A condition for spontaneous capillary flow in open microgrooves

In this work, we investigate the behaviour of liquids in symmetric open microgrooves and give a criterion for spontaneous capillary flow. To that end, we use a two-dimensional model and analyse the liquid morphologies minimizing the Gibbs energy of the system. We find that the condition of a flat liquid surface, which was hitherto assumed, is indeed the solution minimizing the Gibbs energy, so that it can safely be accepted to investigate whether open capillaries fill spontaneously. Furthermore, we find a condition for spontaneous capillary flow that depends on the cross-section of the channel alone. We use the findings to derive the critical contact angle, below which spontaneous capillary flow happens, for three examples including V-grooves, Gaussian grooves, and lenticular grooves.