In large magma chambers, gradients of temperature and composition develop due to cooling and to fractional crystallization. Unstable density differences lead to differential motions between melt and crystals, and a major goal is to explain how this might result in chemical differentiation of magma. Arriving at a full description of the physics of crystallizing magma chambers is a challenge because of the large number of processes potentially involved, the many coupled variables, and the different geometrical shapes. Furthermore, perturbations are caused by the reinjection of melt from a deep source, eruption to the Earth's surface, and the assimilation of country rock. Physical models of increasing complexity have been developed with emphasis on three fundamental approaches. One is, given that large gradients in temperature and composition may occur, to specify how to apply thermodynamic constraints so that coexisting liquid and solid compositions may be calculated. The second is to leave the differentiation trend as the solution to be found, i.e., to specify how cooling occurs and to predict the evolution of the composition of the residual liquid and of the solid forming.

The third is to simplify the physics so that the effects of coupled heat and mass transfer may be studied with a reduced set of variables. The complex shapes of magma chambers imply that boundary layers develop with density gradients at various angles to gravity, leading to various convective flows and profiles of liquid stratification. Early studies were mainly concerned with describing fluid flow in the liquid interior of large reservoirs, due to gradients developed at the margins.

More recent work has focused on the internal structure and flow field of boundary layers and in particular on the gradients of solid fraction and interstitial melt composition which develop within them. Crystal settling may occur in a surprisingly diverse range of regimes and may lead to intermittent deposition events even with small crystal concentrations. Incorporating thermodynamic constraints in the study of the dynamics of settling has only just begun. Many dynamical phenomena have been found using theoretical arguments, laboratory experiments on analog systems, and numerical calculations on simplified chemical systems. However, they have seldom been applied to natural silicate melts whose phase diagrams and important physical properties such as thermal conductivity and chemical diffusion coefficients remain poorly known. There is a gap between model predictions and observations, as many models are designed to explain large-scale features and many observations deal with the local texture and mineral assemblages of the rocks. This review stresses the relevance to the geological problem of the work carried out in parallel in other disciplines, such as physics, fluid dynamics and metallurgy. ¿ American Geophysical Union 1995