Spontaneous shrinkage of drops and mass conservation in phase-field simulations

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.