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What properties does volcanic ash have that make it a hazard to aircraft jet engines which are not posed by other sources of atmospheric dust, such as Saharan dust? Is it merely a question of atmospheric concentration or relative height?

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Particle size is the key issue. Saharan loess (wind-blown dust) must have a small enough particle size that it can be lofted by ordinary wind speeds: typically, it is in the 20-50μm size range.

Particle sizes lofted into the upper atmosphere during explosive volcanic eruptions can be much higher: "The explosive ash was bimodal in size distribution with peaks at about 25- and 200-μm diameter... For the typical ash, diameter peaked at approximately 500μm" (Gislason et al., 2011), though this effect only has particular significance in close proximity to the vent.

The risk to aircraft is explained:

Fears about danger to aircraft arose from an incident when a British Airways 747 flew through an ash cloud during the 1982 eruption of Mount Galunggung in Indonesia. The pilot reported sparks from the windows and wings as ash sandblasted all surfaces and all four jet engines failed when melted ash coated their interior.

(There's an absolutely classic paper on this, and a lot of the literature is well worth a read for the sheer understated "well, yep, that was a problem.")

In fact the ash lofted across Europe following the Eyjafjallajökull eruption was mostly below 63μm in diameter, since that's what can persist without rapidly sedimenting out, but the explosive nature of the initial eruption meant that "... even the nanoparticles are far from round. Their sharpness makes them particularly abrasive." In contrast, loess has been extensively weathered. The authors add: "The very sharp, hard particles put aircraft at risk from abrasion on windows and body and from melting in jet engines."

For more details on volcanic ash and turbine engines, see Gunn & Wade and, for that matter the rest of the volume.

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