Ever shake your BBQ propane tank? The propane is sloshing around but it does not quite feel like a tank of water. It's more mushy somehow. A glass pressurized container would be interesting to see what is happening inside. maybe there is a you tube on that...
I cannot tell you about what is all going on inside a paint container, but I think what you describe is pretty good. However, I can tell you exactly what is happening inside the propane tank. I have done what you are wondering about and much much more.
Without getting too complicated, propane is a hydrocarbon that is a gas at standard atmospheric temperature and pressure - each molecule of that propane is a combination of three carbon atoms and eight hydrogen atoms - C3H8.
The equilibrium vapour pressure of propane varies quite significantly with temperature. The higher the temperature, the higher the pressure. At normal temperatures, a pressure vessel is required. The lower the temperature, the lower the pressure. In fact, at -45, you can carry propane around in a pail and it looks and sloshes around a lot like water. At first, it will boil a little. But that isn't the propane, that is the butane and other gasses boiling off that are in there too. When they are gone, all that is left is liquid propane and other lower pressure molecules.
C3H8 Propane is a much bigger molecule than H2O water. Even though it is much bigger, it is much lighter than water. Basically, the individual molecules are much further apart - which has a lot to do with its higher vapour pressure too. In fact, a pail of liquid propane weighs about half of what a pail of liquid water weighs.
Now, to answer your question. When you agitate a container of propane you add energy and because the propane is in a state of perfect balance between gas and liquid, it starts to boil a bit and all the gas and liquid mixes more readily than water does because its so much lighter. Basically, it foams easier and forms a foamy mixture. The pressure goes up a tiny bit (hard to even measure) but it's enough to maintain the higher gas liquid ratio until it settles back down to a more stratified equilibrium of liquid at the bottom and gas at the top.
It's worth adding here that the other stuff in there (butane etc) can change that behaviour a fair bit. So your propane bottle may not act exactly like mine.
Also, it very much depends on how full the container is. A full container (about 80%) cannot foam as much as a nearly empty one can.
Note - The industry tried unsuccessfully to get standards for propane. But as far as I know it never happened. So nobody can predict exactly what is all in there - and it can include some very nasty stuff....
In essence, what you perceived is correct. But it's better to call it foam than slush.
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