A model for the theoretical description of one- and two-dimensional structure formation in bubble-liquid mixtures is developed. It consists of a coupled system of partial differential equations describing the spatiotemporal evolution of the sound field amplitude and the redistribution of bubbles in a liquid. A linear stability analysis of the (unstable) uniform bubble distribution is presented. Numerical simulations of the evolution of the sound field amplitude and the bubble concentration show self-organization phenomena. The relation between this system and the nonlinear Schrödinger equation is discussed. © 1996 The American Physical Society.

• Received 26 July 1995

DOI:https://doi.org/10.1103/PhysRevE.54.4990