Growth kinetics for a system with a conserved order parameter

A theory of spinodal decomposition for an ordering system with a conserved, scalar order parameter is presented. The theory supports a scaling solution for the order parameter correlation function with a growing characteristic length given by the Lifshitz-Slyozov-Wagner growth law L∼${\mathit{t}}^{1/3}$. The structure factor satisfies Porod’s law ${\mathit{Q}}^{\mathrm{-}(1+\mathit{d})}$ at large scaled wave number Q, for spatial dimensionality d, and ${\mathit{Q}}^4$ at small wave number. This result for small Q is nontrivial. Comparison of the theory with numerical results shows good agreement for the order parameter scaling function. The theory builds on the post-Gaussian approximation scheme developed previously by the author [Phys. Rev. E 49, 3717 (1994)] for the nonconserved order parameter case. It is shown that in the lowest-order post-Gaussian approximation the unphysical result in the Gaussian theory, namely that the scaling function for an auxiliary Gaussian field is negative for small wave numbers, is remedied.