Governing Equations

Sublimation Rate (Mass Flux):
  dm/dt = (A · ΔP) / Rp
  where ΔP = Pice(Tproduct) - Pchamber
  Rp = cake resistance (increases with dry layer thickness)

Collapse Temperature (Tc):
  Tc ≈ Tg' - 2°C (glass transition of maximally freeze-concentrated)
  Safety margin: Tproduct < Tc - 2°C

Shelf Temperature Profile:
  Tshelf(t) = Tfreezing + ramp_rate · t (primary drying)
  Tshelf(t) = Tsecondary (secondary drying)

Drying Time:
  t_primary = L₀² · ρ / (2 · Kv · ΔT)
  where L₀ = fill height, Kv = vial heat transfer coefficient

Moisture Content:
  KF = KF₀ · exp(-k_secondary · t)
  Target: ≤ 1% (often ≤ 0.5% for biologics)