Microcantilevers are often deployed in flowing fluids to measure local flow velocities or to detect rapidly the nanomechanical binding of trace quantities of target analytes. The authors investigate the flow-induced mechanics of microcantilevers by deriving a semianalytical theoretical model for the nanoscale deflections of an elastic microcantilever due to a laminar viscous flow incident upon it. Conversely, the model allows for the estimation of the local flow velocities based on measured microcantilever deflection. Careful experiments performed on silicon microcantilevers in flowing nitrogen confirm the theoretical predictions up to a critical flow rate, beyond which unsteady flow-induced vibrations are seen to occur.
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Temperature fluctuations at the flow cell outlet measured by a thermocouple were random, with a maximum variation of over . Also, comparing the deflections during flow rate ramp up and ramp down showed a drift of only .
The parameters ,, and change by less than 5% over the range of . For more accurate results, one may use the following phenomenological relationships extracted from our ADINA simulations: , , . Note that power law relationships between the drag coefficient and the Reynolds number are common in the literature. By setting in Eq. (2) and then proceeding with linear regression, a power law relationship can be obtained here as well. A poorer fit results.
The following uncertainties are assumed in computing the error bounds: thickness 1%, position of measurement 10%, free stream velocity 5%, attack angle 5%, and rest 0.1%.
Above the critical flow rate, the flow entering the flow cell remains laminar (Reynolds number, based on the inlet radius of 0.625 mm); and the cantilever natural frequencies remain far apart (no mode coalescence).
