Deriving nonequilibrium interface kinetics from variational principles

TL;DR

This paper introduces a variational principle-based method to derive interface kinetics and boundary conditions in nonequilibrium systems, demonstrated through elastodynamic effects and stability analysis of stressed solid surfaces.

Contribution

It presents a novel, general approach to derive interface equations from variational principles, including elastic and surface effects, applicable to complex nonequilibrium phenomena.

Findings

Derived equations of motion and boundary conditions from variational principles.

Analyzed stability of a stressed solid surface with surface tension.

Validated the approach with the Asaro-Tiller-Grinfeld instability.

Abstract

Nonequilibrium dynamics at interfaces is generally driven by a chemical potential. Here we demonstrate a generic technique to derive the basic equations of motion, boundary conditions and the chemical potential in a consistent way from fundamental variational principles. As a particular example, we consider a solid surface with elastodynamic effects, together with surface energy and tension. We apply the generic results to perform a linear stability analysis of a planar front subjected to uniaxial stress (Asaro-Tiller-Grinfeld instability), here also with surface tension.