Metastable capillary filaments in rectangular cross-section open microchannels

Spontaneous capillary flow (SCF) in microchannels occurs for specific geometrical and wetting conditions. When the channel walls form corner angles with the channel bottom, liquid filaments may form in the corners. These capillary filaments are often called Concus-Finn (CF) filaments, and they can theoretically spread infinitely.In this work we consider rectangular open U-grooves of varying cross-section width, and we theoretically determine the flow conditions as a function of the aspect ratio of the channel and the liquid-solid contact angle. These flow conditions are numerically checked. Especially, we analyze the configurations where precursor capillary filaments form. We show that these filaments can be metastable, i.e. disappear into a bulk capillary flow if the proper conditions are met. A diagram of the flow regimes is deduced from theoretical developments and checked using numerical modeling.