Dynamics of Oscillating Microcantilevers in Viscous Fluids

The dynamics of micromechanical beams and cantilevers in viscous fluids are studied by analytical, computational, and experimental means with an emphasis on applications to Atomic Force Microscopy (AFM) and microcantilever biosensors. The first part of the thesis is on an computational approach to predict the hydrodynamic loading of a single microcantilever of different geometries using a three-dimensional, finite element based fluid-structure interaction model. The effects of microcantilever geometry, operation in higher bending modes, and orientation and proximity to a surface are analyzed in detail. In the second part of the thesis, the hydrodynamic coupling in arrays of micromechanical oscillators in viscous incompressible fluids is studied by means of a boundary integral method. The oscillations of nearest neighbor and the next neighbor microbeams couple hydrodynamically in unanticipated ways depending on the gap, frequency, and the relative phase and amplitude of their oscillation. Finally, the last part of the thesis is on experimental and theoretical investigations of the dynamics of AFM microcantilever tapping on elastic samples in liquid environments. A mathematical model is developed for the tip dynamics using a rational tip-sample interaction model and two interacting flexural modes that correctly captures measured tip dynamics on different elastic substrates.