The present work examines the role of instability and diffusive phenomena in controlling the limits of detonations subject to lateral strain. Experiments were conducted in mixtures with varying levels of cellular instability, i.e., stoichiometric methane-oxygen (CH4/2O(2)), ethylene-oxygen (C2H4/3O(2)), and ethaneoxygen (C2H6/3.5O(2)). These detonations were propagated in channels with exponentially enlarging cross-sections, following the recent works of Radulescu and Borzou (2018) and Xiao and Radulescu (2020). Steady detonation waves were obtained at the macro-scale, with the near-limit reaction zone structures characterized by significant unreacted gas pockets. The turbulent flame burning velocity of these pockets was evaluated to be 30 m/s to 70 m/s, which is larger than the theoretical laminar value by a factor of 2 to 7 and smaller than the CJ deflagration speed by a factor of 2 to 3. For all the mixtures tested, the characteristic D - K relationships, relating the detonation mean propagation speed with lateral flow divergence, were obtained directly from experiments and as well from the generalized ZND model with lateral strain rates using detailed chemical kinetics. The results showed that the degree of departure between experiments and the theoretical predictions increases significantly with the detonation instability level. As compared to the laminar ZND wave, the more unstable detonations are much more detonable than the more stable detonations, with substantially larger limiting divergence rates and maximum velocity deficits. Such enhanced detonability with detonation instability can be manifested in the significantly enhanced global rates of energy release with the notably suppressed thermal character of ignition for the more unstable detonations. This globally enhanced burning mechanism is found to be realized by the intensified auto-ignition assisted by the turbulent diffusive burning of the unreacted gas pockets, substantially shortening the characteristic reaction zone lengths. Finally, the relatively good universality of the D/D-CJ - K-eff lambda relations implicitly suggests that cell size is also a function of the detonation wave stability, since it is controlled by the reaction zone thickness of unstable detonations. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.