Influence of surface tension on two fluids shearing instability

TL;DR

This paper analytically examines how surface tension influences the nonlinear growth and stability of bubble and spike structures in combined Rayleigh-Taylor and Kelvin-Helmholtz instabilities, revealing conditions for stabilization and oscillations.

Contribution

It provides new analytical solutions for the velocity and curvature of bubble and spike tips considering surface tension effects in combined instabilities.

Findings

Surface tension reduces bubble and spike velocities beyond a critical value.

Surface tension stabilizes the motion under certain conditions.

Nonlinear oscillations depend on surface tension and velocity shear.

Abstract

Using extended Layzer's potential flow model, we investigate the effects of surface tension on the growth of the bubble and spike in combined Rayleigh-Taylor and Kelvin-Helmholtz instability. The nonlinear asymptotic solutions are obtained analytically for the velocity and curvature of the bubble and spike tip. We find that the surface tension decreases the velocity but does not affect the curvature, provided surface tension is greater than a critical value. For a certain condition, we observe that surface tension stabilizes the motion. Any perturbation, whatever its magnitude, results stable with nonlinear oscillations. The nonlinear oscillations depend on surface tension and relative velocity shear of the two fluids.