Numerical study on nonlinear evolution of pressure waves in bubbly liquids: Effective range of initial void fraction

Abstract

A KdV-Burgers (KdVB) equation describing an weakly nonlinear evolution of pressure waves in liquids uniformly containing many spherical microbubbles has been derived by many researchers and our group under the assumption that the initial void fraction is of the order of unity. However, an effective range of initial void fraction has not been clarified quantitatively. In this paper, we numerically solve the KdVB equation via a split step Fourier method. As a result, we find that (i) pressure wave evolves into an attenuated soliton due to a balance among the nonlinear, dissipation, and dispersion effects; (ii) it is implied that an upper limit of the effective range of the initial void fraction is from 0.69 to 0.7 for the case of the initial bubble radius is 1 mm.