2004/11/15 by Y. S. Djikaev, Yuri Djikaev
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Classical mechanics #Computer science #Contact angle #Function (biology) #Geometry #Histogram #Image (mathematics) #Line (geometry) #Material Dynamics and Properties #Mathematics #Moment (physics) #Monte Carlo method #Phase (matter) #Phase Equilibria and Thermodynamics #Physics #Scaling #Series (stratigraphy) #Statistical physics #Statistics #Surface tension #Tension (geology) #Ternary operation #Theoretical and Computational Physics #Thermodynamics #cond-mat.mtrl-sci #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1063/1.2056548
arxiv created 2004/11/15 · openalex publication_date 2005/11/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A method is proposed for determining the line tension, which is the main physical characteristic of a three-phase contact region, by Monte Carlo (MC) simulations. The key idea of the proposed method is that if a three-phase equilibrium involves a three-phase contact region, the probability distribution of states of a system as a function of two order parameters depends not only on the surface tension, but also on the line tension. This probability distribution can be obtained as a normalized histogram by appropriate MC simulations, so one can use the combination of histogram analysis and finite-size scaling to study the properties of a three phase contact region. Every histogram and results extracted therefrom will depend on the size of the simulated system. Carrying out MC simulations for a series of system sizes and extrapolating the results, obtained from the corresponding series of histograms, to infinite size, one can determine the line tension of the three phase contact region and the interfacial tensions of all three interfaces (and hence the contact angles) in an infinite system. To illustrate the proposed method, it is applied to the three-dimensional ternary fluid mixture, in which molecular pairs of like species do not interact whereas those of unlike species interact as hard spheres. The simulated results are in agreement with expectations.