Cell-spacing selection in directional solidification is investigated. An integral equation describing steady-state cells in the limit where the solute diffusion length is much larger than the cell spacing is derived and solved numerically by Newton's method. With surface tension and no crystalline anisotropy present the spatial periodicity of a one-dimensional array of cells with cusp singularities is found to be determined uniquely by a solvability condition. The inclusion of crystalline anisotropy has no other effect to shift the value of the selected spacing.
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Alain Karma (1986) studied this question.
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