Modeling Approach to Determine Static Rivulet Height in Regular Polygonal Capillary Tubes

Area of Science:

• Fluid dynamics
• Capillary phenomena
• Surface science

Background:

• Partially wetting liquids rise along corners of noncircular capillary tubes in applications like wastewater treatment, oil recovery, and blood flow.
• Corners alter liquid distribution under incomplete wetting conditions.

Purpose of the Study:

• To investigate rivulet rise at the corners of polygonal capillary tubes for partially wetting liquids.
• To develop geometrical models for capillary rise and flow behavior at tube corners.

Main Methods:

• Geometrical models were developed for capillary rivulet height and profile under gravity in triangular, square, and pentagonal tubes.
• The study examined the influence of contact angle, polygon sides, and liquid properties on capillary rivulet height.

Main Results:

• The ratio of liquid surface tension to density directly affects corner rise, inversely related to other factors.
• Maximum rivulet height (91.6 mm) observed in a triangular tube (1 mm side, 30° contact angle) with PDMS-20.
• Minimum rivulet height (6.2 mm) observed in a pentagonal tube (3 mm side, 30° contact angle).

Conclusions:

• The developed analytical approach was validated against literature and experimental data, showing good agreement.
• The study provides quantitative insights into how capillary tube shape influences fluid flow behavior.
• Results are valuable for controlling and optimizing transport phenomena in noncircular tube systems.