Helium Balloon 3D: Buoyancy & Slow Deflation

Balloon

Balloon radius 11 cm

Latex thickness 0.20 mm

Initial helium purity 95%

Environment

Ambient temperature 20 °C

Time compression 600×

Click the balloon itself to release or re-tether it. "Clip weight" adds a small paperclip to the string — find how much it takes to ground a balloon that still has plenty of helium.

Live Readouts

Helium purity inside

95.0%

Net lift force

0.00 N

Height

0.0 m

Elapsed (real)

0.0 h

Status

Tethered

Volume vs. full

100%

The real physics

Two independent real effects run at once. Buoyancy is plain Archimedes: the net upward force on the balloon is the weight of the air it displaces minus the weight of the balloon-plus-gas system, F = (ρ_air − ρ_gas,inside)·V·g − m_latexg. Deflation is Fickian permeation through the latex membrane: each gas species leaks through at a rate set by that gas's own permeability, the membrane's surface area and thickness, and the partial-pressure gradient across it, dn/dt = −(Permeability/thickness)·A·Δp. Helium's small, non-polar molecule diffuses through rubber roughly an order of magnitude faster than N₂/O₂, so helium leaves much faster than ambient air diffuses in to replace it — the balloon slowly shrinks and its internal gas mix dilutes toward ordinary air, which raises ρ_gas,inside and kills the lift long before all the helium is gone.

F_net = (ρ_air − ρ_gas)·V·g − m_balloon·g
dn_He/dt  = −k_He(T)/thickness · A · p_He,inside
dn_air/dt = +k_air(T)/thickness · A · (p_atm − p_air,inside)   [k_air ≈ k_He/9]

Radius / thickness set surface area and membrane resistance — a bigger, thinner balloon deflates faster per the same purity. Purity sets how much trapped air already dilutes the fill at t = 0. Temperature raises both ambient air density (Archimedes term) and the diffusion rate (permeability rises with temperature). Time compression only speeds up the diffusion clock — real deflation takes many hours — the buoyant rise/fall itself still plays out at its own real dynamic timescale.

Balloon (helium + air mix) String / weight clip

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