Non-Darcy behavior of two-phase channel flow

Area of Science:

• Multiphase flow dynamics
• Porous media physics
• Computational fluid dynamics

Background:

• Understanding macroscopic two-phase flow in porous media is crucial for various scientific and engineering applications.
• Existing models often simplify the complex interactions at the pore scale, necessitating advanced theoretical frameworks.
• Phase-field modeling offers a powerful approach to capture interface dynamics and phase transitions in complex geometries.

Purpose of the Study:

• To derive and analyze the macroscopic behavior of two-phase flow in porous media using a phase-field model.
• To investigate the influence of surface properties (homogeneous vs. chemically patterned) on flow dynamics.
• To establish theoretical force-velocity relationships and understand deviations from Darcy's law.

Main Methods:

• Development of a phase-field model to simulate two-phase flow.
• Homogenization techniques to derive macroscopic dissipation laws from the pore-scale model.
• Analysis of scaling relations for dissipation rate and velocity in different channel geometries.

Main Results:

• A dissipation law was derived from the phase-field model, enabling explicit force-velocity relations.
• For homogeneous surfaces, Darcy's law remains valid with a modified permeability that includes contact line slip.
• Chemically patterned surfaces exhibit non-Darcy linear scaling of dissipation rate with velocity, linked to depinning forces.

Conclusions:

• The phase-field model provides a theoretical basis for understanding macroscopic two-phase flow behavior.
• Contact line slip significantly modifies permeability in homogeneous porous media.
• Deviations from Darcy's law in patterned media are explained by depinning phenomena, offering insights into experimental observations.