We examine the behaviour of twin premixed flames in a symmetric counterflow, subject to radiation losses, a problem motivated by recent drop-tower experiments. A simple asymptotic strategy is adopted which complements recent numerical simulations and provides new insights. Parameters are chosen to emulate, in a rough way, lean methane - air mixtures, and the flame response to varying strain-rates is calculated for different mixture strengths. For strengths below the standard flammability limit, but above an inferior limit, sub-limit solutions are obtained for which the flame-position versus strain-rate defines an isola with low- and high-strain-rate quenching points. For mixture strengths greater than a critical value above the standard limit the isola opens up, and there are two solutions (rather than none) for a vanishing strain rate. An intermediate response characterized by two disjoint solution curves exists for a minute range of mixture strengths. Five different catastrophe (jump) events are identified, one of which is related to the standard flammability limit. It is shown that the inferior flammability limit monotonically decreases with decreasing Lewis number (Le), and that sub-limit solutions are possible for Le < Lec where Lec is a critical value greater than 1. Sub-limit solutions exist primarily because of geometric effects.
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