The thickness of the falling film of liquid around a Taylor bubble
We present the results of laboratory experiments that quantify the physical controls on the thickness of the falling film of liquid around a Taylor bubble, when liquid–gas interfacial tension can be neglected. We find that the dimensionless film thickness l (the ratio of the film thickness to the pipe radius) is a function only of the dimensionless parameter Nf = rgD3/m, where r is the liquid density, g the gravitational acceleration, D the pipe diameter and m the dynamic viscosity of the liquid. For Nf 10, the dimensionless film thickness is independent of Nf with value l ≈ 0.33; in the interval 10 Nf 104, l decreases with increasing Nf; for Nf 104 film thickness is, again, independent of Nf with value l ≈ 0.08. We synthesize existing models for films falling down a plane surface and around a Taylor bubble, and develop a theoretical model for film thickness that encompasses the viscous, inertial and turbulent regimes. Based on our data, we also propose a single empirical correlation for l(Nf), which is valid in the range 10−1 < Nf < 105. Finally, we consider the thickness of the falling film when interfacial tension cannot be neglected, and find that film thickness decreases as interfacial tension becomes more important.
An analytical model for gas overpressure in slug-driven explosions: Insights into Strombolian volcanic eruptions
Strombolian eruptions, common at basaltic volcanoes, are mildly explosive events that are driven by a large bubble of magmatic gas (a slug) rising up the conduit and bursting at the surface. Gas overpressure within the bursting slug governs explosion dynamics and vigor and is the main factor controlling associated acoustic and seismic signals. We present a theoretical investigation of slug overpressure based on magma-static and geometric considerations and develop a set of equations that can be used to calculate the overpressure in a slug when it bursts, slug length at burst, and the depth at which the burst process begins. We find that burst overpressure is controlled by two dimensionless parameters: V′, which represents the amount of gas in the slug, and A′, which represents the thickness of the film of magma that falls around the rising slug. Burst overpressure increases nonlinearly as V′ and A′ increase. We consider two eruptive scenarios: (1) the “standard model,” in which magma remains confined to the vent during slug expansion, and (2) the “overflow model,” in which slug expansion is associated with lava effusion, as occasionally observed in the field. We find that slug overpressure is higher for the overflow model by a factor of 1.2–2.4. Applying our model to typical Strombolian eruptions at Stromboli, we find that the transition from passive degassing to explosive bursting occurs for slugs with volume >24–230 m3, depending on magma viscosity and conduit diameter, and that at burst, a typical Strombolian slug (with a volume of 100–1000 m3) has an internal gas pressure of 1–5 bars and a length of 13–120 m. We compare model predictions with field data from Stromboli for low-energy “puffers,” mildly explosive Strombolian eruptions, and the violently explosive 5 April 2003 paroxysm. We find that model predictions are consistent with field observations across this broad spectrum of eruptive styles, suggesting a common slug-driven mechanism; we propose that paroxysms are driven by unusually large slugs (large V′).