This paper presents a fluid flow analytical model of a micro check valve based on an ortho-planar spring. The comparison with a coupled fluid-structure finite-element model shows that the analytical model gives results very close to the finite-element model (FEM). These models are then validated using flow rate measurements on valve prototypes.
Smal, O., Raucent, B., & Jeanmart, H. (2009). Fluid flow modelling of a micro-valve. International Journal for Simulation and Multidisciplinary Design Optimization, 3(2), 356-362. https://doi.org/10.1051/ijsmdo/2009011 (Original work published 2009)