Cahn–Hilliard equation - Wikipedia

The Cahn–Hilliard equation (after John W. Cahn and John E. Hilliard)[1] is an equation of mathematical physics which describes the process of phase separation, spinodal decomposition, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. If 𝑐 is the concentration of the fluid, with 𝑐 = ± 1 indicating domains, then the equation is written as where 𝐷 is a diffusion coefficient with units of Length 2 / Time and 𝛾 gives the length of the transition regions between the domains. Here ∂ / ∂ 𝑡 is the partial time derivative and ∇ 2 is the Laplacian in 𝑛 dimensions. Additionally, the quantity 𝜇 = 𝑐 3 − 𝑐 − 𝛾 ∇ 2 𝑐 is identified as a chemical potential. Related to it is the Allen–Cahn equation, as well as the stochastic Allen–Cahn and the stochastic Cahn–Hilliard equations. Of interest to mathematicians is the existence of a unique solution of the Cahn–Hilliard equation, given by smooth initial data. The proof r

Cahn–Hilliard equation - Wikipedia Jump to content From Wikipedia, the free encyclopedia Description of phase separation The Cahn–Hilliard equation (after John W. Cahn and John E. Hilliard ) [ 1 ] is an equation of mathematical physics which describes the process of phase separation, spinodal decomposition , by which the two components of a binary fluid spontaneously separate and form domains pure in each component. If c {\displaystyle c} is the concentration of the fluid, with c = ± 1 {\displaystyle c=\pm 1} indicating both domains, then the equation is written as ∂ c ∂ t = D ∇ 2 ( c 3 − c −

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