This article presents a mathematical model that describes the evaporation aerodynamics of a mist in the wake of a shattering drop behind a detonation front. The model is based on a previously obtained distribution function for stripped droplets by size. Stripped droplets are considered as a multivelocity continuum, and a system of differential equations describing two-phase polydisperse spray dynamics is proposed. The mathematical problem is formulated at a one-dimensional spatial approximation of flowfield and is solved in closed form in dynamic 3D space. This study includes a detailed calculation of the ballistics of an evaporating spray generated in the wake of a kerosene drop fragmented by an air stream. The following issues are also investigated: the internal structure of the spray as it relates to the dynamic process of spray formation; the evolution of the dispersive characteristics of the liquid-phase jet of spray; the stabilization and range of a jet; and the structure and processes of jet and vapor cloud formation. By rough estimations, the intensification of liquid transfer into the vapor phase due to shattering leads to over-riching and cooling of the air-vapor combustible mixture in a wake, essentially increasing the induction period of ignition.