A mechanism of a strong acoustic instability is proposed for flames propagating in sprays or particle-laden gases, enclosed in a tube. A complete one-dimensional analysis is provided for the homogeneous burning regime occuring when the particles are small enough and suflficiently volatile to vaporize before they reach the combustion region. Inertia and drag of particles oscillating upstream of the flame front are responsible for the coupling of the acoustic waves and the heat release (through modifications to the flame structure). This velocity coupling mechanism leads to a vibratory instability which is much stronger than the one associated with the pressure coupling. The analysis is based on a multiscale method associated with an asymptotic expansion in the limit of large Zeldovich number. Analytical expression of the transfer function and of the growth rate are obtained in terms of different parameters: vaporization temperature, latent heat, flame temperature, particle size, diffusive properties of the gas. The instability is found to be maximum at acoustic frequencies of the order of magnitude of the inverse of the transit time across the flame. Quantitative results are provided in the discussion.
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