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The application of the Young–Laplace equation to a solid–liquid interface is considered. Computer simulations show that the pressure inside a solid cluster of hard spheres is smaller than the external pressure of the liquid (both for small and large clusters). This would suggest a negative value for the interfacial free energy. We show that in a Gibbsian description of the thermodynamics of a curved solid–liquid interface in equilibrium, the choice of the thermodynamic (rather than mechanical) pressure is required, as suggested by Tolman for the liquid–gas scenario. With this definition, the interfacial free energy is positive, and the values obtained are in excellent agreement with previous results from nucleation studies. Although, for a curved fluid–fluid interface, there is no distinction between mechanical and thermal pressures (for a sufficiently large inner phase), in the solid–liquid interface, they do not coincide, as hypothesized by Gibbs.
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This content will become publicly available on March 1, 2026
Nonideal Incompressible Lattice-Boltzmann Method for Multicomponent Phase Separating Systems
Understanding and predicting the dynamics of complex fluid systems including liquid–liquid phase separation, relevant to both biological and engineered applications, typically uses a nonideal free energy. Introducing such a thermodynamic constraint into the Lattice-Boltzmann Method can be accomplished by altering either the equilibrium distribution function or the external force. The former requires a lengthy parameterization for a free energy of multiple independent variables which becomes cumbersome for more than three components. The latter has been done for a multicomponent compressible system, but a correction term for the force is required to recover the expected conservation equations. This work builds upon the incompressible single component forcing method from He et al. (Journal of Computational Physics, Vol. 152, No. 2, 1999) by deriving and implementing the required force needed to successfully recover the expected mass conservation from a nonideal free energy with an arbitrary number of components. This allows the simulation of more realistic phase separating fluid systems by including many interacting components, which is demonstrated here for up to five components and phases.
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- Award ID(s):
- 2048051
- PAR ID:
- 10620615
- Publisher / Repository:
- arc.aiaa.org
- Date Published:
- Journal Name:
- AIAA Journal
- Volume:
- 63
- Issue:
- 3
- ISSN:
- 0001-1452
- Page Range / eLocation ID:
- 1013 to 1024
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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