We present experimental measurements and mathematical predictions concerning
the hydrodynamics induced by spinning rods in viscous fluids. Recent advances in
nano-technology have enabled controlled manipulation of nanoscale objects
immersed in fluids. Such advances allow for new biological measurements (such as
physical properties of cell membranes) on length scales smaller than the wavelength of
visible light, and direct observations are challenging. Moreover, on such scales, the
hydrodynamics are thermally fluctuating, and observational tracers experience strong
Brownian signals on top of coherent motion induced by nanoscale manipulation. As
such, predictive mathematical theories are essential to interpret the observations. We
discuss the hydrodynamic solutions we have developed for rods sweeping upright cones
in viscous fluids. These quasi steady, three dimensional, exact and asymptotic solutions
of the Stokes equations are used to study the motion of passive tracers. These predictions
are shown to quantitatively match low Reynolds number experiments performed on
a scaled up, table top version of the nanoscale measurements performed. In turn, the
predictions on the nano-scale are considered where agreement is good, but not as good
as on the macro scale. The uncertainty of the nanoscale measurements as regards missing
observational information and stochastic dynamics will be discussed.
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