Kinetic roughening in two-phase fluid flow through a random Hele-Shaw cell

Area of Science:

• Physics
• Fluid Dynamics
• Materials Science

Background:

• Two-phase fluid flow in porous media is complex, influenced by wettability and viscosity.
• Understanding interface dynamics in disordered systems like Hele-Shaw cells is crucial for various scientific and engineering applications.

Purpose of the Study:

• To derive a nonlocal interface equation for two-phase flow in a disordered Hele-Shaw cell.
• To explicitly relate capillary and viscous pressure fluctuations to microscopic quenched disorder.
• To identify length scales governing scaling regimes and compare simulation results with experiments.

Main Methods:

• Derivation of a nonlocal interface equation for two-phase fluid flow.
• Modeling porous media as a Hele-Shaw cell with random gap variations.
• Analysis of conserved, nonconserved, and power-law correlated noise terms.
• Numerical simulations to obtain forced fluid invasion exponents.

Main Results:

• A nonlocal interface equation was derived, accounting for arbitrary wettability and viscosity contrast.
• Fluctuations in capillary and viscous pressure were explicitly linked to quenched disorder.
• Two characteristic length scales, dependent on the capillary number (Ca), were identified: l(1) ~ b(0)(cCa)^(-1/2) and l(2) ~ b(0)Ca^(-1).

Conclusions:

• The derived equation and identified length scales provide a framework for understanding scaling regimes in disordered porous media.
• Numerical simulations support the theoretical findings and show good agreement with experimental data.
• This research offers insights into the fundamental physics of fluid invasion in complex, heterogeneous environments.