Dynamical scaling of imbibition in columnar geometries

Area of Science:

• Physics
• Materials Science
• Fluid Dynamics

Background:

• Interfacial fluctuations in columnar geometries during imbibition exhibit dynamic scaling inconsistent with standard nonlocal models.
• Surface tension-driven macroscopic models fail to explain observed interfacial dynamics.

Purpose of the Study:

• To investigate the discrepancy between experimental observations and theoretical models of imbibition in disordered columnar systems.
• To analyze the behavior of interfacial dynamics under varying degrees of columnar disorder using a phase-field model.

Main Methods:

• Numerical integration of a phase-field model incorporating dichotomic columnar disorder.
• Systematic analysis of interface evolution under spontaneous and forced-flow imbibition conditions.
• Comparison of simulation results with experimental data.

Main Results:

• Two distinct dynamic regimes were identified based on capillary contrast.
• High capillary contrast leads to disorder-dominated interface evolution, anomalous scaling, and requires a local model for interface motion.
• Low capillary contrast results in interfacial tension dominance, allowing for modeling with a nonlocal approach.

Conclusions:

• The study provides a comprehensive set of scaling exponents for both spontaneous and forced-flow imbibition.
• Findings reconcile experimental observations with theoretical frameworks by distinguishing between local and nonlocal dynamics based on disorder strength.
• The phase-field model effectively captures the complex interfacial behaviors observed in disordered porous media.