The resemblance between flow patterns in submerged or open-to-air outlet hydrophobic capillary tubes and water infiltration in hydrophobic porous media

Porous media (PM) flow is essential in many natural and industrial processes. The PM can be either hydrophilic or hydrophobic, substantially affecting its imbibition and flow. As opposed to a decreasing infiltration rate with time (concave shape) in hydrophilic PM, an increasing rate with time (convex shape) has been observed in hydrophobic PM. A commonly accepted mechanism to explain the convex infiltration pattern is still lacking. The current study elucidates the latter by focusing on flow in hydrophobic capillary tubes under different boundary conditions. A convex-shape meniscus propagation in a hydrophobic capillary tube was observed for low ponded water depth at the tube inlet, whereas a concave shape propagation was observed for high ponded water depths. To the best of our awareness, such a finding is innovative. Once the meniscus reached the tube outlet, the hydraulic conductivity of the hydrophobic tube depended on the driving head for an open-to-air outlet while having a constant value for a submerged one. The saturated hydraulic conductivity for an open-to-air capillary tube depends on the ratio between ponded water depth and tube water-entry head,R₀, and reaches a constant value measured for a submerged tube for R₀ > 20.8. While successfully predicting the wetting-front propagation for R₀> 20.8, the modified Lucas-Washburn (LW) equation with slip boundary condition failed to predict the convex infiltration patterns. The observed infiltration patterns in hydrophobic porous media in general and soils in particular, seem inherent since capillary tubes are fundamental units in such media. Moreover, flow in PM has been frequently modeled using a bundle of nonuniform capillary tubes. The failure of the modified LW equation to predict the measured data for R₀< 20.8 calls for a new approach to model water flow in hydrophobic tubes and PM.