A Nanothermodynamic Approach to the Shuttleworth and Lippman Equations.

Claire Chassagne, Dick Bedeaux, Signe Kjelstrup

Abstract read

In one paragraph

Article in Entropy (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

0numbers the graph read from it

0cells of the map it votes in

0citing papers in PubMed

–field-weighted citation impact

1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

0 citing papers in PubMed.

No citing paper in PubMed yet.

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

3 authors.

Claire ChassagneSection of Environmental Fluid Mechanics, Department of Hydraulic Engineering, Delft University of Technology, 2628 CN Delft, The Netherlands.ORCID 0000-0003-3223-8657

Dick BedeauxPoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway.ORCID 0000-0003-1697-2835

Signe KjelstrupPoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway.ORCID 0000-0003-1235-5709

Funding

The Research Council of Norway 262644 PoreLab

6 · The paper itself

Abstract

The Shuttleworth and Lippman equations are well-known equations used to link surface tension and stress (Shuttleworth) and surface tension and electric surface potentials (Lippmann). We show that the Shuttleworth and Lippman equations have a common thermodynamic basis, common to systems that possess a relatively large interfacial energy. This is relevant for problems of droplet stability, colloidal suspensions, electrode surfaces and more. Both equations are derived for systems that are not Euler homogeneous in the manner classical systems are. Hill's thermodynamics for

Indexed as

Helfrich curvature energyintegral and differential surface tensionLippman equationnanothermodynamicsShuttleworth equationsubdivision potentialsurface excess variables

Identifiers

PMID42352155

DOI10.3390/e28060645

PMCPMC13298343

What OpenQuestion holds

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LicenceCC BY

Read underepoch 390

Registered trials

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.