Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Maxwell's Thermodynamic Relations

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...

Principle of Linear Impulse and Momentum for a System of Particles

Principle of Linear Impulse and Momentum for a System of Particles

In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...

Reaction Mechanisms: The Steady-State Approximation

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...

Application of the Linear Momentum Equation

Application of the Linear Momentum Equation

The application of the linear momentum equation can be used to analyze the forces needed to hold a 180-degree pipe bend in place with flowing water. In this case, water flows through the bend with a constant cross-sectional area of 0.01 square meters and a flow velocity of 15 meters per second. The pressure at the entrance is 0.2 Megapascals and the pressure at the exit is 0.16 Megapascals.
The goal is to determine the force components in the x and y directions to hold the pipe in place. Since...

Energy Conservation and Bernoulli's Equation

Energy Conservation and Bernoulli's Equation

Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...

Thermodynamic Systems

Thermodynamic Systems

A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of tea boiling in a kettle. The tea and...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

A New Analytical Formulation for the Electrophoretic Mobility of a Colloidal Sphere.

Entropy (Basel, Switzerland)·2025

Same author

A model for maxilloturbinate morphogenesis in seals.

PloS one·2025

Same author

On the Elimination of Fast Variables from the Langevin Equation.

Entropy (Basel, Switzerland)·2024

Same author

Effect of the Ion, Solvent, and Thermal Interaction Coefficients on Battery Voltage.

Journal of the American Chemical Society·2024

Same author

Nanoparticle Dynamics in Composite Hydrogels Exposed to Low-Frequency Focused Ultrasound.

Gels (Basel, Switzerland)·2023

Same author

Transport coefficients for ion and solvent coupling. The case of the lithium-ion battery electrolyte.

The Journal of chemical physics·2023

Search research articles

Related Experiment Video

Updated: Jun 27, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

A Nanothermodynamic Approach to the Shuttleworth and Lippman Equations.

Claire Chassagne¹, Dick Bedeaux², Signe Kjelstrup²

¹Section of Environmental Fluid Mechanics, Department of Hydraulic Engineering, Delft University of Technology, 2628 CN Delft, The Netherlands.

Entropy (Basel, Switzerland)

|June 26, 2026

Summary

The Shuttleworth and Lippman equations share a common thermodynamic basis, particularly for systems with significant interfacial energy. Hill

Keywords:

Helfrich curvature energy Lippman equation Shuttleworth equation integral and differential surface tension nanothermodynamics subdivision potential surface excess variables

More Related Videos

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

Published on: December 1, 2023

Related Experiment Videos

Last Updated: Jun 27, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

Published on: December 1, 2023

Area of Science:

Thermodynamics
Surface Science
Physical Chemistry

Background:

The Shuttleworth and Lippman equations relate surface tension to stress and electric potentials, respectively.
These equations are crucial for understanding phenomena like droplet stability and colloidal suspensions.
Classical thermodynamics often assumes Euler homogeneity, which may not apply to systems with large interfacial energies.

Purpose of the Study:

To demonstrate the common thermodynamic basis of the Shuttleworth and Lippman equations.
To extend classical thermodynamics to systems with size- or shape-dependent interfacial energies.
To rigorously define and differentiate between differential and integral surface tension.

Main Methods:

Application of Hill's thermodynamics for small systems.
Derivation of an extended Hill-Gibbs-Duhem equation.
Analysis using Helfrich's equation to establish scaling laws.

Main Results:

A unified thermodynamic framework for the Shuttleworth and Lippman equations was established.
Two distinct types of surface tension (differential and integral) were rigorously defined.
A scaling law for the subdivision potential as a function of interfacial curvature was derived and predicted.

Conclusions:

The Shuttleworth and Lippman equations are unified under a common thermodynamic basis derived from Hill's thermodynamics.
Hill's thermodynamics provides a robust framework for analyzing systems with significant interfacial energy.
The study clarifies the relationship between different surface tension definitions and their dependence on system curvature.