Let me start by saying that I'm SLF, not a pilot and I'm also not a geologist. However, I have a friend who IS a geologist and one that specialises in volcanoes. A couple of us asked her about why THIS eruption is causing such a problem and also about the prospects for the future. Her reply might be of interest here:
To answer your question, It ALL depends on the type of magma that is erupting - how viscous it is and how much there is going to be erupted. The volcano /could/ - it has before - erupt for up to two years or more. If the magma is basaltic then yes, pretty much as soon as it runs out of water it will go from phreatoplinian style (phreato indicating the presence of water, plinian being the eruption type - see pic below - it's v. recent) back to the effusive Hawaiian lava fountain type that was happening last month - it's a bit like pouring water on a chip pan fire (which I can tell you from seeing this done in controlled conditions is a /most/ impressive fireball). Samples collected last month and analysed suggested that the lava being erupted was a alkali-olivine basalt, with a silica content
of about 47% (silica being the thing that makes a lava all sticky and gooey and therefore more difficult for gas to escape). So it was all fairly fluid and gas trapped in the lava could easily escape. So far as that goes it would cause relatively few problems once the glacier had melted (10-15% of this has already gone according to my sources.)
However, the ice isn't really a massive problem in the long term especially if the lava IS still the same composition because once the ice has gone the eruption will settle down - locally however it could (and has) caused MASSIVE damage from jokulhlaup (meltwater floods). Roads, infrastructure, and farmlands have all been destroyed but so far there have been no fatalities as people had been evacuated from hazardous areas. Iceland being prepared for these eventualities.
It is currently erupting from a series of vents along a 2 km long north-south oriented fissure, with meltwater flowing down northern slopes of the volcano, but also to the south. The eruption has been fairly steady throughout this phase and will continue to be so for days at the least. Chemical analyses of the ash samples from this phase of the eruption however reveal fluorine rich intermediate eruptive products with silica contents of 58% (a more sticky magma than that erupting earlier) so it has evolved from the initial lava producing phase of the eruptive activity possibly by crystal fractionation in the magma chamber.
The eruption at Eyjafjallajokull is however still going strong with frequent regular cycles of steaming and phreatomagmatic explosions. The Icelandic Met Office is heading up to the volcano to conduct a survey of the crater area to find out (1) what it looks like and (2) how much new water (i.e., ice) is there available for the erupting magma. More water is likely to mean more explosive eruptions in this phreatoplinian style - however, like I mentioned earlier, the bulk andesitic composition of the ash implies it might have a decent ability to produce explosive eruptions without a lot of extra water (but it helps). You can see a great sequence of images from the eruption on this video (although the music might not be the most fitting). It shows the "puffing" nature of the eruption, which might imply periods of melt water getting into the conduit and flashing to steam (very loosely like a geyser behaves). The Icelandic Met Office has excellent information on the ash and the flooding, which has been somewhat forgotten in the news. There has been extensive flooding around the volcano due to the melting ice.
SO FAR there is little or no evidence that Eyjafjallajokull erupting is affecting her big sister Katla (who can cause far bigger eruptions) and is likewise sitting under an ice cap.
Eyjafjallajokull could keep erupting like this for months. It may not. It depends on many factors. We just have to wait and see (and pray Katla doesn't get set off - she is overdue for an eruption)
The weather patterns certainly aren't helping either so it really is a combination of things.
I haven't bothered recreating the links she posted, mainly because they're ones I've already seen in PPRuNe.
However, what seems to come out of this is that the particular combination of Magma erupting under a glacier is why this is creating "the wrong type of ash" and causing the problems we are seeing. My friend's post also explains why it it misleading to assume that, because a previous volcano did or didn't cause problems, there is a precedent in this case. This eruption is a particular combination of circumstances--I quite like the analogy to pouring water on a chip pan fire--and I, for one, am happy to leave the decision about when it is safe to fly to the experts.
Hope this is of use.
Bob