Liquid Morphologies in Open Microfluidic Intersections

When a liquid fills an open capillary, the shape of the liquid “front” can be treated as quasi-steady, since its shape remains virtually unchanged when the liquid advances through the channel. Previous investigations have shown that the associated morphology for steady-state flow represents a shape that is bulged inwards at the liquid front (caused by the capillary pressure) and becomes flat when the flow has stopped for a system connected to an infinite reservoir. Even though complex liquid networks inherently require intersections, the morphologies or minimal energy shapes formed at intersections have not yet been investigated in detail. In this work, we are investigating liquid morphologies inside crossing V-shaped and Gaussian microchannels and derive guidelines on how to hinder dewetting when evaporation is present. To this end, we perform gradient descent simulations with the “Surface Evolver”. Similar to the case of single microchannels, we find that the minimal energy shapes of a system being connected to an infinite reservoir are represented by a flat liquid surface for a wetting liquid, and that no steady-state can be found for wetting liquids. Additionally, we find that the energy contribution stemming from the intersection is negatively proportional to the energy contribution scaling with the filling length of single microchannels. This allows us to predict whether dewetting will happen when evaporation is present and allows us to design liquid intersections, where dewetting will not happen.