Solid aerosol particles have long been proposed as an alternative to sulfate aerosols for solar geoengineering. Any solid aerosol introduced into the stratosphere would be subject to coagulation with itself, producing fractal aggregates, and with the natural sulfate aerosol, producing liquid-coated solids. Solid aerosols that are coated with sulfate and/or have formed aggregates may have very different scattering properties and chemical behavior than uncoated non-aggregated monomers do. We use a two-dimensional (2-D) chemistry-transport-aerosol model to capture the dynamics of interacting solid and liquid aerosols in the stratosphere. As an example, we apply the model to the possible use of alumina and diamond particles for solar geoengineering. For 240 nm radius alumina particles, for example, an injection rate of 4 Tg yr-1 produces a global-average shortwave radiative forcing of -1.2 W m-2 and minimal self-coagulation of alumina although almost all alumina outside the tropics is coated with sulfate. For the same radiative forcing, these solid aerosols can produce less ozone loss, less stratospheric heating, and less forward scattering than sulfate aerosols do. Our results suggest that appropriately sized alumina, diamond or similar high-index particles may have less severe technology-specific risks than sulfate aerosols do. These results, particularly the ozone response, are subject to large uncertainties due to the limited data on the rate constants of reactions on the dry surfaces.