Effect of meniscus on the permeability of mono-layered and multi-layered packed spheres

This study aims to numerically investigate the effect of meniscus curvature on the permeability of closely-packed spheres, which have widely used for heat pipes and vapor chambers. The shape of the meniscus curvature in the hexagonally-packed spheres is estimated based on surface energy minimization algorithm. The estimated meniscus shape is then imported into a CFD study for numerically predicting the permeability of the packed spheres. Based on the numerical results, the effect of contact angle and the number of sphere layers are investigated. The results show that the permeability is nearly independent to the contact angle when the contact angle is larger than 10. However, the permeability significantly increases with the contact angle decreases when the contact angle is lower than 10. The permeability quasi-linearly increases as the liquid filling ratio increases when 1 < l* < 2, where l* is liquid filling ratio. When contact angle is 5, the permeability is shown to slightly deviate from the linear behavior with respect to the liquid filling ratio. As the number of layers increases, the permeability significantly increases and approaches that obtained from Blake-Kozeny's equation. As the number of layers increases, the influence of meniscus curvature on the permeability decreases whereas the bottom surface plays an important role in determining the permeability. Based on extensive numerical results, correlations for predicting the packed spheres are proposed.ope