brooksjg,
I'm not sure if you're aware of the monumental question content that you're asking.
The science of turbine cooling, alone, requires a firm understanding of the complexity of jet engine technology. The cooling air is derived from many different sources, all of which would be contaminated by the air entering the intake. As previously explained by MFgeo the volcanic particles are extremely hard; not to mention miniscule, which have abrasive qualities that are extreme. Due to the massive volume of air required by a jet engine it's not possible to filter the air entering the air intake; especially such fine particles similar to those of talcum powder!
The dammage to the compressor stage prior to the combustion process is (alone) allready contributing to a huge loss of engine efficiency. The fuel spray nozzles would very quickly become clogged, further increasing the likelyhood of flameout.
As for defining the particle count per cubic metre... where would you accurately gain such data? Risk another aeroplane incident by sending it into an ash cloud to gain such data!
Ask the crew of the BA Jakarta incident if they would again risk flying within such conditions and they would give you a resounding thumbs down. They were extremely lucky to get away with a successful landing. Were it not for the Flight Engineer continuing to make relight attempts they would have ended-up in the water; the Captain had already made the decision to ditch and the cabin crew were making those preparations to do so.
Engine technolgy has come a long way since that particular incident; however, the powers of nature are all encompassing... don't mess with volcano's!
TCF