Dynamical Response of Nanomechanical Oscillators in Immiscible Viscous   Fluid for in vitro Biomolecular Recognition
  Dynamical response of nanomechanical cantilever structures immersed in a viscous fluid is important to in vitro single-molecule force spectroscopy, biomolecular recognition of disease-specific proteins, and the detection of microscopic dynamics of proteins. Here we study the stochastic response of biofunctionalized nanomechanical cantilevers beam in a viscous fluid. Using the fluctuation-dissipation theorem we derive an exact expression for the spectral density of the displacement and a linear approximation for the resonance frequency shift. We find that in a viscous solution the frequency shift of the nanoscale cantilever is determined by surface stress generated by biomolecular interaction with negligible contributions from mass loading. 
Jerome Dorignac, Agnieszka Kalinowski, Shyamsunder Erramilli and   Pritiraj Mohanty