Three-dimensional Optical Reconstruction of colloidal electrokinetics via multiplane imaging

Abstract

Sorting, filtering, moving and controlling colloidal particles is crucial in many fields, ranging from chemistry to biology and physics. Dielectrophoresis is an outstanding tool for the manipulation of small particles by AC electric fields, due to its high selectivity and the absence of the need for labels. We use a new theoretical-experimental approach to study the dynamics of fluorescently labeled polystyrene nanoparticles of 200 nm under positive and negative dielectrophoresis conditions. Our multiplane widefield microscopy technique combined with single particle tracking offers real-time ($>$ 100 fps) superresolved visualization of colloidal dynamics in three spatial dimensions. This real-time 3D imaging technique allows the reconstruction of superresolved trajectories, enabling the visualisation of local forces with unprecedented detail. To interpret this data, a dedicated multiscale modeling approach was developed, targeting a direct comparison between theory and experiment. In the current model DEP and electro-osmotic forces were considered. Under positive DEP conditions, this resulted in a very good agreement with experiment. Under negative DEP conditions, the agreement is less clear, indicating the importance of other effects. This illustrates the potential of this combined 3D imaging and modeling approach to validate and refine our theoretical understanding of AC field induced colloidal dynamics. This framework is broadly applicable to other complex fluid or microfluidic motion.

Figures (6)

• Figure 1: (A) Sketch of the quadrupole (top and side view). Red and blue colors represent that each electrode is connected with a phase shift of $\pi$. Side view also includes contour plots of the normalized electric field intensity. Higher yellow color intensity indicates higher electric field intensity, showing that the highest intensity is at the edges of the electrodes. (B) The velocities associated to dielectrophoresis $v_\text{DEP}=\mu F_\text{DEP}$, AC electro-osmosis $v_\text{EK}$ and the characteristic diffusion velocity $v_\text{diff}=\mu kT/a$ with $\mu=(6 \pi \eta a)^{-1}$ the NP mobility and $a$ the NP radius. These values are obtained from theoretical modeling, close to the gap between the electrodes. (C) Schematic representation of streamlines at both working frequencies. The top panel shows the combination of pDEP and electrokinetic flow and the bottom panel the streamlines expected for pure nDEP.
• Figure 2: 3D imaging experimental setup with experimental and theoretical workflows: A) a 488 nm laser is focused on the back aperture of the objective to generate widefield illumination. The light emitted from the sample is collected via an 8f system. A prism beamsplitter splits the image in 8, each of the split paths having a different optical path length, which leads to eight images focused at different depth inside the sample, resulting in a true volumetric image. The images are collected 4 by 4 by two synchronized sCMOS. a) Photograph of the microfluidic device containing the quadrupole electrode. b) scattering image of the quadrupole electrode under the microscope. B) Experimental workflow: A 3D time lapse of the imaged volume si acquired under application of an alternating electric field. Individual particles are tracked in 3D, and their speed is calculated and mapped out in all dimensions. C) Theoretical workflow: The space is discretized and the finite difference method is used to calculate electric potential and $F_\text{DEP}$ in all the system. The $v_\text{slip}$ is propagated to the bulk to calculate EK flow in all the system using libmobility libmobility. Then the total speed field is calculated with pyvista streamlines pyvista and the NPs dynamics are solved with UAMMD-structured Brownian solver UAMMD_structured
• Figure 3: Experimental and theoretical analysis of pDEP. A) Time-averaged image in absence of any voltage showing a homogeneous intensity distribution. B) Time-average image under 100kHz and 0.75V AC field showing preferential location of particles inside the electrode gap where the electric field gradient is strongest. C) Localization density at the electrode combining data from multiple periods of 10 second exposure to 100 kHz at 0.5 V (pDEP). D) Simulation showing the logarithm of the calculated particle distribution probability under these conditions in arbitrary units E) Representative 3D traces of different typical behavior: (i) ejection from center at 45 degrees w.r.t. the electrode arm, (ii) trapping at the electrode, (iii) moving from bulk solution to electrode gap, and (iv) escape from the trap, moving perpendicular to the electrode arm entering a vortex flow. Time color-code is given relatively for clarity (for each particle, the beginning of its trace is depicted in blue, while later times are depicted in yellow). F) Top-view of all the trajectories showing an overview of the characteristic behavior, notably ejection from the quadrupole center at 45 degrees from the electrode arms and ejection perpendicular to the electrode arm. G) Top-view of all the traces from the theoretical dynamical simulation showing the predicted behavior in a good match with experimental results.
• Figure 4: Comparison of experimental and theoretical velocity fields averaged over the corridor direction. The red transparent zone overlaid with the experimental figure indicates where theoretical predicted velocity is higher than $110$$\mu\text{m/s}$ and proximity to the surface, resulting in inaccurate experimentally recovered velocities.
• Figure 5: Experimental and theoretical analysis of nDEP. A) Time-averaged image in absence of an AC field, showing a homogeneous intensity distribution. B) Time-averaged image under a 1MHz and 1V AC field, showing preferential location of particles just outside the electrode corridor. C) Localization density combining data from multiple cycles of 10 second exposure to 5MHz at 1V (nDEP). D) Simulation showing logarithm of the particle distribution probability in nDEP in arbitrary units. E) Representative 3D traces of different typical behavior: (i) movement along electrode corridor, moving above the electrode edge, (ii) full cycle, moving from bulk solution to horizontal movement along the electrode gap, and finally repulsion in a vortex toward the bulk after reaching the center of the quadrupole, (iii) shows similar behaviour as (ii) but is expelled more vertically, and (iv) shows Brownian motion in the bulk. Time color-code is given relatively for clarity (for each particle, the beginning of its trace is depicted in blue, while later times are depicted in yellow). F) Top-view of all the detected traces gives an overall view of the the characteristic behaviors, notably the absence of particles inside the gap between the electrodes and the attraction towards the center of the quadrupole G) Top-view of all the traces from the theoretical dynamical simulation showing the predicted behavior, which mostly corresponds to particle being pushed away from the elctrodes and subsequent random, diffusion dominated motion.