The set of equations governing reacting two-phase flows in liquid-propellant rocket engines is simplified and linearized around a steady base flow. In the particular case of a liquid/gas coaxial injector, models for the atomization, evaporation and combustion source terms are derived from a simplified physical description of both the oxidizer liquid core and spray. The resulting equations are projected onto a modal basis, leading to a quasi-linear dynamic description of the evolution of the system. In this paper, detailed model reduction focuses on the evaporation of polydisperse sprays and on the propagation of acoustic waves within the gas.