Stratospheric aerosol injection (SAI) might alleviate some climate risks associated with accumulating greenhouse gases. Reduction of specific process uncertainties relevant to the distribution of aerosol in a turbulent stratospheric wake is necessary to support informed decisions about aircraft deployment of this technology. To predict aerosol size distributions we apply microphysical parameterizations of nucleation, condensation and coagulation to simulate an aerosol plume generated via injection of calcite powder or sulphate into a stratospheric wake with velocity and turbulence simulated by a three‐dimensional (3D) fluid dynamic calculation. We apply the model to predict the aerosol distribution that would be generated by a propeller wake in the Stratospheric Controlled Perturbation Experiment (SCoPEx). We find that injecting 0.1 g s‐1 calcite aerosol produces a nearly monodisperse plume and that at the same injection rate, condensable sulphate aerosol forms particles with average radii of 0.1 µm at 3 km downstream. We test the sensitivity of plume aerosol composition, size, and optical depth to the mass injection rate and injection location. Aerosol size distribution depends more strongly on injection rate than injection configuration. Comparing plume properties with specifications of a typical photometer, we find that plumes could be detected optically as the payload flies under the plume. These findings test the relevance of in situ sampling of aerosol properties by the SCoPEx outdoor experiment to enable quantitative tests of microphysics in a stratospheric plume. Our findings provide a basis for developing predictive models of SAI using aerosols formed in stratospheric aircraft wakes.