A finite element model for the frequency spectrum estimation of a resonating microplate in a microfluidic chamber

Resonating microplates appear as ideal candidates for microcantilever-based real-time biosensing, because their low planar aspect ratio allows for effectively large Q factors, even in highly viscous fluids like water and other biological liquids. Since, a complete analytical treatment of a plate vibrating in liquid is missing; a fully numerical approach is needed for an effective design of a microcantilever-based Lab-On-Chip, as well as for its correct operation. We here report on a three-dimensional finite element model for an accurate and general solution methodology of the Fluid–Structure interaction for a plate vibrating in a transverse flexural mode within a viscous fluid environment. The model directly allows extracting vibration mode shapes, frequencies and Q factors through an eigenfrequency analysis, thus avoiding time-consuming and time-dependent simulations. A benchmark with the available analytical results (that rely on the classical beam theory) and a comparison with experimental data on a fabricated microcantilever-based Lab-On-Chip confirm the accuracy and the reliability of our numerical calculations. The here proposed model works in a very general context, without limitations about the cantilever planar geometry and material, as well as about the shape of the fluid domain.