A microfluidic flow restrictor that uses micron-sized beads to impede flow is described. The flow rate can be adjusted by adding or removing the beads using injection needles through self-sealing ports, one injection needle injecting or aspirating beads and another injection needle pushing or pulling fluid from outside of a bead trap within the flow restrictor. In alternative embodiments, the beads or other filler material can be trapped in a manifold bead trap such that they block a subset of fluid channels of the flow restrictor, allowing fluid to flow freely through the rest of the fluid channels. The flow restrictor can be integrated with a contact lens or implantable medical device for use in dispensing liquid therapeutic agents at flow rates of microliters per minute or moving body fluids at a controlled rate from one part of the body to another.