  Recent studies within the diffusive-thermal (constant-density) approximation
have shown that, for premixed flames freely propagating in narrow adiabatic
channels, the instabilities induced by differential diffusion may result in
non-symmetric solutions and/or oscillating and rotating propagation modes. This
has been shown in the context of lean mixtures, for which a single species
transport equation with a single Lewis number (corresponding to the ratio of
thermal to molecular diffusivity of the deficient reactant) can be used to
describe the flame propagation problem. In the present work we extend the
analysis to mixtures of any equivalence ratio. To this end, we consider a
two-reactant model, where the different diffusivities of the two reactants
introduce two different Lewis numbers. Steady-state computations and linear
stability analysis are carried out for mixtures with large disparity between
the Lewis number of the fuel (LeF) and the oxidizer (LeO), such as
hydrogen-oxygen systems. It is shown that both differential diffusion and
preferential diffusion have influence on the stability of the symmetric flame
shape. For sufficiently lean and rich mixtures, the flame behaves as dictated
by the Lewis number of the deficient reactant, i.e., the flame destabilizes
toward non-symmetric solutions for large mass flow rates when the mentioned
Lewis number is less than one. In near-stoichiometric mixtures the stability of
the symmetric flame depends on a weighted average value of LeF and LeO. In
particular, the symmetric solution is stable for large mass flow rates because
of the difficulties found by the less diffusive reactant to reach the reactive
zone of the flame.
