It is now generally recognised that volcanic eruptions have an important effect on climate variability from inter-annual to decadal timescales. Several outstanding questions remain and concern the behaviour of various SO₂ emission rate into the stratosphere after eruptions such as those that did occur during the last centuries. To contribute to the on-going effort to reduce the large uncertainties regarding the climatic responses to large volcanic eruptions we discuss results from process-oriented sensitivity experiments using the state-of-the-art IPSL global climate model forced with a well-established global aerosol process model containing a fully explicit size-resolving aerosol microphysical module. The effects of the eruption season are also evaluated. Climate simulations reveal that there is no canonical linear relationship between the global cooling and the magnitude of the eruptions, due notably to self-limiting microphysical aerosol processes. These processes explain the relatively weak global cooling that never exceeds 2.5°C in our model for the very large eruptions. For comparable latitude, the aerosol microphysical processes and evolution differ significantly depending on the eruption season and strength. The implication of these results for the climate variability following volcanic eruptions will be discussed.