Highly efficient passive Tesla valves for microfluidic applications

A multistage optimization method is developed yielding Tesla valves that are efficient even at low flow rates, characteristic, e.g., for almost all microfluidic systems, where passive valves have intrinsic advantages over active ones. We report on optimized structures that show a diodicity of up to 1.8 already at flow rates of 20 μl s^{- 1} corresponding to a Reynolds number of 36. Centerpiece of the design is a topological optimization based on the finite element method. It is set-up to yield easy-to-fabricate valve structures with a small footprint that can be directly used in microfluidic systems. Our numerical two-dimensional optimization takes into account the finite height of the channel approximately by means of a so-called shallow-channel approximation. Based on the three-dimensionally extruded optimized designs, various test structures were fabricated using standard, widely available microsystem manufacturing techniques. The manufacturing process is described in detail since it can be used for the production of similar cost-effective microfluidic systems. For the experimentally fabricated chips, the efficiency of the different valve designs, i.e., the diodicity defined as the ratio of the measured pressure drops in backward and forward flow directions, respectively, is measured and compared to theoretical predictions obtained from full 3D calculations of the Tesla valves. Good agreement is found. In addition to the direct measurement of the diodicities, the flow profiles in the fabricated test structures are determined using a two-dimensional microscopic particle image velocimetry (μPIV) method. Again, a reasonable good agreement of the measured flow profiles with simulated predictions is observed.