Young's law predicts the contact angle of a liquid droplet resting on a surface: the angle where liquid, solid, and vapor meet is determined by the balance of surface tensions. The law is a cornerstone of wetting theory, derived from force balance at the contact line. It applies whenever the dominant physics is capillary — surface energy minimization with no other long-range interactions.
Goldman, Novaga, and Prade (arXiv:2603.24483) ask what happens when the droplet is electrically charged. In their variational model, a two-dimensional droplet minimizes a functional that includes perimeter (surface tension), a substrate adhesion energy, and a nonlocal Coulomb repulsion term representing the electrostatic self-energy of the charge distribution. The droplet is constrained to be convex.
For small charges, Young's law survives. The contact angle adjusts but the classical relationship between surface energies and angle holds. The proof establishes that the minimizing shape remains a circular arc meeting the substrate at the angle predicted by the surface tension balance, with the charge contributing a perturbative correction.
But the result is explicitly limited to small charges. The authors don't prove Young's law fails at large charge — but they don't prove it holds, either. The convexity constraint keeps the droplet from developing the instabilities (Taylor cones, charge-driven fingering) that real charged droplets exhibit. Within the convex regime, geometry dominates; at some threshold, electrostatics must win.
The structural point is that classical geometric laws often hold in regimes where additional physics is present but weak. Young's law doesn't require the absence of charge — it requires that charge be subordinate to surface tension. The law is not a statement about capillarity alone but about the dominance regime of capillarity. When the auxiliary physics grows strong enough, the geometric law breaks, and the contact angle becomes a function of something Young never considered.