Perlite expansion (2D)

Why perlite pops

Perlite is a volcanic glass holding 2 to 5 wt% dissolved water. When a grain is heated above its softening point (about 850 to 1000 C) the glass turns from brittle to viscous, the water leaves solution as steam, and the steam inflates the grain into a foam. Expanded perlite has a bulk density of roughly 30 to 150 kg/m³, against about 1100 kg/m³ for the raw grain.

Model equations

• Heating of a sphere (lumped): T(t) = Tf + (T0 − Tf) e−t/τ, with τ = R2/(π2α).
• Viscosity (VFT): log10 η = −3 + 10500/(T[K] − 73), tuned to about 10^6.6 Pa s near 850 C.
• Steam pressure: Pg = ng R T / Vg with the exsolved water ng = nw (1 − e−(T−Tx)/150).
• Viscous bubble growth (Rayleigh-Plesset, inertia neglected): dr/dt = r (Pg − Pa − 2σ/r) / (4η).

Growth stops when the foam porosity reaches a burst value, because the cell walls open and gas escapes, and when the quench raises the viscosity again.

Honest simplifications: one bubble per grain instead of a population; the exsolution curve is an empirical shape, not a full solubility law; no water diffusion out of the grain, no coalescence, no sintering; viscosity and exsolution constants are tuned to typical values, not measured for a specific ore. Treat the numbers as illustrative.

• Compare the 800, 950 and 1150 C furnaces: below the softening point the viscosity is too high and the grain barely expands.
• Make the residence time very short: the quench freezes the foam early.
• Raise the dissolved water: more steam means higher pressure and expansion, until the burst porosity caps it.
• Use a coarse grain: it heats more slowly (graph of temperature).