Theoretical Study on an Effect of Thermal Conductivity on Nonlinear Propagation of Pressure Waves in Bubbly Liquids

Abstract

Thermal effect on nonlinear pressure waves in bubbly liquids is theoretically studied through a derivation of KdV-Burgers equation by incorporating energy equation at the bubble-liquid interface established by Prosperetti (1991) and effective polytropic exponent describing thermodynamics inside the bubble. Main results are as follows: (i) Two types of dissipation term appear: one is a second-order derivative including the effect of liquid viscosity and acoustic radiation and the other is newly discovered term without differentiation including the effect of thermal conduction; (ii) Thermal effect contributes not only dissipation effect but also nonlinear effect, and the nonlinearity increased compared with that in the previous studies; (iii) Thermal dissipation effect in this study is comparable with that by Prosperetti (1991) although the form of dissipation term describing the effect of thermal conduction differs.