Unified theory of gas damping of flexible microcantilevers at low ambient pressures

Bidkar, Rahul A.; Tung, Ryan C.; Alexeenko, Alina A.; Sumali, Hartono; Raman, Arvind
April 2009
Applied Physics Letters;4/20/2009, Vol. 94 Issue 16, p163117
Academic Journal
Predicting the gas damping of microcantilevers oscillating in different vibration modes in unbounded gas at low pressures is relevant for increasing the sensitivity of microcantilever-based sensors. While existing free-molecular theories are valid only at very high Knudsen numbers, continuum models are valid only at very low Knudsen numbers. We solve the quasisteady Boltzmann equation and compute a closed-form fit for gas damping of rectangular microcantilevers that is valid over four orders of magnitude of Knudsen numbers spanning the free-molecular, the transition, and the low pressure slip flow regimes. Experiments are performed using silicon microcantilevers under controlled pressures to validate the theory.


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