Microscopic Derivation of Stochastic Thin-Film Equation and Extensions to Two-Layer and Evaporating Films
Abstract
While classical thin-film hydrodynamics models widely govern macroscopic fluid layers, they fail to capture the molecular-level thermal fluctuations that dictate nanoscale interfacial dynamics. Standard stochastic extensions rely on the long-wave approximation of the continuum fluctuating Navier-Stokes equations; however, this top-down paradigm lacks a formal connection to microscopic particle trajectories and cannot readily accommodate complex, non-equilibrium boundary mechanisms. We resolve this limitation by deriving the stochastic thin-film equation directly from the exact underlying N-particle Hamiltonian dynamics. This is achieved via a systematic, bottom-up coarse-graining framework based on a generalized fluctuating dynamic density-functional theory. Crucially, this first principles formulation offers unparalleled flexibility, enabling the seamless integration of multi-layered interfaces and non-conserved dynamics such as evaporation. For these complex configurations, our framework rigorously yields entirely novel stochastic thin-film equations featuring emergent noise terms that encapsulate microscopic fluctuations missing from classical top-down models.
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BibTeX
@misc{kay2026microscopic,
title = {{Microscopic Derivation of Stochastic Thin-Film Equation and Extensions to Two-Layer and Evaporating Films}},
author = {Toby Kay and Serafim Kalliadasis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35422},
eprint = {2610.35422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35422},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Microscopic Derivation of Stochastic Thin-Film Equation and Extensions to Two-Layer and Evaporating Films
AU - Toby Kay
AU - Serafim Kalliadasis
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35422
UR - https://arxiv.org/abs/2610.35422
AB - While classical thin-film hydrodynamics models widely govern macroscopic fluid layers, they fail to capture the molecular-level thermal fluctuations that dictate nanoscale interfacial dynamics. Standard stochastic extensions rely on the long-wave approximation of the continuum fluctuating Navier-Stokes equations; however, this top-down paradigm lacks a formal connection to microscopic particle trajectories and cannot readily accommodate complex, non-equilibrium boundary mechanisms. We resolve this limitation by deriving the stochastic thin-film equation directly from the exact underlying N-particle Hamiltonian dynamics. This is achieved via a systematic, bottom-up coarse-graining framework based on a generalized fluctuating dynamic density-functional theory. Crucially, this first principles formulation offers unparalleled flexibility, enabling the seamless integration of multi-layered interfaces and non-conserved dynamics such as evaporation. For these complex configurations, our framework rigorously yields entirely novel stochastic thin-film equations featuring emergent noise terms that encapsulate microscopic fluctuations missing from classical top-down models.
ER -