Pressure wave propagation in high viscous magma containing crystals and bubbles

The presence of bubbles and crystals in highly viscous liquid (e.g., glass, magma) has been important for the purpose of both basic and practical viewpoints. In this presentation, especially, we focus on a magma, and investigate theoretically P-wave (i.e., pressure wave) propagation in the magma containing many bubbles. Based on an averaged theory of dispersed multiphase flow, we can regard the mixture of crystals (i.e., solid phase) and melt (i.e., liquid phase) as a single liquid phase, i.e., single non-Newtonian liquid, which is approximated to a Newtonian liquid by using the concept of an effective viscosity composed of various parameters (especially crystals). The system of basic equations for multiphase flow containing the effective viscosity, can be reduced to the KdV-Burgers equation as a nonlinear evolution equation via theoretical approximation based on singular perturbation method. As a result, the effect of fraction of crystals and bubbles on the acoustic characteristics (e.g., waveform evolution, nonlinearity, attenuation) is discussed.