Three-phase Model of Visco-elastic Incompressible Fluid Flow and its Computational Implementation.

Area of Science:

• Multiphase fluid dynamics
• Thermodynamics
• Biophysics

Background:

• Modeling complex fluid mixtures requires thermodynamically consistent approaches.
• Existing models may not fully capture the behavior of Newtonian and visco-elastic fluids simultaneously.
• Understanding fluid dynamics is crucial for biological and biophysical applications.

Purpose of the Study:

• To derive a novel, thermodynamically consistent three-phase model for Newtonian and visco-elastic fluid mixtures.
• To incorporate fluid elasticity into boundary conditions for moving contact line problems.
• To develop and validate an energy-stable numerical scheme for the model.

Main Methods:

• Energetic Variational Approach to derive the three-phase model.
• Coupled Navier-Stokes and Cahn-Hilliard equations form the model's core.
• Development of an energy-stable numerical scheme for efficient computation.
• Simulation of a droplet sliding on an inclined plane to verify numerical scheme convergence.
• Modeling of venous blood clot deformation under shear flow conditions.

Main Results:

• A novel, thermodynamically consistent three-phase fluid mixture model was successfully derived.
• The model satisfies energy dissipation laws and is Galilean invariant.
• A modified Navier boundary condition accounting for fluid elasticity was introduced.
• Numerical simulations confirmed the scheme's stability and convergence.
• The model accurately predicted blood clot deformation, matching experimental observations.

Conclusions:

• The developed three-phase model provides a robust framework for simulating complex fluid mixtures.
• The model's ability to capture visco-elastic effects and its numerical stability are significant advancements.
• This model holds promise for advancing research in biophysical problems, particularly those involving blood flow and clot dynamics.