PSI - Issue 68

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Boyu Li et al. / Procedia Structural Integrity 68 (2025) 59–65 B. Li et al. / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 5. Capillary shapes considered in this study: circular (C), diamond (D), star (S), and triangular (T).

Table 1. Cross-section properties for studied capillaries. Cross-sectional area Cross-section perimeter

Area-to-perimeter ratio ⁄2 (0.5 ) √2 8 (0.3133 ) (4 − ) 2 (0.1366 ) 2 (4 (2 − + ) ) (0.0834 )

* *

2 4√2 2 (2 + )

Circular (C)

Diamond (D)

(4 − ) * (4 − ) * 2

Star (S)

Triangular (T)

Table 2. Material properties of PETG and fluid (from Romero et al., 2023). Property fluid surface tension (N/m) 0.07275 contact angle θ (degree) 54° viscosity (Pa∙s) 1.0016 × 10 +,

3. Results and discussion Fig. 6 illustrates the evolution of capillary flow length across various geometries with different area-to-perimeter ratios as presented in Table 1. According to Eq. (3), the air pressure, the water pressure and the dynamic pressure are all proportional to the cross-sectional area of the capillary, while the capillary force is proportional to the perimeter of the capillary cross-section. Capillaries with triangular and star-shaped geometries, with smaller cross-sectional areas, exhibit longer penetration distances and higher flow speeds compared to other geometries, due to their lower area-to perimeter ratios. A more detailed analysis of various forces provides additional insight. The circular and star-shaped capillaries with the same perimeter (Table 1) demonstrate equal capillary forces (Fig. 7a). In contrast, the diamond-shaped capillary exhibits a significantly higher capillary force due to its larger perimeter. Although the circular and diamond capillaries have identical cross-sectional areas, their different perimeters lead to varying capillary forces. Additionally, while the