[katieHaylor (OP)]

Michael asks:

If you were to make a helium-air blend with just enough helium to make a balloon float, when filling balloons with this blend would the air act as a “plug” at the bottom of the balloon keeping the helium in for longer than in a 100% helium balloon? (Would it slow the escape of the small helium molecules?)

Would the gases separate in the balloon with a higher density of helium at the top of the balloon?

What do you think?

[chiralSPO]

I don't think the helium is escaping out the bottom of the balloon, it's actually diffusing right through the material of the balloon. (and the added air wouldn't separate out into the bottom, they would be thoroughly mixed)

Replacing helium with airwould change the overall rate that helium escaped (this rate is proportional to the pressure of helium in the balloon), but also less would need to leave before the balloon sank. Also, to achieve greater buoyancy, one might fill the balloon with a greater volume of the helium-air mixture than helium alone, leading to a thinner, and therefore more permeable, balloon skin.

To lengthen the liftetime of the balloon, get the thicker rubber ones or the aluminized mylar ones (more expensive, but they last much, much longer)

You can also fill the balloons with methane (natural gas). This has the drawback (or bonus!) of being flammable. But it is slightly less than half the density of air and is much slower to diffuse out of balloons.

[jeffreyH]

Correct me if I am wrong here but helium, and neon, do not form molecules.

[chiralSPO]

Yes, I think technically single atoms don't count as molecules. Honestly I don't see much point differentiating between "monoatomic molecules" and polyatomic molecules anymore than between diatomic molecules vs triatomic molecules.

[Bored chemist]

"Would the gases separate in the balloon with a higher density of helium at the top of the balloon?"
Not significantly.

[evan_au]

For long-duration balloon flights, the main problems are that:
- if you fill the balloon at ground level, when it rises high in the atmosphere, there is a large helium pressure difference between inside and outside, so helium escapes rapidly. This is solved by injecting the minimum possible helium at ground level, leaving the balloon mostly empty. The helium expands at altitude, filling the balloon.
- the Sun heats the balloon during the day, increasing the pressure and increasing the rate at which helium diffuses out of the balloon
- the balloon cools down at night, increasing in density, so the balloon loses height, and you have to inject more helium from (heavy) tanks, or drop (heavy) ballast weights. But you want the balloon to be as light as possible!

One solution was the Rozière balloon; this uses a balloon with two compartments, one of which is a helium balloon, and the other is a hot-air balloon. This allows active control of height, and the pilot can use different wind directions at different altitudes for navigation.

Another approach is to use a very tough material which minimizes helium diffusion, and pump it up to a high pressure, so it still floats, even though much of the helium has diffused out.

[alancalverd]

Exercise for the reader! Beer cans are made from 0.1 mm aluminum with a plastic coating. The diffusion of He through Al is negligible compared with balloon fabric, so how large a beer can would (a) lift its own weight and (b)lift a tonne of payload?

The answers on my old airline napkin (boy, was I bored!) suggested that a Guinness airship was  practical possibility, but I've lost the napkin!

[chiralSPO]

at 0.1 mm thickness, a Al foil would have a "density" of 270g/m²
If the balloon were spherical, then the mass of the envelope would increase as 270g/m² 4π*r² (r in meters)

If the interior of the balloon were filled with helium at STP, the internal has a density of 162g/m³, so the mass of the gas is 162g/m³ *(4π/3)*r³ where r is in meters.

The density of air is about 1200 g/m³, and the density of the balloon as a function of r (in meters) should be:

ρ = (162g/m³ *(4π/3)*r³ + 270g/m² 4π*r²)/((4π/3)*r³)
= 162g/m³ +3*(270g/m²)/(r)
This value will be less than 1200g/m³ for any r > 0.78 m (big, but not huge). This decreases to about 0.725 m if we switch to hydrogen (not important here, but see below)

For a ton of payload we have to add a term to the equation:
ρ = (10⁶ + 162g/m³ *(4π/3)*r³ + 270g/m²*4π*r²)/((4π/3)*r³)
= 162g/m³ +3*(270g/m²)/(r) + 10⁶/((4π/3)*r³)

which I don't have the patience to try for an algebraic solution to, but numerically, I say 10 m works, 8 m works, 6 meters doesn't, 7 meters works, 6.5 just works. r > 6.5 m

[alancalverd]

...which looks entirely feasible to me. Many thanks.

The joy of a spherical balloon is its inherent robustness. If it gets dented, you can pressurise it or suck out the dents quite easily, so an aluminum lighter-than-air craft could be a practicable flying machine if only it had less drag when propelled laterally, and some means of descending without losing all the helium.

The next phase, then, is to generalise the equations to a dirigible shape with neutral buoyancy and aerodynamic lift.

I often fly over the "flying bottom" https://www.hybridairvehicles.com/aircraft/airlander-10 at Cardington and wonder whether a streamlined beer can, perhaps with some rigidising creases,  might be easier to mass-produce and fly?     

[nizam]

Although a half-helium balloon floats better than a completely air-filled balloon, it will also deflate faster, based on principles governed by Graham's law, which holds that the rate at which gas escapes from a container is directly related to the molecular weight of the gas.
Because helium is so much lighter than nitrogen and oxygen, the primary components of the atmosphere, it will escape at a faster rate.
If you intend to keep your half-helium balloon airborne for a substantial length of time, you'll have to periodically replace the lost helium.