What causes tire sealant to seal? I've heard from others that air is what causes sealant to seal. People have said they've read that "somewhere" but I never seem to be able to find those articles.

The reason I think air can't be the sole factor is that there is air inside the tires—in mountain bike tires there is a lot of it. Why wouldn't it just coagulate there? And if you say, well, over time it dries out, that's true—but a puncture doesn't take months to seal.

On top of that, I've accidentally left a bottle of orange sealant with the cap off literally for months, and there was only the barest trace of "rubbery" sealant on the threads of the cap neck.

I imagine this must have something to do with either 


the cold produced by the expanding gas coming out of a puncture, or  
the low pressure caused by the expanding gas moving rapidly (see
Bernoulli's Principle)
some other unexplained factor.


The reason I want to know is because if I knew the principle behind sealant sealing I might be able to figure out a way to prevent undetectable slow leaks, which I've been getting off and on since I switched to tubeless on my road bike.
Here's a photo of sealant failing inside a tyre.  These are the latex molecules lumping up together rather than staying in suspension in the carrier liquid which is glycol-based but varies by brand.

These have the glorious name of "boogers" and are a sign the sealant is not going to work very well.  This tyre should be cleaned out completely and a new serve of sealant added.



This is what should happen at the hole when a tyre punctures.  

The carrier is either a water-based glycol/propylene with cellulose and thickener agents like aramid/ceramic fibres, or non-water based latex mix which doesn't need extra thickeners but does have a limited effective life.  Latex also has some level of Ammonia which can contribute to corrosion.
Either product will distribute around the inside of the tyre while you ride.  This leaves a thin layer waiting just inside the area where the puncture forms.

The lighter-weight carrier fluids exit the hole along with the escaping air.  This leaves a visible wet spot on the outside.



As the carrier flows through the hole with the air, the heavier/larger suspended particles get stuck and form a blockage, which slows the air leakage and eventually seals.   In theory, the plug will flex and more air will leak, but the sealant will do the same, continuously packing into the weak spots and stopping the leak.

This only works if the sealant is liquid.  The carrier is volatile and will bleed out through your tyre over time anyway, leaving a dried mess in the tyre.  If your bike is not ridden much, the sealant will pool at the bottom and that's not a lot of use plus it will unbalance the tyre.

Many sealants can be re-energised by adding more fresh product, but mixing brands is an unknown because the chemistry will vary between brands.  Best to dismount the tyre and do a complete clean before changing brands.  Some riders recommend changing tyres every 12 months regardless of wear.