Dynamics of explosive volcanic eruptions

Simple component exchange between solid phases is accomplished by diffusion. If only two components (such as Fe and Mg) are exchanging, the diffusion is binary. The boundary condition is often such that the exchange coefficient between the surfaces of two phases is constant at constant temperature and pressure. The concentrations of the components on the adjacent surfaces may be constant assuming interface equilibrium. The solution to the diffusion equation 

If one of the two phases is a fluid phase, such as exchange between 

The two crystals in contact at x = 0 can be considered to be two halves of a diffusion couple. The two interdiffusion species are denoted as 1 and 2, and the left and right halves (phases) are denoted as A and B. The interdiffusion coefficient in the left-hand side, or phase A (x 0), is D, and that in the other side, or phase B (x 0), is D . Use subscripts to denote components 1 and 2 and superscripts to denote phases A and B. The initial condition is 

If diffusion distance is small compared to the size of either phase, because each side satisfies separately the conditions for applying the Boltzmann transformation (r =x/s/4Dt), the solution for species 1 in each phase is 

Example 4.1. Suppose olivine and garnet are in contact and olivine is on the left-hand side (x 0). Ignore the anisotropic diffusion effect in olivine. Suppose Fe-Mg interdiffusion between the two minerals may be treated as one dimensional. Assume olivine is a binary solid solution between fayalite and forsterite, and garnet is a binary solid solution between almandine and pyrope. Hence, Cpe + CMg= 1 for both phases, where C is mole fraction. Let initial Fe/(Fe- -Mg) = 0.12 in olivine and 0.2 in garnet. Let Xq = (Fe/Mg)gt/ (Fe/Mg)oi = 3, Fe-Mg,oi = 10 ° mm+s, and Dpe-Mg,gt = 

---

Dynamics of explosive volcanic eruptions are in many aspects similar to beer and champagne dynamics. They are driven by the exsolution of a gas from a liquid. Figure 4-31 describes the various stages of an explosive eruption. In the magma chamber, much H2O (such as 6 wt%) and some CO2 (such as 40 ppm) are... 

---