V-BO-04 — Uniform zero-order burnout: exact thickness through park cascades

Tags: ale, burnout, depletion, kinetics, exact

References:

• closed form L(t) = L₀ exp(−r t/ρ_s)

Problem statement

An adiabatic slab at uniform T₀ with one zero-order reaction solid → gas, γgas = 0 and no heat of reaction. The temperature stays at T₀ exactly (no heat source, no gradient), so the volumetric rate r = A·exp(−E/RT₀) is a constant and every cell loses the same fraction r/ρs of its current volume per unit time. Under ALE the solid concentration stays at ρ_s (dilation removes volume, not concentration) and the exact thickness is

L(t) = L₀ · exp(−r t / ρ_s).

Every cell reaches the depletion threshold at the same instant, so the parking machinery meets its worst case: a cascade of park events, one per step, surface-first, halving the live cell count at tk = ln(2^k·20) ρs/r. L(t) and the solid mass must follow the exact law through every cascade, and ξs must stay at ρs to roundoff.

Quantities of interest (n = 40)

Solver configuration