The Taylor flow is the laminar single-phase flow induced by gas injection through porous walls, and is assumed to represent the flow inside solid propellant motors. Such a flow is intrinsically unstable, and the generated instabilities are probably responsible for the thrust oscillations observed in the aforesaid motors. However particles are embedded in the propellants usually used, and are released in the fluid by the lateral walls during the combustion, so that there are two heterogeneous phases in the flow. The purpose of this paper is to study the influence of these particles on stability by comparison with stability results from the single-phase studies, in a plane two-dimensional configuration. The particles are supposed to be chemically inert and of a uniform size. In order to carry out a linear stability study for this flow modified by the presence of particles, the mean particle velocity field is first determined, assuming that only the gas exerts forces on the particles. This field is sought in a self-similar form, which imposes a limit on the size of the particles. However, the particle mass concentration cannot be obtained in a self-similar form, but can only be described by a partial differential equation. The mean flow characteristics being determined, the spectrum of the discretized linear stability operator shows first that particle addition does not trigger any new ''dangerous'' modes compared with the single-phase flow case. It also shows that the most amplified mode in the case of the single-phase flow remains the most amplified mode in the case of the two-phase flow. Moreover, the addition of particles acts continuously upon stability results, behaving linearly with respect to the particle mass concentration when the latter is small. The linear correction to the monophasic mode, as well as the evolution of the modes with weak values of the particle mass concentration at the wall, are shown to be proportional to the ejection velocity of the particles. Then, the evolution of the eigenmodes from a given injection speed of the particles to another one is deduced by affinity, all other parameters being fixed. With a fixed Stokes number, stability results for a finite Reynolds number and results for the inviscid flow bring together when augmenting the particle mass concentration at the wall. Therefore, by knowing single-phase flow results and the evolution of stability characteristics of the two-phase flow in the inviscid case, it is easy to determine whether particle-laden Taylor flow is more or less stable than the monophasic Taylor flow for large particle mass concentration.

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