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PreprintCC BYChemRxiv

Nanothermodynamic Generalization of the Young–Laplace and Young Equations for Sessile Droplets with Line Effects

  • Vitor H. C. Cunha1,2
  • Signe Kjelstrup1,2
  • Dick Bedeaux1,2
  1. 1Department of Chemistry
  2. 2Norwegian University of Science and Technology
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Abstract

Thermodynamic investigations of wetting phenomena require that we handle the nanoscale. By combining Hill’s small-system thermodynamics with a Gibbsian composite-system description, we formulate the equilibrium thermodynamics of a sessile nanodroplet. We consider a one-component liquid droplet resting on an ideal, flat, inert solid substrate and in contact with reservoirs that fix the temperature and chemical potential. Finite-size effects are retained in the liquid bulk phase, the liquid–vapor interface, and the three-phase contact line, while the solid–vapor and solid–liquid interfaces are assumed to follow regular thermodynamics and treated macroscopically. The distinction between integral and differential pressure, surface tension, and line tension is used to derive nanothermodynamic generalizations of the Young–Laplace and Young equations. The resulting equations account for the size-and shape dependence of the finite thermodynamic contributions and recover the classical equilibrium equations in the macroscopic limit.

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Cite

BibTeXRIS
BibTeX
@misc{cunha2026nanothermodynamic,
  title = {{Nanothermodynamic Generalization of the Young–Laplace and Young Equations for Sessile Droplets with Line Effects}},
  author = {Vitor H. C. Cunha and Signe Kjelstrup and Dick Bedeaux},
  howpublished = {ChemRxiv},
  year = {2026},
  month = sep,
  doi = {10.26434/chemrxiv.15008838/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008838/v1},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - Nanothermodynamic Generalization of the Young–Laplace and Young Equations for Sessile Droplets with Line Effects
AU  - Vitor H. C. Cunha
AU  - Signe Kjelstrup
AU  - Dick Bedeaux
PY  - 2026
DA  - 2026/09/15
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15008838/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008838/v1
AB  - Thermodynamic investigations of wetting phenomena require that we handle the nanoscale. By combining Hill’s small-system thermodynamics with a Gibbsian composite-system description, we formulate the equilibrium thermodynamics of a sessile nanodroplet. We consider a one-component liquid droplet resting on an ideal, flat, inert solid substrate and in contact with reservoirs that fix the temperature and chemical potential. Finite-size effects are retained in the liquid bulk phase, the liquid–vapor interface, and the three-phase contact line, while the solid–vapor and solid–liquid interfaces are assumed to follow regular thermodynamics and treated macroscopically. The distinction between integral and differential pressure, surface tension, and line tension is used to derive nanothermodynamic generalizations of the Young–Laplace and Young equations. The resulting equations account for the size-and shape dependence of the finite thermodynamic contributions and recover the classical equilibrium equations in the macroscopic limit.
ER  -