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A ternary mixture model with dynamic boundary conditions.

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This study models ternary mixtures interacting with solid walls, revealing how wall interactions and dynamic conditions influence phase separation and droplet behavior. These findings are key for understanding complex fluid dynamics in confined systems.

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Area of Science:

  • Multiphase flow dynamics
  • Materials science
  • Chemical engineering

Background:

  • Short-range interactions between multi-component mixtures and solid walls are critical in confined geometries for life sciences and engineering.
  • Existing models often simplify these complex interactions, limiting their applicability.

Purpose of the Study:

  • To extend the Cahn-Hilliard model to ternary mixtures with dynamic boundary conditions.
  • To develop an efficient and stable numerical scheme for simulating these systems.
  • To investigate the impact of wall-mixture interactions and boundary conditions on phase separation, coarsening, and droplet wettability.

Main Methods:

  • Extension of the Cahn-Hilliard model to ternary mixtures using the Onsager principle.
  • Development of a linear, second-order, unconditionally energy-stable numerical scheme via invariant energy quadratization.
  • Simulation of spontaneous phase separation, coarsening, and droplet behavior on surfaces.

Main Results:

  • Wall-mixture interactions significantly affect surface phenomena (e.g., contact angles) and bulk patterns.
  • Dynamic boundary conditions and relaxation rates control droplet spreading.
  • Cross-coupling relaxation rates in the bulk influence coarsening patterns.

Conclusions:

  • The developed framework comprehensively studies multi-component mixtures in confined geometries.
  • This model provides insights into the interplay between bulk and surface phenomena in complex fluid systems.
  • The findings have implications for designing materials and processes involving confined multi-component fluids.