....not much accumulations are found within the engine. The coarse stuff hugs the outer walls and goes out the rear after slowly eroding blades. The fine stuff flows freely through the cooling holes and finally ends up out the rear of the engine. The in-between stuff either dirt or ash may get stuck in the cooling holes....
So: there are two completely different situations:
1 - where there's enough VA (especially large particles) coming through the combustion chamber, getting hot enough to melt and coat the first stage blades and vanes with a layer of glass-like material, and therefore cause rapid blade failure and/or the engine actually stopping due to disruption of gas flows. No-one has yet identified (here, at least) a ball-park figure for ash density where this starts to be a possibility but it seems that it's going to be at least one, if not two, orders of magnitude greater than the current Black area average.
2 - where there's NOT enough VA melted inside the combustion chambers to permanently coat blades to a dangerous level and any VA that goes through the cooling system is fine enough to go through and not get stuck inside galleries or holes. From what has been discussed here,
unless an engine has already been exposed to a lot of VA, any ash that does get into the cooling system will not go above its melting point (ie. the cooling system will still be doing its job!) and will therefore continue through the blade holes and slots, and out the back with relatively little effect.
Given the nature of the current Iceland eruption, the VA particles will be very small (otherwise they wouldn't float around for so long). If / when the ice and water around the vents and leaking into the volcano has mostly gone, any VA particles still being formed will be much larger and will therefore fall to ground / sea much more quickly and become of little significance (eg.) above FL10 and /or more than 100 miles from Iceland.
These (under-informed) conclusions are supported by the lack of published evidence of VA discovered inside engines during the current Iceland situation. There may of course be other evidence and other people who already know very different!