The formation of filamentary structures from molten silicates: Peleʼs hair, angel hair, and blown clinker

We conduct an analysis of the concomitant, competing phenomena at play in the formation of long filamentary structures from a stream of hot, very viscous and cohesive liquid as it is blown by a fast, cool air stream. The situation is relevant to a broad class of problems, namely volcanic glass threads or fibers formed when small particles of molten material are thrown into the air and spun out by the wind into long hair-like strands (called Peleʼs hair), to the process of prilling, the manufacture of glass fibers, and the formation of coke in furnaces and combustion chambers.The air stream blowing on the molten material both breaks up the liquid into fragments stabilized by capillarity, and cools the liquid down to solidification. There are, in this problem, four characteristic times. First, a deformation time of the liquid masses, setting the rate at which drops elongate into ligaments. Then, two timescales set the time of capillary breakup of these ligaments, one prevailing on the other depending on the relative weight of inertia on viscous slowing (that point is illustrated by an original experiment). Finally, a solidification time of the ligaments. Thin solid strands will only form when solidification occurs before capillary breakup. We have discovered that this condition is likely to apply when the liquid is strongly viscous, as for clinker in the cement industry, considered here as a generic example. We formulate recommendations to remove (or enhance) the formation of these objects.