The Soap Bubble Lifetime Bound: Drainage and Evaporation Set a Ceiling No Recipe Crosses

An upper bound on the lifetime of a plain soap-and-water bubble is computed from the two processes that thin its film. Gravity drainage, modelled with a Reynolds-type law dh/dt = -K h^3 with K = rho g/(3 mu R) and integrated from 1.0 um to a rupture thickness of 25 nm, takes 2.45e6 s at a radius of 1 cm and 4.90e7 s at 20 cm, because an h^3 law chokes as the film thins. Evaporation into still air at 20 C, from the exact diffusion solution for an isolated sphere, thins the film at a constant 21.56 nm/s at 1 cm and 50 per cent relative humidity, falling as 1/R to 1.08 nm/s at 20 cm, and dominates the thinning of any film at or below about 4 um. The combined lifetime ceiling is 45.0 s at a radius of 1 cm, 225 s at 5 cm and 901 s at 20 cm at 50 per cent relative humidity, and 28.2 s, 141 s and 564 s at 20 per cent relative humidity. Multiplying the effective viscosity by ten for surface viscosity, or by six for a 50 weight per cent glycerol solution, changes the combined lifetimes by less than one per cent, because viscosity acts only on the channel that is not in control. Long-lived bubbles of record use polymer solutions and humectants, which change the physics and lie outside the plain soap-water bound. All numbers are produced by the deposited compute.py. AI use is disclosed: drafting and computation assistance was provided by Dave, an AI system built and operated under the author's direction. The author, William Alexander Aldred, directed the work and is sole author of record.