Nonlinear hydrodynamic theory of crystallization

TL;DR

This paper develops a nonlinear hydrodynamic theory for crystallization in molecular liquids, integrating density functional theory with fluid dynamics to describe elastic responses and interface fluctuations.

Contribution

It introduces a parameter-free kinetic coupling between free energy functionals and Navier-Stokes equations for crystallization modeling.

Findings

Reproduces classical phonon spectrum

Matches steady-state growth front behavior

Aligns capillary wave spectrum with molecular dynamics

Abstract

We present an isothermal fluctuating nonlinear hydrodynamic theory of crystallization in molecular liquids. A dynamic coarse-graining technique is used to derive the velocity field, a phenomenology, which allows a direct coupling between the free energy functional of the classical Density Functional Theory and the Navier-Stokes equation. Contrary to the Ginzburg-Landau type amplitude theories, the dynamic response to elastic deformations is described by parameter-free kinetic equations. Employing our approach to the free energy functional of the Phase-Field Crystal model, we recover the classical spectrum for the phonons and the steady-state growth fronts. The capillary wave spectrum of the equilibrium crystal-liquid interface is in a good qualitative agreement with the molecular dynamics simulations.