  We report on two- and three-dimensional numerical simulations of
Rayleigh-Taylor instabilities in immiscible fluids. A diffuse-interface model
that combines the Cahn-Hilliard equation, governing the evolution of the volume
fraction of one fluid, and the Navier-Stokes equations, governing the bulk
velocity and pressure, is used. The study is limited to low Atwood numbers
owing to the use of the Boussinesq approximation. The code is based on a
pseudo-spectral method. A linear analysis is first performed in a
two-dimensional case of Rayleigh-Taylor instability to confirm that the model
very well captures this phenomenon in the case of inviscid or viscid fluids.
One key aspect of this work is that the influence of the thermodynamic
parameters related to the Cahn-Hilliard equation (interface thickness and
mobility) is quantitively studied. Three-dimensional results of Rayleigh-Taylor
instabilities in viscous fluids are then presented to show the possibilities of
this modeling. We observe the effect of the viscosity and the wavelength of an
initial single-mode perturbation on the mass transport during the nonlinear
regime.
