Size limits for rounding of volcanic ash particles heated by lightning
Fabian B. Wadsworth , Jérémie Vasseur, Edward W. Llewellin, Kimberly Genareau,
Corrado Cimarelli and Donald B. Dingwell, 2017
(a) A scanning electron microscopy image of a representative sample from a fall deposit of the 2009 Redoubt eruption for which rounded glass spheres are marked by arrows. (b) The simplified particle geometry used in the model set up where the radial coordinate is r and the asperity length scale is L.
Volcanic ash particles can be remelted by the high temperatures induced in volcanic lightning discharges. The molten particles can round under surface tension then quench to produce glass spheres. Melting and rounding timescales for volcanic materials are strongly dependent on heating duration and peak temperature and are shorter for small particles than for large particles. Therefore, the size distribution of glass spheres recovered from ash deposits potentially record the short duration, high-temperature conditions of volcanic lightning discharges, which are hard to measure directly. We use a 1-D numerical solution to the heat equation to determine the timescales of heating and cooling of volcanic particles during and after rapid heating and compare these with the capillary timescale for rounding an angular particle. We define dimensionless parameters—capillary, Fourier, Stark, Biot, and Peclet numbers—to characterize the competition between heat transfer within the particle, heat transfer at the particle rim, and capillary motion, for particles of different sizes. We apply this framework to the lightning case and constrain a maximum size for ash particles susceptible to surface tension-driven rounding, as a function of lightning temperature and duration, and ash properties. The size limit agrees well with maximum sizes of glass spheres found in volcanic ash that has been subjected to lightning or experimental discharges, demonstrating that the approach that we develop can be used to obtain a first-order estimate of lightning conditions in volcanic plumes.
(a) The dependence on the time required for the particle rim to cool to Tg after t = λ on T0 and R. Shown for reference is the Rc for each value of T0, and we note that particles larger than these values did not fully melt on heating. (b–e) Observations from the 27 October 2013 eruption of Sakurajima volcano filmed at 3000 frames per second demonstrating that after a peak discharge intensity (Figure 8b), the discharge afterglow is sustained for time t* (in this case t* = 16 ms). Times recorded from the first indication of discharge are t = λ = 3 ms (Figure 8b), 4 ms (Figure 8c), 10 ms (Figure 8d), and t = t* = 16 ms (Figure 8e).
Airborne volcanic ash particles that are engulfed by volcanic lightning discharges [Paxton et al., 1986; Genareau et al., 2015], or are ingested by jet engines [Shinozaki et al., 2013; Song et al., 2014, 2016], are subjected to rapid heating. In either case, if a particle’s temperature is raised above the glass transition, in the case of glassy ash, or the solidus, in the case of crystalline ash, it behaves as a viscous droplet and becomes susceptible to capillary processes—i.e., deformation induced by the action of surface tension. Capillary processes are important in a variety of phenomena, including droplet rounding and sticking of a droplet to a surface.
Lightning occurs commonly in plumes of volcanic ash produced by moderate to high explosivity eruptions [McNutt and Williams, 2010; Aizawa et al., 2016; Cimarelli et al., 2016] and in laboratory experiments of volcanic ash production and proximal transport [Cimarelli et al., 2014]. During discharges, temperatures can reach 103–104 K [Paxton et al., 1986; Farzaneh and Chisholm, 2009; Rakov, 2013] and the discharge can take several milliseconds to dissipate [Paxton et al., 1986; Cimarelli et al., 2016]. Genareau et al. [2015] suggest that this is sufficient time to heat fine volcanic particles (<63 μm diameter) to temperatures well in excess of the glass transition or solidus, and even liquidus, implying that the particles can become fully molten liquid droplets. We propose that this melting allows ash particles, which are initially angular, to round to spherical under the action of surface tension. The observation of abundant glass spheres in deposits of otherwise angular volca- nic ash from eruptions such as the 2009 Redoubt eruption (Figure 1) provides tantalizing evidence for this process.
Here we investigate the thermal response of a volcanic particle that is rapidly heated, by applying a nondi- mensional 1-D spherical heat transfer model. We constrain the critical volcanic particle size below which heat transfer raises the entire particle to a temperature above the glass transition, or a critical melting temperature, in the time available for heat transfer. Then, by way of an example, we focus on the volcanic lightning case. We constrain the timescale for surface tension-driven capillary rounding of the particle, to determine the con- ditions under which volcanic lighting may transform ash particles into glass spheres.
The utility of volcanic lightning as a monitoring tool is being established [Behnke and McNutt, 2014], and better constraint of the temperatures, durations, and length scales of volcanic discharges is necessary. Using the framework developed here, minimum temperatures or durations could be extracted from the size distribution of glass spheres found in fall deposits. The framework can also be used to understand the thermal behavior of ash in jet engines, which is crucial to airlines and aviation authorities because mol- ten ash droplets can stick to engine components, causing loss of thrust and engine failure [Giehl et al., 2016]. In what follows we focus primarily on the volcanic lightning case but emphasize that the framework developed in this study is applicable to other scenarios in which thermal disequilibrium is induced at the particle scale.