We develop a physical framework for the evolution of vesicular magma fragments after their formation by fragmentation in explosive eruptions. These fragments are carried by a gaseous jet through the volcanic conduit and into the atmosphere and are thus subjected to a decrease of pressure and temperature. We derive equations for the evolution of void fraction, internal gas pressure and temperature as a function of time and position in the fragment. The driving terms for the evolution are the pressure and temperature history external to the fragment. We show that a magma fragment can expand significantly before being quenched. The influence of melt viscosity is introduced as a dimensionless number that relates melt viscosity, pressure drop between fragmentation within the conduit and expansion in the atmosphere, and duration of the pressure drop. For melt viscosities larger than 10(9) Pa s, corresponding to high-silica-content rhyolitic melt with small amounts of dissolved water, expansion of vesicles is negligible so that quenched pumice samples record the state of vesicular magma at the moment of fragmentation. Over the viscosity range of 10(6) to 10(9) Pa s, the amount of vesicularity is a function of melt viscosity and the history of external pressure. For viscosities lower than 10(6) Pa s, melt viscosity is not important, and gas pressure within vesicles is always close to the external pressure. Available data for four Plinian deposits show that pumice vesicularity varies significantly both as a function of time during an eruption and between eruptions. For the magma compositions and volatile contents of the Bishop Tuff, United States; Taupo, New Zealand; and Minoan, Santorini, eruptions, the void fraction of pumice is predicted to be a decreasing function of melt viscosity, in agreement with observations. During an eruption, a change of fragmentation conditions will produce a small difference in pumice vesicularity, so that a systematic change in the average vesicularity within a pumice deposit may record a change of eruption dynamics.
