Inverse problem of capillary filling

Area of Science:

• Physics
• Materials Science
• Fluid Dynamics

Background:

• The inverse problem of capillary filling aims to determine capillary radius profiles from meniscus position over time.
• This is crucial for applications like nanopore characterization and microfluidic design.
• The problem is mathematically ill-posed, leading to multiple possible solutions.

Purpose of the Study:

• To develop and validate a robust method for solving the inverse problem of capillary filling.
• To accurately determine capillary radius profiles from experimental imbibition data.
• To investigate the applicability of the Lucas-Washburn relation beyond uniform capillaries.

Main Methods:

• Measuring capillary filling kinematics in both forward and reverse tube directions.
• Applying the proposed method to experimental data from glass capillaries (150 μm radius) and anodized alumina membranes (30 nm pore radius).

Main Results:

• The proposed method successfully identified the radius profile for both glass capillaries and alumina membranes.
• Demonstrated the ability to characterize capillary geometry across a wide range of length scales.
• Confirmed that the Lucas-Washburn relation (l(t)∝t^1/2) is not limited to uniform cross-sections.

Conclusions:

• A novel approach using bidirectional flow measurements effectively solves the inverse problem of capillary filling.
• The method provides accurate capillary radius profiling for diverse materials and scales.
• This work expands the understanding of capillary flow dynamics and the applicability of the Lucas-Washburn relation.