Abstract
A metal spark generated by grinding carbon steel has been recognized proceeding multiple bursting events, akin to the luminous branching fireworks. The mechanism of successive fragmentation observed in carbon steel spark, however, has not been elucidated yet. In the present study, we develop a new comprehensive analytical framework for estimating the droplet size of carbon steel sparks, time of flight, and time-variant temperature, combined with high-speed images of the spreading sparks, for the quantitative discussion of the timescale of bursting metal sparks. We find that the flight time to burst for a mother droplet is independent of the content of carbon, corresponding to the Fourier number for the molecular diffusion of unity. The successive fragmentation of carbon steel sparks is rate-controlled by the molecular diffusion of ambient oxygen inside the droplet. Since the measured temperature indicates that the heat is produced by the oxidation of iron, the successive fragmentation stops when the iron in the spark is fully oxidized, immediately becoming a solid particle.
