Hydrodynamic coupling between micromechanical beams oscillating in viscous fluids

We analyze the hydrodynamic coupling between long, slender micromechanical beams (microbeams) deployed in an array and oscillating in a viscous, incompressible fluid. The unsteady Stokes equations are solved using a boundary integral technique in a two-dimensional plane containing the microbeam cross sections. 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. A rational basis is provided for choosing the gap between neighboring microbeams in an array in order to either decouple their hydrodynamics or to couple them strongly. The results clearly suggest that the dynamics of microbeams in an array can be tuned in a cooperative manner so as to minimize or maximize the hydrodynamic resistance on individual microbeams.