Multiple Meniscus Depinning Transitions in Open Capillary Slits

We study edge-induced meniscus depinning transitions in confined fluids using a combination of macroscopic theory and classical density functional theory (DFT). The study focuses on macroscopically long slit geometries of width L bounded by planar walls where the open end has an overlap D, where sharp edges introduce distinct meniscus morphologies and continuous depinning transitions. The macroscopic analysis predicts four distinct condensed states: fully pinned, partially pinned, and depinned whose stability depends sensitively on the wall separation ratio D/L and the Young contact angle θ. These transitions are second order, if the walls are partially wet, and third order if they are complete wet (θ = 0) or completely dry (θ = π). Microscopic DFT calculations confirm the existence and sequence of these morphologies in very good quantitative agreement with the macroscopic predictions, except for complete wetting, where the presence of thick adsorbed films effectively reduces the accessible slit width.