The exact solution of the Koga-Widom-Indekeu model and related models of wetting in fluid mixtures
File(s)
Published version
Author(s)
Parry, Andrew
Rascon, Carlos
Type
Journal Article
Abstract
We show how a broad class of two-component square-gradient models of wetting may be solved exactly for the surface tensions and density profile paths, and clarify how the presence or absence of critical point wetting, in binary and ternary mixtures, is related to universality and symmetry principles at critical end points. We begin by solving a model of fluid interfaces, first introduced by Koga and Widom, in ternary mixtures showing three phase coexistence. Numerical studies
had revealed interesting wetting transitions, as well as curious geometrical properties of the profile paths in the density plane, and led these authors to conjecture expressions for the surface tensions. These conjectures were extended by Koga and Indekeu and predicted that partial wetting may persist up to the line of critical end points, i.e. critical point wetting was, unexpectedly, absent. Here, we obtain the exact density profiles and surface tensions for the Koga-Widom-Indekeu
(KWI) model using complex analysis and drawing on the theory of algebraic curves. The exact solution determines the location and order of wetting transitions in the surface phase diagram, confirming that critical point wetting is absent. The model also displays the remarkable property that microscopic density profiles are mapped, by a conformal transform, onto the shape of a macroscopic drop near the contact line whose tensions satisfy the Neumann triangle. Two related
models, which illustrate the role of the component isotropy, are also discussed: First, wetting by a critical layer where the critical singularities reflect an XY-like Casimir interaction mediated by the wetting film. Secondly, wetting in a binary mixture near a wall where critical point wetting is also absent and component density profiles can be obtained exactly revealing unexpected symmetries and connections to the mesoscopic disjoining pressure. These models suggest that a universality principle governs wetting in fluid mixtures, resolving contradicting results from
earlier studies: Critical point wetting is present if the order-parameter components of the mixture
describe Ising-like criticality, but is absent if there is a local XY symmetry. Implications for wetting
transitions in more microscopic models and in experiments are discussed
had revealed interesting wetting transitions, as well as curious geometrical properties of the profile paths in the density plane, and led these authors to conjecture expressions for the surface tensions. These conjectures were extended by Koga and Indekeu and predicted that partial wetting may persist up to the line of critical end points, i.e. critical point wetting was, unexpectedly, absent. Here, we obtain the exact density profiles and surface tensions for the Koga-Widom-Indekeu
(KWI) model using complex analysis and drawing on the theory of algebraic curves. The exact solution determines the location and order of wetting transitions in the surface phase diagram, confirming that critical point wetting is absent. The model also displays the remarkable property that microscopic density profiles are mapped, by a conformal transform, onto the shape of a macroscopic drop near the contact line whose tensions satisfy the Neumann triangle. Two related
models, which illustrate the role of the component isotropy, are also discussed: First, wetting by a critical layer where the critical singularities reflect an XY-like Casimir interaction mediated by the wetting film. Secondly, wetting in a binary mixture near a wall where critical point wetting is also absent and component density profiles can be obtained exactly revealing unexpected symmetries and connections to the mesoscopic disjoining pressure. These models suggest that a universality principle governs wetting in fluid mixtures, resolving contradicting results from
earlier studies: Critical point wetting is present if the order-parameter components of the mixture
describe Ising-like criticality, but is absent if there is a local XY symmetry. Implications for wetting
transitions in more microscopic models and in experiments are discussed
Date Issued
2026-09-01
Date Acceptance
2026-05-14
Citation
Physica A: Statistical Mechanics and its Applications, 2026, 697
ISSN
0378-4371
Publisher
Elsevier
Journal / Book Title
Physica A: Statistical Mechanics and its Applications
Volume
697
Copyright Statement
© 2026 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
10.1016/j.physa.2026.131693
Publication Status
Published
Article Number
131693
Date Publish Online
2026-05-26