Experimental characterization and modelling of microfluidic radial diffusers for passive self-regulating valves

A microfluidic radial diffuser typically comprises a hole in a membrane facing a concentric pillar separated by a small gap where the fluid is forced to flow radially between the membrane and the pillar. Such diffusers are notably used to make passive flow rectification valves for drug delivery devices, wherein several holes are machined into a flexible membrane progressively deflecting against pillars as the pressure increases on top of it. The fluidic modelling of such a diffuser is made difficult by the presence of a transition region between the hole and the diffuser itself. An experimental investigation has been conducted using SOI wafers to form membranes having only one central hole and Pyrex wafers for the substrate and pillars. Both wafers are anodically bonded together after alignment. A simple fluidic model accounting for the specific geometry of the diffuser is proposed and compared to experimental results. A good match is obtained, for Reynolds number in the range 0.5 to 35, using the analytical formula of a radial diffuser in the laminar regime with an effective inner radius 40% smaller than the actual one, in order to correctly simulate the flow constriction at the entrance of the diffuser.