Mathematical model of a valveless micropump with a hydraulic diode

The development of efficient valveless fluid pumping systems requires the creation of specialized models that account for directed flow transmission through hydrodiodes. The aim of the research is to develop a simplified mathematical model of the volumetric micro-pump with hydrodiodes for laminar flow conditions and to derive calculated dependencies of volumetric efficiency on the diodicity of the hydrodiode. The authors describe the operating process by the continuity equation considering liquid compressibility and harmonic variation of the chamber volume. Moreover, the research determine the flow rates through the hydraulic diodes by linear hydraulic features and define the diodicity as the ratio of forward hydraulic conductance to reverse hydraulic conductance. The steady-state operating cycle is obtained by numerical integration. For a micropump with the 50 nL displacement volume and the 0.2 bar pressure difference the chamber pressure variation, flow rates through the hydraulic diodes and volumetric efficiency are calculated. The results show that increasing diodicity reduces the reverse leakage and increases the useful flow rate. Under the selected operating conditions, a noticeable net flow begins to develop at the diodicity of 9–10, while at the diodicity of 25 the volumetric efficiency based on the positive discharge reaches approximately 81 %. The developed model can be used for the preliminary selection of hydraulic-diode parameters and for the minimum diodicity estimation to provide the specified micropump flow rate.