This study investigates the dynamics of water droplets within a Batchelor vortex. Such an analytically described flow structure serves here as a model that may capture the essence of a trailing vortex. A Lagrangian approach is used to analyse the coupling between droplet motion and the flow field generated by the vortex. Under certain thermodynamic and hydrodynamic conditions, droplets may undergo evaporation and condensation when circulating the vortex core due to sharp changes in the environmental conditions induced by the vortex. The vortex-induced pressure drop is quantified using a non-dimensional vortex Euler number, revealing conditions required for condensation initiation within the vortex core. The onset of condensation is characterised by defining a mass transfer coefficient, indicating the direction and extent of mass transfer to the droplets. Our study uncovered a distinct clustering phenomenon linked to the initial Stokes number, with droplets showing a tendency to aggregate at higher Stokes numbers. The presented model may offer valuable insights into droplet dynamics within trailing vortices, contributing to improved modelling and prediction of droplet transport phenomena near trailing vortices.