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

TL;DR

This study investigates the Rayleigh-Taylor instability at the molecular level in a compressible Brownian fluid mixture, revealing how interfacial tension and external forces influence instability patterns and interface dynamics.

Contribution

It provides the first molecular-scale analysis of Rayleigh-Taylor instability in compressible Brownian fluids, validating classical formulas under certain conditions and exploring deviations at high driving forces.

Findings

Classical Rayleigh-Taylor formula applies at molecular scales with rescaled interfacial tension.

Interface self-healing occurs through local density increases near the interface.

High driving forces lead to microscopic lane formation, deviating from classical predictions.

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 $\lambda_c$ 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 $\lambda_{c}$ 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 $\lambda_c$ 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.