Fig. 4

CF size-lifetime scaling law. a Filament gap length as a function of the relaxation time. The increase of the gap length from zero marks the moment of CF disruption which we defined as lifetime τ. b Filament disruption time as a function of initial filament diameter d₀. The size-time scaling for thin filament (d₀ ≪ 10 nm, h = 10 nm) well agrees with Herring’s law \(\tau \sim d_0^4\) with a slope of 4, while, on the other hand, for thick filament (d₀ > 10 nm), the lifetime more rapidly increases with the lateral size as a stable capillary bridge is formed, marking an increase of the lifetime from microseconds to years with increasing filament diameter. Inset: snapshot of a stable capillary bridge formed from filament with initial diameter d₀ = 14 nm. The stability of this shape originates from the two principle radii of surface curvature having equal modulus and opposite signs. In the bottleneck point, the horizontal radius of the surface curve r₁ > 0, whereas the vertical radius r₂ < 0, resulting in the surface curvature κ tending to zero