From the physics perspective, it is illuminating that among the three basic linear models, the thin spring is by far closest to reality. That tells us that for the most typical dimensions, the valves do act approximately like thin springs. On the other hand, the need for the inclusion of other basic models is dictated by extreme conditions, namely, thickest membranes and smallest widths, where the volume effects become more prominent.
The final linear model presents a useful practical approximation for most applications in the field. However, it is clear that further improvements in the accuracy of predictions would require the development of nonlinear models, especially for very large strains where the stress-strain curve significantly departs from the initial linear regime. We would be happy to share our detailed experimental data with workers willing to undertake that endeavor.
The experimental part of the work also revealed interesting information about the occurrence of device failure. The only observed such was due to the valve membrane being so flabby that it would get stuck to the substrate and become bound to it during the fabrication process, producing a nonfunctional valve. This is a well-known phenomenon and was observed in our study to become frequent when both lateral dimensions exceeded 115 and 130 μm for 2500 and 2000 rpm, respectively. No such collapse was observed with the 1500 rpm devices, probably because the corresponding membrane is significantly thicker while the maximal lateral dimensions were limited to 300 μm.