Particle Concentrations and Sizes for the Onset of Settling-Driven Gravitational Instabilities: Experimental Validation and Application to Volcanic Ash Clouds

Abstract

Settling-driven gravitational instabilities (SDGIs) can form at the base of buoyant particle-laden suspensions, modulating particle sedimentation in various settings such as meteorological and volcanic clouds, fluvial plumes, magma chambers, submarine hydrothermal plumes, or industrial emissions. These instabilities result in the formation of rapidly descending currents called ‘fingers’ within which fine particles settle faster collectively than individually. This study investigates SDGI triggering conditions underneath volcanic ash clouds through analogue experiments considering sedimentation from aqueous particle suspensions. We confirm that the conditions for which SDGIs develop are controlled by two dimensionless numbers: B_f (ratio of the characteristic finger velocity to the individual particle settling velocity); and B_i (ratio of timescale for individual particle settling to that for collective settling controlled by inertial drag). SDGIs are triggered for values of B_f and B_i > 1 for which particles are fully coupled with the flow within fingers. Using these parameters, we produce a regime diagram for the 2010 eruption of Eyjafjallajökull (Iceland) that describes particle settling as a function of particle concentration and size. More studies are needed to produce a general regime diagram accounting for the evolution of SDGIs properties with eruption and atmospheric parameters. Nonetheless, our study confirms that fingers affect sedimentation from volcanic clouds with high ash volume fractions above 10⁻⁶ vol.%. Our validation of criteria predicting the onset of fingers due to SDGIs constitutes a step forward toward the incorporation of these collective settling processes in volcanic ash transport and dispersion models.