Passive ow control valves are usually intended to deliver or drain a uid at a constant rate independently of pressure variations. Micro uidic devices made of a stack of two plates are considered here: the rst plate comprises a exible silicon membrane having through holes while the second plate is a rigid substrate with a cavity, an outlet hole and pillars aligned with the through holes of the membrane. The liquid ows through the holes etched in the membrane and through the gap be- tween the membrane and the pillars. Each gap can be considered as a valve which progressively closes as the pressure increases. Numerical modelling of the uid dynamics inside the device associated with FEM simulations of the membrane dis- tortion have been performed to design a device that exhibits a constant ow rate in a speci ed range of pressure. To make the design more reliable, the device charac- teristics have been optimized using a genetic algorithm, the tness function taking notably into account machining and alignment tolerances. This algorithm has been nally used to design ow control valves for wearable injectors dedicated to the in- fusion of viscous drug formulations (hyaluronic acid, adalimumab, golimumab ...) at high pressure. Prototypes have been characterized using solutions of 12 and 24 cP. It has been demonstrated experimentally that this technology is suitable to passively infuse biological products at ow rates up to 1 mL/min. The numerical model has then been re ned further so as to obtain a good correlation with experimental data.