Rayleigh-Taylor instability of viscous fluids with phase change

Area of Science:

• Fluid dynamics
• Heat and mass transfer
• Phase transitions

Background:

• Film boiling on horizontal surfaces exemplifies Rayleigh-Taylor instability.
• Stability analysis requires considering phase changes, heat/mass transfer, and viscous fluid flow.
• Previous studies often assumed equal viscosities or thin fluid layers.

Purpose of the Study:

• Derive an analytical dispersion relation for Rayleigh-Taylor instability under more general conditions.
• Investigate the influence of differing fluid properties and finite vapor layer thickness.
• Analyze the coupled effects of viscosity, phase change, and vapor thickness.

Main Methods:

• Analytical derivation of the dispersion relation for Rayleigh-Taylor instability.
• Consideration of two fluids with different properties and a finite vapor layer.
• Analysis of viscous flow and phase change effects at the interface.

Main Results:

• Phase change has a stabilizing effect on interface growth rate.
• For thin vapor layers, viscosity, phase change, and thickness jointly affect the critical wave number.
• For thick vapor layers, both liquid and vapor viscosities influence the critical wave number.

Conclusions:

• The most unstable wavelength is independent of phase change for thin vapor layers.
• For thick vapor layers, the most unstable wavelength increases with the phase change rate.
• The derived dispersion relation offers a more generalized understanding of film boiling instability.