Viscous Effects on Wave Propagation in a Bubbly Liquid

The effects of viscosity on wave propagation in a bubbly liquid with a finite gas volume fraction are studied using the effective equations of Miksis and Ting [Phys. Fluids 29, 603 (1986)]. Both the linear and nonlinear versions of their equations are considered. For linear waves an exact solution of the microscopic problem is found. At finite Reynolds number the attenuation caused by viscosity is found. The Crespo wave speed and the Wood wave speed are shown to be the effective sound speed for the two limiting cases of infinite Reynolds number and zero Reynolds number, respectively. In the nonlinear case viscous effects are accounted for by using Levich’s method. This new nonlinear system of effective equations including the viscous effects is analyzed.