First-principles prediction of detonation cell size from mixture chemistry
In plain words
The front of a gas detonation is a pattern of crossing shock waves that scratches a fish-scale pattern on a sooted wall, and the width of these cells decides whether a detonation can pass through a pipe or an opening. At present the width can only be estimated from chemistry to within a factor of a few.
Precise statement
For gaseous detonations (H2-O2-Ar, H2-air, hydrocarbon-air) at initial pressure $p_0$ and temperature $T_0$, predict the mean cell width $\lambda$ from the detailed chemical mechanism. Empirical correlations $\lambda = A \Delta_I$, with $\Delta_I$ the induction length of the one-dimensional steady detonation, need $A$ between about 10 and 50 depending on mixture. An answer predicts $\lambda$ within 20 percent across mixtures and initial conditions with no fitted $A$.
What would settle it
Three-dimensional resolved simulations with validated chemistry, or a reduced theory, that reproduce measured cell widths for several mixtures and pressures without mixture-specific tuning.