Mass diffusion and bending in dynamic wetting by phase-field and sharp-interface models.

Area of Science:

• Fluid Dynamics and Interface Science
• Computational Physics

Background:

• Classical sharp-interface models face contact line singularities due to the no-slip condition, often requiring empirical Navier boundary conditions.
• Phase-field models naturally handle contact line dynamics via mass diffusion, but can be computationally intensive.
• A need exists for efficient sharp-interface methods that capture diffusive mass transport at the contact line.

Purpose of the Study:

• To develop a computationally efficient sharp-interface toy model that incorporates mass diffusion at the contact line.
• To regularize contact line singularities without empirical parameter fitting.
• To provide a practical alternative for simulating dynamic wetting phenomena.

Main Methods:

• Developed a theoretical relation from Cahn-Hilliard equations linking diffusive mass transport to wall curvature.
• Estimated chemical potential on a curved interface to derive the highly curved region width (δ) and apparent contact angle.
• Introduced a fictitious boundary within the sharp-interface framework with a dynamic apparent contact angle condition.

Main Results:

• The toy model successfully accounts for mass diffusion at the contact line within a sharp-interface framework.
• Model validation against phase-field simulations showed good agreement for liquid bridge steady states and drop spreading transients.
• The model provides an efficient and practical method for solving contact line problems.

Conclusions:

• The proposed sharp-interface toy model effectively resolves contact line singularities by incorporating mass diffusion.
• This approach offers a computationally less expensive alternative to phase-field methods for dynamic wetting simulations.
• The model's parameters can be informed by phase-field simulations, bridging the gap between methods.