AC electrokinetics of polarizable tri-axial ellipsoidal nano-antennas and quantum dot manipulation

By realizing the advantages of using a tri-axial ellipsoidal nano-antenna (NA) surrounded by a solute for enhancing light emission of near-by dye molecules, we analyze the possibility of controlling and manipulating the location of quantum dots (similar to optical tweezers) placed near NA stagnation points, by means of prevalent AC electric forcing techniques. First, we consider the nonlinear electrokinetic problem of a freely suspended, uncharged, polarized ellipsoidal nanoparticle immersed in a symmetric unbounded electrolyte which is subjected to a uniform AC ambient electric field. Under the assumption of small Peclet and Reynolds numbers, thin Debye layer and 'weak-field', we solve the corresponding electrostatic and hydrodynamic problems. Explicit expressions for the induced velocity, pressure, and vorticity fields in the solute are then found in terms of the Lamé functions by solving the non-homogeneous Stokes equation forced by the Coulombic density term. The particular axisymmetric quadrupole-type flow for a conducting sphere is also found as a limiting case. It is finally demonstrated that stable or equilibrium (saddlelike) positions of a single molecule can indeed be achieved near stagnation points, depending on the directions of the electric forcing and the induced hydrodynamic (electroosmotic) and dielectrophoretic dynamical effects. The precise position of a fluorophore next to an ellipsoidal NA, can thus be simply controlled by adjusting the frequency of the ambient AC electric field.