6:15 PM - 7:30 PM
[SCG59-P05] Shape, propagation style and velocity of a buoyancy-driven crack : a parameter study
Keywords:magma ascent, crack propagation, viscoelasticity, fluid viscosity, bouyancy
Experimental method: We conducted (1) rheology measurement of an agar and (2) fluid injection experiments. We inject magma (CsCl solution to which a thickener is added) using a syringe from the top of a cylindrical acrylic tank (height of 250 and 500 mm). The fluid has a volume of 1ml, a density difference with the agar of 0.580 and 0.770 g/ml, and is injected at a constant rate of 1 ml/s. We vary the agar concentration(C) in the range of C = 0.06-0.5 wt% and the fluid viscosity(η) in the range of η = 10^-3 - 1300 Pas. As we increase the agar concentration in this range, the yield stress and the rigidity of the agar increases by 3 and 2 orders of magnitude, respectively. From creep test conducted under a constant shear stress, we find that the agar can be approximated by a Voigt model to which a spring is connected in series for C › 0.1wt%, and a Burgers model for C ‹ 0.1wt%. The experiments are recorded using video cameras from two sides and from the bottom of the tank.
Result: From the crack shape, propagation style and velocity, we classified the experiments into the following 3 regimes. RegimeⅠ: The crack has a 2D(blade-like) shape, a straight trajectory and stops propagating in a short distance. We fit the distance(z) vs time(t) data to a power-law(zt^n) relation, and find that the power law exponent is n〜1/5. The migration velocity depends on viscosity as 〜 1/n. RegimeⅡ: The crack shape transforms from 2D to 3D( i.e. , having a bulged head) and its trajectory is curved or meanders. The power-law exponent varies as n=1/3-1. We find that as the fluid viscosity increases, the amplitude of the meandering becomes smaller and transforms to a straight path. The same transformation was observed when the fluid density becomes smaller (Sumita and Ota, 2011). The migration velocity is intermediate from those of regimes Ⅰ and Ⅲ. RegimeⅢ: The crack shape is 3D, the trajectory is straight and the propagation distance is long. The power-law exponent is n〜1. The dependence of migration velocity on viscosity is small.
Discussion: The condition for the regime Ⅰ-Ⅱ transition can be approximately described using the dimensionless buoyancy B=△ρgV^1/3/G(△ρ: density difference, g: gravity, V: crack volume)as B〜1. However in detail, we find that the B value becomes larger for a high viscosity fluid. This is because when the propagation velocity is small, a larger fraction of the fluid is left along the crack tail such that the crack head volume become smaller, which results in a smaller effective B value . The migration velocity was found to be comparable to or smaller than the channel flow velocity(n=1/3:Taisne et al. (2011)) in regimeⅠ and comparable to the Stokes settling velocity(n=1) and shear wave velocity in regimeⅢ. This suggests that the propagation velocity is also rate-limited by rupture velocity. We indeed confirmed that the propagation becomes faster when there is a preexisting crack. We find that the meandering of regimeⅡ no longer occurs under a large viscosity. This suggests that in addition to B〜1, there is a critical velocity, or a critical Reynolds number required for meandering to occur.
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Sumita, I. and Y. Ota, 2011. Earth Planet. Sci. Lett., 304, 337-346.
Taisne, B. et al., 2011, Bull. Volcanol., 73, 191-204.