A microfluidic valve for implantation in an eye of a patient is disclosed. The valve may include a chamber formed between a substrate and a flexible membrane. The valve may also include a boss disposed in the chamber and having a top edge in selective contact with the flexible membrane. The top edge includes a relief portion and a non-relief portion, with the relief portion being structurally arranged so that a pressure required to separate the membrane from the relief portion is less than a pressure required to separate the membrane from the non-relief portion. The valve also may include an inlet extending through the boss and the substrate through which fluid enters the chamber and an outlet configured to allow fluid to exit the chamber. Methods for priming a microfluidic valve are also disclosed.