Imbibition dynamics in an open-channel capillary with holes

Spontaneous capillary flow is generally described by Washburn's equation. However, the modification must be made for imbibition dynamics in an open channel. Moreover, the presence of the holes in the capillary for flow division or bifurcation complicates the outcome of the imbibition process. In this work, capillary imbibition into a two-rail channel with/without holes is investigated by many-body dissipative particle dynamics (MDPD). The influences of channel height (h), channel width (w), hole size (w_h), and surface wettability (θ_Y) on the imbibition rate are examined. For two-rail channel without holes, the simulation results agree reasonably with Washburn's equation with the correction 1-(h/w)/cosθ_Y. The penetration rate grows with reducing the channel height or enlarging the channel width. However, in the presence of holes, the wicking dynamics is slowed down and four types of outcomes are observed: “covering”, “separation”, “pass/stop”, and “stoppage”. These states depend on the size and (symmetric or asymmetric) position of the rectangular hole. Finally, the phase diagrams which vary with θ_Y, w_h/h, and w/h are constructed. The domains of those states agree reasonably with the equations acquired simply from the analyses of surface free energy.