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Wetting, Algebraic Curves, and Conformal Invariance.

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This study exactly solves a fluid mixture interface model, revealing profile paths as conformally invariant curves. The findings confirm critical point wetting is absent, contrary to typical expectations.

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Area of Science:

  • Physical Chemistry
  • Fluid Dynamics
  • Statistical Mechanics

Background:

  • Studies of wetting phenomena in fluid mixtures reveal complex interface behaviors.
  • A two-component square-gradient model with three-phase bulk coexistence exhibits surprising features in interface profiles.
  • Previous numerical results suggested non-wetting might persist to critical endpoints, challenging standard critical point wetting theories.

Purpose of the Study:

  • To provide an exact analytical solution for the two-component square-gradient model of interfaces.
  • To elucidate the geometric properties of density profile paths and their relation to surface tensions.
  • To investigate the phenomenon of critical point wetting in this specific model.

Main Methods:

  • Exact analytical solution of the square-gradient model.
  • Representation of harmonic profile paths using analytic functions in the complex plane.
  • Conformal mapping techniques to transform profile paths into straight lines.

Main Results:

  • Density profile paths are identified as conformally invariant quartic algebraic curves that change genus at the wetting transition.
  • The exact solution derives the conjectured forms of surface tensions.
  • The geometric properties of the tricuspid shape and its relation to the Neumann triangle for contact angles are explained.

Conclusions:

  • The exact solution confirms the absence of critical point wetting in the studied square-gradient model.
  • Conformal invariance and genus change are key features of the wetting transition in this model.
  • The findings provide a theoretical framework for understanding interface behavior and wetting phenomena in fluid mixtures.