Rayleigh-Taylor stability boundary at solid-liquid interfaces

A previous model for the Rayleigh-Taylor instability [A. R. Piriz, J. J. López Cela, and N. A. Tahir, Phys. Rev. E 80, 046305 (2009)] has been extended in order to study an interface between an elastic-plastic solid and a Newtonian liquid and determine the stability region given by the initial perturbation amplitude ${\xi }_0$ and wavelength $\lambda$. The stability region is found to be enhanced by the effect of the liquid viscosity, but it reaches an asymptote for a sufficiently high viscosity. In addition, it is also found that the boundary for the transition from the elastic to the plastic regime get closer to the stability boundary up to both boundaries coincide for a high enough liquid viscosity, thus making the onset of plastic flow a sufficient condition for instability.

Figure 1

Diagram of the perturbed interface for $t>0$.

Figure 2

Stability region: dimensionless amplitude $\widehat{\xi }$ as a function of the dimensionless perturbation wavelength $\widehat{\lambda }$ for the instability threshold, with the dimensionless viscosity $D_0$ as a parameter ($D_0$ increases from bottom to top).

Figure 3

The EP transition: dimensionless amplitude ${\widehat{\xi }}_{\text{EP}}$ as a function of the dimensionless perturbation wavelength $\widehat{\lambda }$ for the EP boundary and with the dimensionless viscosity $D_0$ as a parameter ($D_0$ increases from bottom to top).

Figure 4

The EP transition (the lower curve of each couple with the same outline) and stability (upper curve) boundaries for different values of the parameter $D_0$ ($D_0$ increases from bottom to top).