Cahn–Hilliard–Navier–Stokes diffuse interface model

Summary

The Cahn–Hilliard–Navier–Stokes model describes the flow of two immiscible incompressible fluids with an interface of small but positive thickness. A phase field $\phi$ takes values near $+1$ in one fluid and near $-1$ in the other, and it varies smoothly across the interface. The phase field evolves by the Cahn–Hilliard equation with an extra transport by the flow. The flow obeys the Navier–Stokes equations with a capillary force coming from the phase field. The model handles the breakup and merging of drops without tracking the interface explicitly; with matched densities it is known as model H.