length, i.e., the `electro-static' screening length introduced in the previous work. This screening length is related to the well-known scaling length characterizing the spatial pattern size of a homogeneously growing bicontinuous phase. The corresponding equation of the level function in this scheme is given in a one-parameter form also.

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