Hydrodynamic loading with shifting stimulus in arrays

Conventional atomic force microscope (AFM) comprises of a single cantilever with piezoelectric base excitation and optical read-out. The micro-electromechanical system (MEMS) is raster scanned over a sample surface to generate topographic measures as well as information of selected material properties. For some large sample surfaces and biological processes, a single cantilever scan may render insufficient scan speeds. We therefore consider developing small-size AFM array technology for its application on natural samples in their fluidic environment. As a first step we investigate the collective and interactive fluid dynamics between members in an array away from any sample surface. Our analysis is based on Navier-Stokes equation for incompressible flow and the two-dimensional boundary integral method. We first formulate the generalized equations and then focus on three- and five-beam configurations. The fluid dynamic behaviour of these small-size arrays are investigated for different gaps between members, Reynolds numbers and actuation modes. A special emphasis is laid on the effect of non-neighbouring members, which often, if not always is neglected in existing literature. One of our findings reveals a Reynolds number dependent concave/convex hydrodynamic loading profile across the array which is introduced by the non-neighbouring members