A model for the kinetics of high-temperature reactions between polydisperse volcanic ash and SO2 gas

Abstract

Rapid calcium diffusion occurs in rhyolitic volcanic ash particles exposed to hot SO 2 atmospheres. Such chemical transport is important immediately following fragmentation, during proximal transport in eruption plumes, and during percolative gas transport through a permeable volcanic edifice. Here we analyze published results of experiments designed to constrain the kinetics of this process. The experiments involve crushed rhyolitic glass particles tumbled in SO 2-bearing atmospheres at a wide range of relevant temperatures. We find that the particle-gas reaction is fed by calcium diffusion from the bulk to the particle surfaces where calcium-sulfate crystals grow. The calcium flux is accommodated by local iron oxidation state changes. This process results in time-dependent concentrations of surface calcium that are leachable in aqueous solutions. Those leachate concentrations represent a proxy for the diffusive flux of Ca 2+ out of the particle to form the surface deposits. We formulate a mathematical framework to convolve the starting particle size distributions with the solution to Fickian 1-dimensional diffusion, to find a weighted polydisperse result. Using this framework, we minimize for a temperature-dependent calcium diffusivity and compare our results with published calcium diffusivity data. We demonstrate that calcium diffusivity in rhyolite can be decomposed into two regimes: (1) a high temperature regime in which the diffusivity is given by the Eyring equation, and (2) a low-temperature regime more relevant to rhyolite volcanism and these gasash reactions. As a further test of our model, we compare the output against spatially-resolved data for the calcium gradients in the experimental particles. Our analysis suggests that surface reaction rates are rapid compared with the diffusion of calcium from the particle to the surface such that full diffusion models must be solved to predict the rhyolite-SO 2 reaction. We conclude by suggesting how this framework could be used to make quantitative predictions of sulfur budgets and iron oxidation during rhyolitic eruptions.

The trace-element composition of a Polish stalagmite: Implications for the use of speleothems as a record of explosive volcanism

“…The second mechanism is by deposition of tephra on the Earth's surface above a cave, and subsequent leaching into an aqueous fluid of surface deposits (e.g. volcanogenic salts; Wadsworth et al 2020) or of constituents of the tephra itself (Maters et al 2016). Such leaching can result in groundwater carrying a magmatic signal (Delmelle et al 2018;Maters et al 2016;Martin et al 2009).…”

Dehydration‐driven mass loss from packs of sintering hydrous silicate glass particles

“…In all cases, the mass of the samples decreases nonlinearly but monotonically (Figure 4). The forward model for diffusive mass loss provides the local value of C , which can be converted to a bulk average value $$\langle C \rangle $$ by solving the spherical volume integral 39 $$$$\begin{equation}\left\langle C \right\rangle = \;3\mathop \smallint \limits_0^1 C{\bar r^2}\;{\rm{d}}\bar r\end{equation}$$$$…”

“…18 In an identical manner, we convolve the diffusion law (e.g., Equation 7) with the particle size distribution to find a volume-averaged diffusion time td , shown to accurately predict diffusive mass transport in particles that are polydisperse in size. 39…”

“…To account for this, we convolve the sintering law (e.g., Equation ) with the pore size distribution (found from the particle size distribution via Wadsworth et al., 2017 18 ) to arrive at the convolved average $${\bar t_{\rm{b}}}$$, which has been shown to accurately account for polydisperse sintering 18 . In an identical manner, we convolve the diffusion law (e.g., Equation ) with the particle size distribution to find a volume‐averaged diffusion time $${\bar t_{\rm{d}}}$$, shown to accurately predict diffusive mass transport in particles that are polydisperse in size 39 …”

“…The initial profile of H 2 O is taken to be the measured profile from Figure2. can be converted to a bulk average value ⟨𝐶⟩ by solving the spherical volume integral39…”