Validation test (§4.1)

• 1D
• 2D

Contact angle in wetting phenomena (§4.2)

• Constant mobility
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
• Degenerate mobility
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$

Droplet merging induced by wetting phenomena (§4.3)

• Constant mobility
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
• Degenerate mobility
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$
  $\beta=\frac{4\pi}{12}$
  $\beta=\frac{5\pi}{12}$
  $\beta=\frac{6\pi}{12}$
  $\beta=\frac{7\pi}{12}$
  $\beta=\frac{8\pi}{12}$

Spontaneous shrinking of droplets and droplet collapse (§4.4)

• Supercritical case
• Subcritical case

Phase separation with well-mixed initial condition (§4.5)

• 2D
  • Constant mobility
  • Degenerate mobility
• 3D
  $t=1.5$
  $t=5.0$
  $t=10.0$
  $t=20.0$
  $t=30.0$
  $t=40.0$
  $t=1.5$
  $t=5.0$
  $t=10.0$
  $t=20.0$
  $t=30.0$
  $t=40.0$
  $t=1.5$
  $t=5.0$
  $t=10.0$
  $t=20.0$
  $t=30.0$
  $t=40.0$
  $t=1.5$
  $t=5.0$
  $t=10.0$
  $t=20.0$
  $t=30.0$
  $t=40.0$
  $t=1.5$
  $t=5.0$
  $t=10.0$
  $t=20.0$
  $t=30.0$
  $t=40.0$
  $t=1.5$
  $t=5.0$
  $t=10.0$
  $t=20.0$
  $t=30.0$
  $t=40.0$

Unconditional bound-preserving and energy-dissipating finite-volume schemes for the Cahn-Hilliard equation

Rafael Bailo · José Antonio Carrillo · Serafim Kalliadasis · Sergio P. Perez
Communications in Computational Physics, 34 (3), 2023.

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