Electrokinetic biased deterministic lateral displacement: scaling analysis and simulations.

Deterministic Lateral Displacement (DLD) is a microfluidic technique where arrays of micropillars within a microchannel deflect particles leading to size-based segregation. We recently demonstrated that applying AC electric fields orthogonal to the fluid flow increases the separation capabilities of these devices with a deflection angle that depends on the electric field magnitude and frequency. Particle deviation occurs in two distinct regimes depending on frequency. At high frequencies particles deviate due to negative dielectrophoresis (DEP). At low frequencies (below 1 kHz) particles oscillate perpendicular to the flow direction due to electrophoresis and are also deflected within the device. Significantly, the threshold electric field magnitude for the low frequency deviation is much lower than for deflection at high frequencies by DEP. In order to characterize the enhanced separation at low frequencies, the induced deviation was compared between the two frequency ranges. For high frequencies, we develop both theoretically and experimentally scaling laws for the dependence of particle deviation on several parameters, namely the amplitude of the applied voltage, particle size and liquid velocity where DEP forces compete with viscous drag. A novel theoretical framework is presented that enables simulation of particle trajectories subjected to DEP forces in DLD devices. Deviation angles predicted by simulations are in very good agreement with experimental data. At low frequencies (below 1 kHz), particles follow the same scaling law, but with much lower voltages. This indicates that electrokinetic phenomena other than DEP play an important role in driving particle behaviour. Experiments show that at low frequencies, particle motion is affected by quadrupolar electrohydrodynamic flows around the insulating pillars of the DLD array. We quantify the difference between the two frequency regimes and show that an electrokinetic model based only on DEP forces is limited to frequencies of 1 kHz and above.