Cahn-Hilliard equation Totally Explained

Everything about The Cahn-hilliard Equation totally explained

The Cahn-Hilliard equation is an equation of mathematical physics which describes the process of phase separation, 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=pm1

indicating domains, then the equation is written as ť

frac=0

When one phase is significantly more abundant, the Cahn-Hilliard equation can show the phenomena known as Ostwald ripening, where the minority phase forms spherical droplets, and the smaller droplets are absorbed through diffusion into the larger ones. The Cahn-Hilliard equations finds applications in diverse fields: in interfacial fluid flow, polymer science and in industrial applications. Of interest to researchers at present is the coupling of the phase separation of the Cahn-Hilliard equation to the Navier-Stokes equations of fluid flow.

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