Phase-controlled field-effect micromixing using AC electroosmosis

The exploration and application of electrokinetic techniques in micro total analysis systems have become ubiquitous in recent years, and scientists are expanding the use of such techniques in areas where comparable active or passive methods are not as successful. In this work, for the first time, we utilize the concept of AC electroosmosis to design a phase-controlled field-effect micromixer that benefits from a three-finger sinusoidally shaped electrodes. Analogous to field-effect transistor devices, the principle of operation for the proposed micromixer is governed by the source-gate and source-drain voltage potentials that are modulated by introducing a phase lag between the driving electrodes. At an optimized flow rate and biasing scheme, we demonstrate that the source, gate, and drain voltage phase relations can be configured such that the micromixer switches from an unmixed state (phase shift of 0°) to a mixed state (phase shift of 180°). High mixing efficiencies beyond 90% was achieved at a volumetric flow rate of 4 µL/min corresponding to ~13.9 mm/s at optimized voltage excitation conditions. Finally, we employed the proposed micromixer for the synthesis of nanoscale lipid-based drug delivery vesicles through the process of electrohydrodynamic-mediated nanoprecipitation. The phase-controlled electrohydrodynamic mixing utilized for the nanoprecipitation technique proved that nanoparticles of improved monodispersity and concentration can be produced when mixing efficiency is enhanced by tuning the phase shifts between electrodes.


Device geometry
The proposed micromixer consists of a Y-shaped microchannel with three-finger electrodes that are shaped sinusoidally (s-shape) running parallel to the main channel (Fig. S1a). To compare the efficacy of the proposed electrode geometry to that of rectangular-shaped (r-shape) electrodes, a micromixer with straight electrodes (Fig. S1b) was also fabricated and evaluated. For both designs, L, W, and H correspond to the electrode length, channel width, and channel height, respectively.
The gate, source, and drain electrodes widths are designated as wg, ws, and wd, respectively. The spacing between each electrode pair is d. The design parameters for the s-shape and r-shape micromixers are listed in Table S1. Figure S1. a S-shape b and r-shape electrode micromixer design parameters. Table S1. Geometrical parameters for the s-shape and r-shape electrodes and the microfluidic channel.

Mixing performance: device geometry
Unlike the majority of prior electrokinetic-based micromixers that encompassed rectangular electrode patterns symmetric to the flow direction, the altering configuration of the sinusoidally shaped electrodes introduces asymmetric vortices with respect to the interface of the incoming fluid streams along the mixing length. To assess the mixing enhancement attained with the sinusoidal electrode geometry, a micromixer with parallel rectangular electrodes was fabricated and characterized (Fig. S1b). All parameters including electrode length, channel width, channel height, electrode spacing, and gate electrode width remained constant for both designs for a proper comparison. and excitation voltages of 10 Vpp using biasing scheme 1. As it is observed in this figure, the maximum mixing for the r-shape electrode geometry was obtained at a frequency range of 10-20 kHz. Thus, for the r-shape electrode, the mixing variation with voltage was characterized at 10 kHz and is shown in Fig. S2b. Overall, it can be concluded that in r-shape electrode geometry the mixing was significantly reduced corresponding to an average of 187% decrease in the peak mixing index with the biasing scheme 1.
S-4 Figure S2. a Mixing index versus frequency for r-shape electrode geometry (V = 10 Vpp, Biasing scheme 1). b Mixing index versus voltage for r-shape electrodes. All experiments were performed with a total flow rate of 4 µL/min.

Nanoparticle synthesis
The device geometry was modified to allow the injection of two aqueous streams and a precursorcontaining solvent to demonstrate the applicability of the proposed micromixing mechanism and platform for nanoparticle synthesis. The modified geometry consists of the same s-shape electrode pattern with a widened microfluidic channel with three inlets. The schematic illustration of the modified design is shown in Fig. S3 and the relevant geometrical parameters are listed in Table   S2. Furthermore, the mixing quality for three different flow rate ratios (FRR) of water to ethanol stream was examined. The frequency response and the effect of FRR on the mixing performance are presented in Fig. S4a. According to mixing indices in Fig. S4a, frequencies above 100 kHz for all FRRs resulted in optimized mixing. Next, the effect of the total flow rate (TFR) on the mixing S-5 index was evaluated by operating the mixer at the optimized frequency of 1 MHz and a voltage of 10 Vpp. Fig. S4b shows the mixing performance corresponding to TFR values ranging from 10 µL/min to 400 µL/min at different FRRs. Table S2: Geometrical parameters of the electrodes and the microfluidic channel for the modified platform.