Dynamics of bubble oscillation and wave propagation in viscoelastic liquids

摘要

Decrease of the velocity of a pressure wave in magma by the presence of bubbles is regarded as a fundamental process in seismoacoustic activities of a volcano. However, we show that the large viscosity of magma (≥ 10~5 Pa s) prevents this decrease in wave velocity. To investigate how the acoustic properties of a liquid-bubble mixture depend on liquid rheology, laboratory experiments were conducted using silicone oil and syrup. Both liquids have a viscosity as high as 1000 Pa s. Propagation of a pressure wave and the radial motion of a bubble were observed in a shock-tube-type apparatus, but were quite different in the two liquids. Although the velocity of the pressure wave significantly decreased as the void fraction in silicone oil did, bubbles did not decrease the wave velocity in syrup. From conducting several material tests, we found that both liquids are viscoelastic, and that the rigidity (the shear elasticity) of silicone oil is- smaller than that of the syrup by several orders. The motion of a single bubble and propagation of the pressure wave were calculated using the Oldroyd model for linear viscoelasticity. The numerical solutions explained the difference as a result of the different rigidities of the two liquids. The same mathematical model was then applied to understand pressure wave propagation in bubbly magmas with a variety of viscosities. Results of the experiments and the subsequent numerical analyses suggest that pressure wave propagation in a liquid-bubble mixture and the motion of a single bubble depend significantly on the viscoelastic properties of the liquid. The sound velocities of liquids with large viscosities and rigidities are not decreased by bubbles; magmas with high viscosity are in this category. To evaluate propagation velocity and attenuation of a pressure wave in a bubbly liquid, we need to deal with the dispersion relationship with an adequate liquid rheology model. The present results give an insight into the bubble dynamics in a viscoelastic liquid, which is important for developing mathematical and experimental methods to investigate seismoacoustic phenomena in volcanoes.