Fast Transverse Migration of Nanoparticles with Oscillatory Electro-Inertial Focusing

Precise manipulation of micro- and nanoparticles in microfluidic systems underpins a range of emerging technologies in diagnostics, drug delivery, and environmental sensing. Strategies that simultaneously use multiple forces have recently demonstrated faster performance and greater control over particle migration, in particular the combination of electrophoresis and inertia. Theoretical models developed for the case of steady forcing, however, predict migration velocities of microparticles in stark discrepancy to experiments. In this work, we extend these investigations to nanoparticles of radii 50 - 250 nm in the case of oscillatory electro-inertial focusing (OEIF), which couples periodic pressure-driven and electrokinetic flows. Frequency synchronization of the fields allows particles to experience repeated consistent cycles of forcing, thus extending the effects of steady driving to arbitrary times, mimicking a set-up with a much longer channel independent of driving frequency. Using fluorescence microscopy and particle tracking and varying a number of control parameters, we find not only that transverse migration velocities greatly exceed theoretical predictions quantitatively, with discrepancies for nanoparticles larger than those for microparticles. We also show that the scaling with particle size qualitatively differs from theory, identifying particle sizes for optimal manipulation in a given set-up. The observed behavior challenges existing theoretical models and underscores the need to re-evaluate the assumptions underlying electro-inertial theory.