Theoretical study on nonlinear wave equations for pressure waves in bubbly flows

Tetsuya KANAGAWA University of Tsukuba

Abstract

Pressure wave in bubbly flows can develop into either a shock wave or an acoustic soliton as the result of long-range propagation. Because physical properties of the shock wave and soliton are considerably different, engineering applications of shock wave and soliton are also quite different. However, there exists a similarity of mathematical expression for shock wave and soliton, i.e., the method of nonlinear wave equation that has both shock wave and soliton as solutions. In this study, we first constructed a methodology to derive nonlinear wave equations describing the weakly nonlinear evolution of pressure waves in a unified manner. Using this methodology, we can derive comprehensively various nonlinear wave equations from the various sets of basic (model) equations for bubbly flows. Some new physics are then pointed out, e.g., the drag force acting on bubbles attenuates not only flows but also waves and the translation of bubbles increases the nonlinearity of waves. Furthermore, aimed towards medical applications, we are developing some nonlinear wave equations to utilize microbubble-enhanced medical ultrasound (e.g., therapy by microbubble-enhanced high-intensity focused ultrasound and diagnosis by coated microbubbles as ultrasound contrast agents).

Keywords

 Bubbly flow, Pressure wave, Shock wave, Soliton, Nonlinear wave equation