Wetting, Algebraic Curves, and Conformal Invariance
Articles
Overview
published in
- PHYSICAL REVIEW LETTERS Journal
publication date
- December 2024
start page
- 1
end page
- 5
issue
- 23
volume
- 133
Digital Object Identifier (DOI)
full text
International Standard Serial Number (ISSN)
- 0031-9007
Electronic International Standard Serial Number (EISSN)
- 1079-7114
abstract
- Recent studies of wetting in a two-component square-gradient model of interfaces in a fluid mixture, showing three-phase bulk coexistence, have revealed some highly surprising features. Numerical results show that the density profile paths, which form a tricuspid shape in the density plane, have curious geometric properties, while conjectures for the analytical form of the surface tensions imply that nonwetting may persist up to the critical end points, contrary to the usual expectation of critical point wetting. Here, we solve the model exactly and show that the profile paths are conformally invariant quartic algebraic curves that change genus at the wetting transition. Being harmonic, the profile paths can be represented by an analytic function in the complex plane which then conformally maps the paths onto straight lines. Using this, we derive the conjectured form of the surface tensions and explain the geometrical properties of the tricuspid and its relation to the Neumann triangle for the contact angles. The exact solution confirms that critical point wetting is absent in this square-gradient model.
Classification
subjects
- Mathematics
keywords
- adsorption; classical statistical mechanics; surface & interfacial phenomena; wetting; density functional calculations; density functional theory