Extended models of nonlinear waves in liquid with gas bubbles

TL;DR

This paper develops advanced models for nonlinear waves in gas-liquid mixtures, incorporating heat transfer, surface tension, and compressibility, resulting in two new differential equations that describe dissipative and dispersive wave behaviors.

Contribution

It introduces two novel nonlinear differential equations derived via reductive perturbation method, accounting for multiple physical effects in liquid with gas bubbles.

Findings

Derived equations include effects of heat transfer, surface tension, and compressibility.

One equation models dissipative wave propagation, the other models dispersive wave propagation.

Enhanced understanding of nonlinear wave dynamics in complex liquid-gas systems.

Abstract

In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.