From 3D to 2D Hydrodynamics in Interacting Micro-rods

Moving micron scale objects are strongly coupled to each other by hydrodynamic interactions. The strength of this coupling decays as the inverse particle separation when the two objects are sufficiently far apart. It has been recently demonstrated that the reduced dimensionality of thin fluid layer gives rise to longer ranged, logarithmic coupling. Using holographic tweezers we show that microrods display both behaviors interacting like point particle in 3D at large distance and like point particles in 2D for distances shorter then their length. We derive a simple analytical expression that fits remarkably well our data and further validate it with finite element analysis.