Effects of compressibility on the flow of lava

Abstract

Lava contains gas bubbles and hence is a compressible liquid whose density increases as a function of pressure. After eruption at the Earth's surface, it spreads at a rate which is a function of its thickness and it is compressed under its own weight. Therefore, both thickness and spreading rate are determined by a balance between viscous and compressible effects. Theoretical equations are derived for the shape and velocity of a compressible liquid spreading on a horizontal surface. Solutions are obtained for a fixed eruption rate Q. The radial extent of the flow increases proportional to t1/2. A dimensionless number C is defined which characterizes the importance of flow compression: \(C = \rho _0 \beta g\left( {\frac{{\mu Q}}{{\rho _0^2 g}}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}}\), where ρ0 is bubbly lava density at atmospheric pressure, β compressibility, μ viscosity and g the acceleration of gravity. C can be thought of as the ratio of two characteristic length-scales, one for compression effects and one for viscous effects. The larger C is, the more important compressibility effects are. As C is increased, the flow becomes thinner because the liquid is compressed more and more efficiently. Compressibility acts to smooth out variations of flow thickness, which provide the driving force. Thus, all else being equal, a compressible liquid flows less rapidly than an incompressible one. When trying to infer the effective viscosity of a flow from its spreading rate, the neglect of compressibility leads to an overestimate. The various factors which act to determine the distribution of gas bubbles in lava flows are reviewed and discussed quantitatively. Comparison with data from Obsidian Dome (Eastern California) shows that disequilibrium effects are important and that bubble resorption during burial in a thick flow is not a pervasive phenomenon. The analysis is applied to the 1979 dome of Soufriere de Saint Vincent (W.I.). An effective value of compressibility for this 100-m-thick dome is 1.5x10−6 Pa−1. This implies that, all else being equal, the viscosity of this lava may be overestimated by a factor of 5 if no account is taken of the compressible nature of the flow.