Molecular view of the Rayleigh-Taylor instability in compressible Brownian fluids

Abstract

The onset of the Rayleigh-Taylor instability is studied a compressible Brownian Yukawa fluid mixture on the ``molecular'' length and time scales of the individual particles. As a model, a two-dimensional phase-separated symmetric binary mixture of colloidal particles of type $A$ and $B$ with a fluid-fluid interface separating an $A$-rich phase from a $B$-rich phase is investigated by Brownian computer simulations when brought into non-equilibrium via a constant external driving field which acts differently on the different particles and perpendicular to the interface. Two different scenarios are observed which occur either for high or for low interfacial free energies as compared to the driving force. In the first scenario for high interfacial tension, the critical wavelength $λ_c$ of the unstable interface modes is in good agreement with the classical Rayleigh-Taylor formula provided dynamically rescaled values for the interfacial tension are used. The wavelength $λ_{c}$ increases with time representing a self-healing effect of the interface due to a local density increase near the interface. The Rayleigh-Taylor formula is confirmed even if $λ_c$ is of the order of a molecular correlation length. In the second scenario for very large driving forces as compared to the interfacial line tensions, on the other hand, the particle penetrate easily the interface by the driving field and form microscopic lanes with a width different from the predictions of the classical Rayleigh-Taylor formula.