Spontaneous rise in open rectangular channels under gravity.

Area of Science:

• Fluid dynamics
• Surface science
• Microfluidics

Background:

• Coupled fluid flow in microfluidic devices, porous media, and textured surfaces is crucial.
• Spontaneous wetting on grooved surfaces serves as a model for studying complex fluid behavior.

Purpose of the Study:

• To numerically investigate the spontaneous capillary rise of liquid in an array of open rectangular channels under gravity.
• To analyze the influence of channel geometry and contact angles on fluid rise dynamics, particularly at corners.

Main Methods:

• Utilized the Volume-of-Fluid (VOF) method for accurate interface tracking.
• Employed adaptive mesh refinement to handle complex flow features and varying scales.
• Simulated liquid rise in rectangular channels, measuring meniscus height at various locations.

Main Results:

• At low contact angles (<45°), rivulets form in interior corners and a cusp at exterior corners.
• Rivulet dynamics follow a one-third power law over time, with minimal geometric dependence.
• Exterior corner cusp transforms into a smooth meniscus when capillary forces dominate, irrespective of contact angle.
• Outer face width and channel size showed no influence on capillary rise in the adjacent region.

Conclusions:

• Corner geometry significantly influences capillary rise dynamics, deviating from classical models that ignore these features.
• The formation of rivulets and cusps highlights the complex interplay between surface tension, gravity, and geometry in confined spaces.
• Findings are relevant for understanding fluid transport in microfluidic devices, porous materials, and textured surfaces.