Electrophoretic slip-tuned particle migration in microchannel viscoelastic fluid flows

Particle migration is the underlying mechanism for continuous-flow focusing, trapping, and sorting of various types of particles in microfluidic devices. We present in this work an experimental investigation of the cross-stream migration of spherical polystyrene particles in a combined pressure- and electric field-driven flow of viscoelastic fluid through a straight rectangular microchannel. We find that particles migrate toward the centerline of the channel if they are leading the hydrodynamic flow due to positive electrophoresis. Conversely, lagging particles due to negative electrophoresis migrate toward the walls of the channel. These migrations are found to be exactly opposite to those in a Newtonian fluid in our control experiment. We attribute this phenomenon to the shear-induced extra lift in a viscoelastic fluid that has been recently predicted to arise from the nonlinear coupling of the electrophoretic particle motion with the local flow field. The effects of hydrodynamic flow rate and electric field magnitude on the bidirectional particle migrations are studied, which can both be reasonably explained using the theoretical formula of the electrophoretic motion-induced extra lift in a viscoelastic shear flow.

Figure 1

Picture of the microfluidic chip used in experiment. The microchannel is filled with green food dye for clarity. The electrodes are shortened stainless steel needles with each end being inserted into a plastic tubing.

Figure 2

Schematic illustration of electrophoretic slip, $U_{\mathrm{ep}}$, tuned particle migration when a particle is leading (a) or lagging (b) a viscoelastic fluid flow, $U\left(y,z\right)$, in a straight rectangular microchannel (see the view in the x-y plane): the wall-induced electrical lift, ${\mathbf{F}}_w$, pushes the particle away from any walls; the flow-induced elastic lift, ${\mathbf{F}}_{\mathrm{eL}}$, directs the particle towards the channel center (where the fluid shear rate is low as seen from the contour in the y-z plane, the darker color the larger magnitude) unless the particle is very close to any corners; the electrophoretic motion-induced extra lift, ${\mathbf{F}}_{\mathrm{ep}}$, directs the leading particle away from the walls (a) and the lagging particle towards the walls (b) (see the view in the y-z plane). Note that the flow-induced viscous drag force, ${\mathbf{F}}_D$, in the y-z plane, which is opposite to the particle moving direction relative to the fluid, is not included on the plots. The origin of the coordinates is at the center of the channel inlet for convenience.

Figure 3

Superimposed images of electrophoretic slip $\left(U_{\mathrm{ep}}\right)$-tuned migration for 10-µm-diameter particles leading (a, positive $U_{\mathrm{ep}})$, along with (b, zero $U_{\mathrm{ep}})$, and lagging (c, negative $U_{\mathrm{ep}})$ the hydrodynamic flow of viscoelastic PEO solution $(U$, positive) at the channel inlet (top row) and outlet (bottom row), respectively. The pressure-driven flow rate is fixed at 125 μl/h, and the DC electric field is 300 V/cm for both the leading (a, negative direction) and lagging (c, positive direction) particles. Panel (d) shows the images of particle motion in a purely electrokinetic flow (i.e., in the absence of any pressure-driven flow).

Figure 4

Superimposed images of electrophoretic slip $\left(U_{\mathrm{ep}}\right)$-tuned migration for 10 µm-diameter particles leading (a, positive $U_{\mathrm{ep}})$, along with (b, zero $U_{\mathrm{ep}})$, and lagging (c, negative $U_{\mathrm{ep}})$ the flow of Newtonian buffer solution $(U$, positive) at the channel inlet (top row) and outlet (bottom row), respectively. The hydrodynamic flow rate is fixed at 25 μl/h (as compared to 125 μl/h viscoelastic fluid flow in Fig. 3), and the DC electric field is 300 V/cm in both (a) (negative direction) and (c) (positive direction).

Figure 5

Superimposed images of electrophoretic slip-tuned migration for 10-µm-diameter particles leading (a), along with (b), and lagging (c) the flow of 1000 ppm PEO solution at the channel outlet under various flow rates. Particles move from top to bottom in all images. The DC electric field is 300 V/cm for both the leading (positive downward direction) and lagging (negative upward direction) particles.

Figure 6

Comparison of electrophoresis-enhanced elastic focusing (for leading particles with a positive electrophoretic slip) with purely elastic focusing (for particles traveling along with the fluid with zero electrophoretic slip) of 10-µm particles in the flow of 1000 ppm PEO solution through a straight rectangular microchannel. The symbols represent the measured values of the focused particle stream width (normalized by the channel width) from the images in Fig. 5. The curves are each the power trendline of the experimental data points.

Figure 7

Superimposed images of electrophoretic slip-tuned migration for 10-µm-diameter particles leading (a) and lagging (c) the flow of 1000 ppm PEO solution at the channel outlet under various DC electric fields. The hydrodynamic flow rate is fixed at 125 μl/h. (b) shows the images of particle motion in purely electrokinetic flows (i.e., in the absence of the pressure-driven flow) under the same DC electric fields as in panels (a) and (c). Particles move from top to bottom in all images.

Figure 8

Electric field effect on electrophoresis-enhanced elastic focusing of 10-µm particles leading the flow of 1000 ppm PEO solution in a straight rectangular microchannel. The symbols represent the measured values of the focused particle stream width (normalized by the channel width) from the images in Fig. 7. The curve is a linear trendline of the experimental data points.