PSI - Issue 68

4

B. Li et al. / Structural Integrity Procedia 00 (2025) 000–000

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

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The basic capillary flow as shown in Eq. (2) presents the force acting on the flow in a capillary. Galpayage et al. (2020) further expanded Eq. (1): #$% = 2 (2) ( + ∆ ) ̈ = 2 + − $ − + , ̇ , − 8 ̇ (3) where is the radius of a circular capillary, is the surface tension of the fluid, is the contact angle of the surface material, is the fluid density, is the depth of the water layer, A is the cross-sectional area, $ is the pressure of the air remaining in the capillary, ̇ is the speed of the capillary flow, is the water viscosity.

Fig. 4. Evolution of force magnitudes acting on flow in a circular capillary.

Fig. 4 illustrates the evolution of all the forces acting on a flow in a circular capillary. The capillary force, water pressure and air pressure are the dominant forces that drive this flow. The viscous force that is consistently lower by an order of magnitude is ignored in the following analysis. From Eq. (3), the capillary force is proportional to the tunnel perimeter. The capillary’s cross-section area influences the air, water, and dynamic pressure. To further explore the effect of shape on the capillary flow, four different capillaries shown in Fig. 5 are considered alongside a circular one: a diamond capillary, a star capillary and a triangular capillary. Their perimeters and cross-sectional areas are given in Table 1. The size of the diamond-shaped capillary is defined as √ to ensure that it has the same cross sectional area as the circular model to explore the effect of the channel perimeter. The star model simulates the round corner at the edge of each printing bead as in many MEAM polymers with parallel deposited filaments. Furthermore, it has the same perimeter as a circular capillary (Table 1). So, the effect of capillary cross-sectional area can be explored. A triangular model is also modelled to account for the impact of gravity and the pressure of the printing nozzle. In Table 1, the listed area-to-perimeter ratio decreases from the top to the bottom. Hence, more complex geometries have a lower area-to-perimeter ratio compared to that of a traditional (circular) capillary contour. The material and fluid properties are listed in Table 2.