No abstract

Magmas discharged during individual volcanic eruptions commonly display compositional variations interpreted as new arrivals at shallow depth of more primitive, hotter, volatile-rich magma batches mixing with resident, colder, partially degassed magma. Heterogeneities in eruption products are often interpreted as evidence of short times of order tens of hours from new magma arrival to eruption, raising concerns for emergency planning. We show here, through numerical simulations, that magma convection and mixing in a shallow magma chamber can result in long-lived, dynamically stable configurations with coexistence of magmas from nearly pure to variably mixed end-member compositions. Short mixing time scales may therefore relate to sin-eruptive processes, as heterogeneities found in the eruptive products are not necessarily the fingerprint of new magma arrival shortly preceding or triggering the eruption.

No abstract

No abstract

Knowledge of the global rates of volcanism is fundamental for modeling the Earth, as those rates closely relate to plate tectonics, crustal growth, mantle dynamics, atmospheric evolution, climate change, and virtually any aspect of the global Earth dynamics. In spite of their huge relevance, the global rates of volcanism have remained unknown, hidden within data that appeared disordered, largely fragmented and incomplete, reflecting poor preservation of small eruptions in the geological record, rareness of large eruptions, and distributions far from normal. Here we describe and validate a model that reproduces global volcanism to high statistical significance, and that is so simple to comfortably fit on a t-shirt. We use the model to compute the expected rates of global terrestrial volcanism over time windows from 1 to 100,000 years, and validate it by comparing with observations back to a few million years. Notably, the model can be tested against independent observations collected in the near future, a feature which is relatively uncommon among global models of Solid Earth dynamics.

For systems in which the rate of mass transfer is controlled by intraparticle diffusion, theoretical prediction of the bf4akthrough curve for a packed bed adsorption column from the simultaneous solution of the differential fluid phase mass balance and the relevant diffusion equation requires considerable computational effort. This has led to the use of simple linear driving force expressions as an approximate representation of the mass transfer rate in diffusion controlled systems: --When the diffusivity is independent of concentration, it has been shown (Glueckauf, 1955) that Equation ( 1) with k, -15 De/R2 provides a good approximation for many boundary conditions. However, this approximation is not valid for adsorbents such as molecular sieves in which the diffusivity is strongly concentration dependent, and the purpose of this note is to develop the equivalent expressions for such systems, For an isothermal plug flow system with equilibrium governed by a Langmuir isotherm and the mass transfer rate controlled by external fluid film resistance, the breakthrough curve for a step change in feed concentration at time zero is given by the solution of the following set of equations: (4) Adsorption: -q ( z , z / u ) = 0; c ( z , d v ) = 0 ; c ( 0 , t ) = co (5) Desorption : --~( z , z / v ) = 4 0 ; C ( Z , Z / U ) = 0; c ( 0 , t ) = 0 ( 6 )Numerical solutions have been given by Zwiebel et al. (1972) and, for the equivalent problem with a Freundlich isotherm, by Kyte (1973). The corresponding solid film linear driving force representation for intraparticle diffusion control is obtained by replacing Equation (3) by Equation 1 and Equation (4) by ( 7 ) bc 4" ---qs 1 + bc For adsorption under constant pattern conditions (adsorption front moving with uniform velocity), Equation ( 2 ) reduces simply to -r#J = c/co = 4 / 4 0 (8)

No abstract

No abstract