Hydrodynamics Across a Fluctuating Interface

TL;DR

This paper develops an exact mechanical formulation of hydrodynamics at a liquid-vapor interface using molecular dynamics, accounting for surface fluctuations and dynamics without equilibrium assumptions.

Contribution

It introduces a novel control volume approach that incorporates surface curvature and movement into hydrodynamic equations, valid far from equilibrium.

Findings

Provides local definitions of hydrodynamic fluxes at the interface.

Balances kinetic and configurational pressures dynamically.

Framework applicable to evolving interface phenomena like bubble nucleation.

Abstract

Understanding what happens inside the rippling and dancing surface of a liquid remains one of the great challenges of fluid dynamics. Using molecular dynamics (MD) we can pick apart the interface structure and understand surface tension. In this work we derive an exact mechanical formulation of hydrodynamics for a liquid-vapour interface using a control volume which moves with the surface. This mathematical framework provides the local definition of hydrodynamic fluxes at any point on the surface. These are represented not only by the flux of molecules and intermolecular interactions acting across the surface, but also as a result of the instantaneous local curvature and movement of the surface itself. By explicitly including the surface dynamics in the equations of motion, we demonstrate an exact balance between kinetic and configurational pressure normal to the surface. The hydrodynamic analysis makes no assumptions regarding the probability distribution function, so is valid for any system arbitrarily far from thermodynamic equilibrium. The presented equations provide a theoretical basis for the study of time-evolving interface phenomena such as bubble nucleation, droplet dynamics and liquid-vapour instabilities.