Theoretical Study on an Effect of Liquid Viscosity and Thermal Conductivity on Weakly Nonlinear Propagation of Short Pressure Waves in Bubbly Liquids

Abstract

This study theoretically clarifies an effect of the liquid viscosity and the thermal conductivity on weakly nonlinear propagation of pressure waves in a liquid containing many spherical microbubbles. As in our preceding paper (Kamei et al., J. JSCE, Ser. A2, 75 (2019), 499) focusing on a long wave, by the use of the method of multiple scales, a nonlinear Schrödinger equation describing the long-range propagation of an envelope wave of short carrier wave is derived from the basic equations incorporating the liquid viscosity and the thermal conductivity. As a result, as in our preceding long wave case, the liquid viscosity and the thermal conductivity affect the dissipation effect, and a nonlinear effect in the adiabatic process decreases in comparison with the previous study (Kanagawa et al., J. Fluid Sci. Technol., 6 (2011), 838). On the other hand, unlike in our preceding long wave case, a dispersion effect in the adiabatic process decreases in comparison with the previous study.