Surface tension in incompressible Rayleigh–Taylor mixing flow

Abstract

We study the effect of surface tension on the incompressible Rayleigh–Taylor instability. We modify Goncharov's local analysis [1] to consider the surface tension effect on the Rayleigh–Taylor bubble velocity. The surface tension damps the linear instability and reduces the nonlinear terminal bubble velocity. We summarize the development of a finite-volume, particle-level-set, two-phase flow solver with an adaptive Cartesian mesh, and results from convergence and validation studies of this two-phase flow solver are provided. We use this code to simulate the single-mode, viscous Rayleigh–Taylor instability with surface tension, and good agreement in terminal bubble velocity is found when compared with analytic results. We also simulate the immiscible Rayleigh–Taylor instability with random initial perturbations. The ensuing mixing flow is characterized by the effective mixing rate and the flow anisotropy. Surface tension tends to reduce the effective mixing rate and homogenizes the Rayleigh–Taylor mixing flow. Finally, we provide a scaling argument for detecting the onset of the quadratic, self-similar Rayleigh–Taylor growth.

Keywords:

• Rayleigh–Taylor instability
• Surface tension
• Anisotropy
• Transition
• Self-similar turbulence

PACS numbers:

• 52.35.Py
• 47.11.Df
• 68.03.−g
• 68.03.Cd
• 47.52.+j
• 47.11.−j
• 47.35.−i
• 47.27.−i
• 47.51.+a
• 47.27.wj

Acknowledgements

We acknowledge the support from the NSF/MRI funded computing cluster at NJIT/DMS. We wish to thank J. Glimm, X. Li, Y. Zhang, P. Ramaprabhu and M. Siegel for helpful discussion.

Notes

*This is when the increase in bubble height deviates from the exponential growth by 5%.