A Two-Cell Interface Loses 39% of Its Surface Tension — The Anisotropy of the Korteweg Stress
Across a flat liquid–vapor interface the normal pressure stays constant and only the tangential pressure dips. That dip is surface tension, and a dz=1 lattice loses up to 39% of it.
I asked for σ₁₂ = 1.00 and got 0.78 — where an absent phase leaks into the interface in three-component Allen–Cahn
Fixing Σc = 1 with a mean projection in three-component Allen–Cahn lets the absent phase leak into the interface and cuts the realized surface tension by 21.9%. A triple-well penalty closes the gap.
Raising the time step 5x ran 1.9x faster; 10x ran no faster at all — the window implicit surface tension opens
At density ratio 1000, raising the capillary step 5x ran 1.9x faster. Pushing to 10x did not. Janodet et al. (2025) measured both walls.
Why a Droplet at Rest Starts to Flow — Parasitic Currents and Well-Balanced Surface Tension
A 3% curvature error drives the residual to 4.8e5, while exact curvature leaves it at 4.1e-10. That gap is the parasitic current.
Why Droplet Simulations Get Trapped by Δt — Solving Surface Tension Implicitly
From N=64 to N=256, dt_sigma falls by 8. omega*dt_sigma stays 2.221 on every mesh, and explicit integration breaks past about 0.9 dt_sigma.
Why Droplets Are Round and Water Climbs the Glass — Surface Tension and Contact Angle
A 5 µm droplet shows a 28800 Pa pressure jump, and a 0.1 mm tube at 30 degrees lifts water 127.1 mm under Jurin's law here.