Yue, P., Zhou, C., & Feng, J. J.
J. Comput. Phys. 223, 1-9 (2007)
Abstract - In this note we examine the
implications of Cahn-Hilliard diffusion on mass conservation when using
a phase-field model for simulating two-phase flows. Even though the
phase-field variable φ is conserved globally, a drop shrinks
spontaneously while φ shifts from its expected values in the bulk
phases. Those changes are found to be proportional to the interfacial
thickness, and we suggest guidelines for minimizing the loss of mass.
Moreover, there exists a critical radius below which drops will
eventually disappear. With a properly chosen mobility parameter,
however, this process will be much slower than the physics of interest
and thus has little ill effect on the simulation.