Carbonation Conelius barrels
Carbonation
Because the barrel is rarely filled completely, there is a small pocket of gas at the top of the barrel. When the barrel is pressurized from the gas cylinder, the gas collects in the small pocket and the pressure builds up. The carbon dioxide gas in the pocket gradually migrates into the beer and the gas pressure in the pocket drops. How much carbon dioxide can be dissolved in the beer depends on the pressure in the pocket. If the pressure in the pocket is too low, the carbon dioxide instead migrates from the beer and up into the pocket. At equilibrium, the pressure in the gas pocket corresponds to the amount of carbon dioxide in the beer. The values ​​stated, e.g. 1.1 bar for lager beer, apply to the equilibrium state and before this has been reached, i.e. enough gas has migrated from the pocket into the beer, you must constantly refill with gas.

The temperature affects how easily the gas dissolves in the beer. The colder the easier, i.e. if you keep the beer cold, you don't need to have such a high pressure in the gas pocket. If 1.1 bar is enough at 5 degrees, 1.4 bar is needed at 10 degrees and somewhere around 2.7 at 25 degrees.

If you connect a gas cylinder with a regulator set to the correct pressure, it will take a couple of days before equilibrium is reached. If you want to speed it up, you can, for example, roll the keg back and forth so the gas quickly sloshes down into the beer.

So:

If the pressure above the beer is high, carbon dioxide migrates into the liquid.
If the pressure above the beer is low, carbon dioxide migrates out of the liquid.
It takes a while before enough carbon dioxide gets down into the beer, i.e. equilibrium is reached, and during that time gas must be refilled.
Draft beer tap
The beer with its carbonic acid is now in equilibrium in the keg. The pressure in the keg is higher than outside the keg. As soon as the beer comes out of the keg, equilibrium no longer exists, but the carbon dioxide wants to migrate from the beer into gaseous form. If the pressure change is rapid, or if the beer splashes into the glass, or if there is dirt or other particles in the glass, all of this helps to cause the dissolved gas to rise into the air, i.e. the beer foams.

The most common reason why beer foams too much is too rapid a pressure drop. 2 dm tapping hoses cause normally carbonated beer to foam unfailingly. The usual thing to do is to lower the pressure before tapping and then restore the pressure to equilibrium pressure. Another (better?) alternative is to increase the hose length so that the resistance in the hose provides sufficient pressure drop and the beer comes out of the tap nicely and nicely. A tap system in the home bar can be tuned in this way so that the kegs can maintain the correct pressure and the flow from the tap is still correct.

The resistance in PE hose with an outer diameter of 1/4" (6.35 mm) is approximately 0.15 bar/meter, i.e. to compensate for 1 bar in the keg, 6-7 meters of hose are needed. (1 bar / 0.15 bar/m = 6.7 m). PE hose with an outer diameter of 3/16" (4.8 mm) has a resistance of approximately 0.5 bar/meter, i.e. 2 meters of hose for 1 bar. If there is a height difference between the keg and the tap, this also slows down - approximately 0.1 bar per meter. The basic principle of a trimmed bar is that height resistance + hose resistance should correspond to the storage pressure in the keg. When serving, a small excess pressure is applied that gives a suitable jet from the tap.

Bottle filling
To get beer from the keg into a bottle without foaming, you can use a bottle filler. There are counter-pressure fillers and bottle fillers that work without counter-pressure, such as the Blichmanns Beergun. Both types of bottle fillers require that the beer has already been carbonated in a pressure vessel (e.g. a Cornelius keg).

Counter-pressure fillers pressurize the empty bottle so that the bottle maintains the same pressure as the beer flowing into the bottle - no carbon dioxide wants to give up as a gas. The beer flows from the keg to the bottle either by natural gravity, i.e. the bottle is held lower than the keg - or by carefully lowering the pressure in the bottle and letting the excess pressure push the beer over to the bottle.

Beergun is based instead on:

using cold beer (approx. 0-1 °C),
lowering the pressure in the cornelius keg immediately before bottling to approx. 0.1-0.2 bar
filling the beer into chilled bottles
With Beergun, it is possible to press a little carbon dioxide into the bottle before the beer begins to be filled, which reduces the risk of oxidation and thus gives the beer a better shelf life in the bottle.