Linear Perturbation Analysis of the Stability of a Dissociating Fluid

An investigation is made of the stability of an infinite expanse of a dissociating, diatomic fluid to infinitesimal disturbances (fluctuations), using a model due to Lighthill. Initially the fluid is at a uniform temperature and is kept stationary by the external removal of the heat produced by dissociation. The results of the linear perturbation analysis of the normal mode resolution of the disturbances shows that: (1) The non-steady-state chemical quasiequilibrium solution is stable if, and only if, the steady-state chemical equilibrium solution is stable; (2) the steady-state chemical equilibrium solution can be stable if, and only if, the partial derivatives of pressure with respect to density and internal energy with respect to temperature are of the same sign. In particular, for an ideal gas the chemical equilibrium solution is stable for all temperatures and amounts of dissociation. Physically, the criterion establishing this corresponds to the ability of the gas to dissipate effectively the heat produced by dissociation.