Capillary flow in Y-shaped junctions with open- and closed-end branches

The capillary flow in asymmetric junctions can delay the liquid invasion of the wide branch, which has important implications for the liquid imbibition in porous media with elongated pores. For the capillary flow in Y-shaped junctions with two open-end branches of different radii, the delay time of the liquid invasion of the wide branch depends on the pressure at the junction. In Y-shaped junctions with open- and closed-end branches, the gas compression in the closed-end branch is required for determining the pressure at the junction. A closer investigation of the capillary flow in such junctions is necessary to predict the liquid imbibition in porous media that comprise continuous and discontinuous elongated pores. This study presents a theoretical model considering the effect of gas compression in closed-end branches and analyzes this effect on the capillary-flow dynamics. The analytical results obtained suggest that the initiation of capillary flow in the open-end wide branch is governed by the trapped-gas pressure in the closed-end narrow branch. In this case, the delay time of the liquid invasion of the open-end branch decreases with a decrease in the length of the closed-end branch; this is because the decreased length causes the pressure difference at the junction to approach that at the liquid–gas interface in the open-end branch early. Additionally, for open- and closed-end branches, the velocity of capillary flow in the open-end branch increases because the volume rate of flow in the closed-end branch decreases owing to the increase in the trapped-gas pressure in this branch.