Monazite, (Ce,La,Nd,Th)PO₄, is "cracked" by hot concentrated NaOH: Monazite + 3NaOH → (Ce,La,Nd,Th)(OH)₃ + Na₃PO₄. Each grain is modelled with the shrinking-core model — an unreacted core shrinks as reaction converts it to a porous hydroxide shell:
X(t) = 1 − (r(t)/r₀)³
r(t) = r₀·max(0, 1 − t/τ), τ = r₀ / k_eff
Three resistances act in series — surface reaction, diffusion through the growing hydroxide product layer, and external mass transfer across the stirred boundary layer — combined like conductances:
1/k_eff = 1/k_rxn + 1/k_diff + 1/k_ext
k_rxn, k_diff ∝ exp(−Ea/RT)·[NaOH]ⁿ (Arrhenius + power-law order)
k_ext ∝ √(stirring intensity)
Overall batch conversion is the volume-weighted average across a small size distribution of grains (±25% around r₀), which is why particles finish at slightly different times — exactly as a real polydisperse ore charge would.