Low-order modeling of resonance for fixed-valve micropumps based on first principles

Micropumps that utilize fixed-valves, i.e., valves having no moving parts, are relatively easy to fabricate and inherently reliable due to their simplicity. Since fixed-valves do not close, pumps based on them need to operate in a well-designed resonant mode in order to attain flow rates and pressures comparable with other designs. However, no methodology currently exists to efficiently investigate all the design parameters including valve size to achieve optimal resonant response. A methodology that addresses this problem is 1) the determination of optimal parameters including valve size with a low-order linear model capable of nonempirical prediction of resonant behavior, and 2) the independent determination of the best valve shape for maximal valve action over a target Reynolds number range. This study addresses the first of these two steps. The hypothesis of this study is that the resonant behavior of a fixed-valve micropump can be accurately predicted from first principles, i.e., with knowledge only of geometric parameters and physical constants. We utilized a new low-order model that treats the valves as straight rectangular channels, for which the unsteady solution to the Navier-Stokes equations is exact and with which the problem was linearized. Agreement with experiment using pump-like devices with valves replaced by straight channels was found to be excellent, thereby demonstrating the efficacy of the model for describing all aspects of the pump except actual valves. Agreement with experiment using pumps with Tesla-type valves was within 20 percent. With such accuracy and without the need for empirical data, the model makes possible reliable, efficient investigation and optimization of over 30 geometric and material parameters.