Nonlinear analysis of the Rayleigh-Taylor instability of viscous finite fluid layers

The nonlinear evolution of Rayleigh-Taylor instability of plane fluid layers is investigated based on an extensive numerical study. Full Navier-Stokes equations and exact boundary equations are solved simultaneously for precise prediction of this phenomenon. An accurate flux line segment model (FLAIR) for fluid surface advection is employed for the interface reconstruction. An accurate scheme for the implementation of the boundary equations at the free surface is presented. The instability is characterized by three stages of development which are defined by monitoring the competition of the bubble and spike growth. This competition is responsible for the development of different spike and bubble morphologies and is decided based on geometrical factors, mainly the amplitude and wavelength of the initial perturbation, and on the fluid properties, mainly viscosity and surface tension. The cutoff wavenumbers and the most unstable wavenumbers are identified numerically based on the effect of the surface tension dimensionless parameter defined as Weber number. The effect of Reynolds number on the growth rate of instability and the role of viscosity in dragging the development of instability are also investigated. Curved layers are found to be more unstable than plane fluid layers. Finally, the problem of liquid drops microexplosion is investigated in view of the hydrodynamics instability associated with the disruptive phenomenon. The size of the internal phase, the Weber number and the characteristics of the surface perturbation are shown to significantly affect the breakup time of the liquid drop.