The process of the formation and early evolution of a condensation trail (‘contrail’) in the near field of an aircraft wake was numerically studied by means of a mixed Eulerian/Lagrangian two-phase flow approach. Large-eddy simulations were used for the carrier phase, while, for the dispersed phase, a Lagrangian particle tracking method was used, coupled with a microphysics model to account for ice nucleation. The basic configuration was an exhaust engine jet loaded with soot particles and water vapour and interacting with a wing-tip trailing vortex. The thermodynamic conditions for contrail formation were identified by tracking the spatial distribution of supersaturation around particles. A strong mass coupling between the two phases was demonstrated by the simulations: the condensation of water vapour over soot particles, induced by exhaust dispersion into cold ambient air, leads to the formation of ice crystals whose size grows until thermodynamic equilibrium between the two phases is reached. Finally, local vapour depletion causes significant deviation from the classical mixing line theory and is also responsible for polydispersion of particle radii.