What makes detonation cells regular in some mixtures and irregular in others?
In plain words
Detonations in mixtures diluted with argon leave neat, regular cells, while in fuel-air mixtures the pattern is chaotic and pockets of unburned gas appear behind the front. What decides this, and does the irregularity change how the detonation survives?
Precise statement
Cell regularity correlates with the stability parameter $\chi = (E_{a}/(R T_{s})) (\Delta_{I}/\Delta_{R})$, the reduced activation energy times the ratio of induction length to reaction length. Determine whether $\chi$ or another parameter quantitatively predicts the width of the cell-size distribution, whether irregular detonations burn unreacted pockets by turbulent mixing, and whether this explains the critical tube diameter $d_{c} \sim 13\lambda$ for irregular mixtures and its larger multiples for regular ones. An answer is a quantitative classification criterion with its mechanism.
What would settle it
A systematic set of experiments and resolved simulations over $\chi$ measuring cell statistics, unburned-pocket consumption and critical diameters, fitted by one criterion.