Curvature-dependent contact-angle errors in a static phase-field lattice Boltzmann model

In the present study, a static D2Q9 Cahn–Hilliard lattice Boltzmann benchmark has been developed to quantify equilibrium contact-angle and liquid-area errors on convex and concave circular boundaries. Intentionally, momentum transport is suppressed to isolate the compound effect of geometric wetting, ghost-node extension, curved-wall reconstruction, and normal-based angle measurement from the hydrodynamic influences. The bulk formulation reproduces the analytical hyperbolic-tangent profile; increasing the interface thickness from 𝜉 = 2 to 5 reduces the normalized 𝐿 2 and maximum chemical-potential residuals by factors of 6.2 and 5.8 in sequence. For a planar wall, the contact angle is underpredicted by 0.4° at 𝜃 s e t = 3 0 ° and by 6.0° at 𝜃 s e t = 1 5 0 ° . In the concave cavity, 74 of 75 cases (98.7%) yield positive errors, with an estimated maximum hitting 21.8°; the only negative error is −2.0° at 𝑅 / 𝛥 ⁢ 𝑥 = 3 6 , 𝜉 = 4 , and 𝜃 s e t = 6 0 ° . For the convex cylinder, the 30° cases remain positively biased, with errors of approximately 8°–16° over the investigated parameter range, whereas intermediate and obtuse angles are predominantly underpredicted. The maximum relative liquid-area drift is 4 . 8 5 × 1 ⁢ 0 − 2 for the concave geometry and 1 . 8 × 1 ⁢ 0 − 2 for the convex geometry. Neither signed contact-angle error nor relative liquid-area drift collapses uniquely with the curvature Cahn number ( C n = 𝜉 / 𝑅 ), demonstrating non-monotonic relationships of curvature sign, wall radius, interface thickness, and prescribed wettability.