Polydimethylsiloxane microfluidic channels are created by making a 10:1 mixture of Sylgard 184 Elastomer Base and Sylgard 184 Elastomer Curing agent. This mixture was manually stirred for 5 min and then degased until all visible air bubbles were removed. The degased mixture is poured over a SU-8 mold slowly to prevent air bubbles from becoming trapped in the mixture. The mold and uncured PDMS mixture is placed in an oven at 80 °C for 1 hour for curing. After curing, the PDMS array of microfluidic channels is peeled from the mold and stored in a wafer box for future use. Current channel dimensions have a height of 6.5 microns and a width varying from chip to chip of 100 to 175 microns wide.

Full detail for chip fabrication has been previously described [24,25]. In summary, photoresist is patterned on to a “100” silicon wafer. A 10 nm Ti adhesion layer is evaporated onto the chip. Next, a 250 nm of a NiFe alloy is evaporated onto the wafer and photoresist to create the magnetic features. The photoresist is then lifted off in acetone, before growing a 125 nm layer of SiO₂ via plasma enhanced chemical vapor deposition. This process must be done via this technique, because PECVD temperatures are low enough to not oxidize the Fe in the magnetic features. The final SiO₂ layer is important because it protects the NiFe magnetic features from oxidation in the device and allows the magnetic features’ surface to be functionalized. The SiO₂ layer is then annealed before a final layer of photoresist is placed over the entire wafer to protect the wafer surface during dicing to create individual chips.

For chip preparation, chips are rinsed twice with acetone in a glass beaker to remove the photoresist. During each rinse, the beaker containing chips and acetone is gently agitated for 30 s. Chips are then washed with ethanol twice to remove any remaining acetone.

Chips are then sonicated three times, for twenty minutes each, in ethanol, 0.5 M KOH and ethanol at room temperature. After each sonication, the chips are rinsed with DI water for a few seconds. The chips are then rinsed twice with isopropanol and then sonicated for 15 min in a silanization solution (49.5 mL isopropanol, 3 microliters glacial acetic acid and 0.5 mL of (3-aminopropyl)triethoxysilane). After silanization, the chips are washed twice in isopropanol then dried in an oven at 90 °C for 30 min.

The PDMS microfluidic channel described in the PDMS molding section of this paper and the chip with the NiFe magnetic features are placed into separate 2 mL conical tubes with ethanol. The tubes are then sonicated for 5 min. The PDMS channel is placed onto the chip, aligning the PDMS channels over the magnetic features. This alignment is done by hand using forceps under an upright microscope at 20× magnification. The assembled device is then covered while the ethanol is allowed to evaporate from the chip to atmosphere. Once dry, silica tubing (180 microns outer diameter, 100 microns inner diameter) is inserted into the inlets of the device and sealed with uncured PDMS. The inlets for the tubing are created during the PDMS molding process. The inlets are patterned as 250 micron wide and 250 micron tall channels that are open to the sides of the device. This side access for tubing is required because the magnetic features are patterned on to an opaque silicon wafer and an inverted microscope is needed for imaging during experiments. The traditional method of punching port holes into the top of the PDMS cannot be used because the device is flipped with the PDMS layer resting on the inverted microscope stage. After sealing, the entire device is placed on an 80 °C hot plate to cure the sealing PDMS.

Streptavidin coated Dynabeads M-280, 2.8 micron in diameter, were obtained from Life Technologies, formerly Invitrogen. For use in experiments, the stock solution of beads is diluted by a factor of 20 in reagent-grade water with 0.1% Tween-20.

A custom aluminum and Delrin fixture is used to suspend a Mabuchi RE-260-2295 DC motor over the stage of a Nikon Eclipse inverted microscope. This fixture allows for x, y, and z positioning of the magnet. Note that non-magnetic materials were used whenever possible so as not to interfere with the magnetic field. A permanent bar magnet (B-882-N52, from K&J Magnetics, Jamison, PA, USA) is affixed to the motor shaft via a custom aluminum fixture, at a defined distance above the microflow channel. Figure 3 shows images of our experimental set-up, including microscope, magnet and motor assembly as well as an image of the assembled PDMS microchannel and chip.

Our simulations indicate that spatial trajectories of beads strongly depend on the magnitude of the magnetic field and its rotation frequency. When the magnetic field strength is low or/and frequency is high beads exhibit aperiodic motion. Illustrative examples of such motion are shown in Figure 6.

Our theoretical model shows that there is a phase lag between the direction of magnetic field and the direction to the rotating bead (Figure 7c). This phase difference increases with increasing rotating speed or decreasing magnetic strength. The lag increase will progress until the beads no longer maintain the same frequency as the magnetic field lines (Figure 7a,b). Because the phase angle lag is due to the fluid drag force acting on the bead, the phase angle lag can be used as an indirect measure of drag force on the bead.

To examine the operating conditions of the experimental device, the phase lag was measured using two linked high speed Phantom cameras (cameras used: v210 and v9.0, Vision Research, Wayne, NJ, USA). One camera was used to image the spinning and the second camera imaged the beads rotating in the device. Knowing the position of the magnet, gives the direction of the magnetic field.

Figure 7 shows images of beads in the device rotating at two different speeds with two different magnetic field strengths. In each image, the magnetic field lines are horizontal. We find a noticeable variance in the phase angle experienced by beads in the same image. We relate this variation in phase between different beads to slightly different hydrodynamic interactions arising among neighboring beads when the lattice is not fully populated. Another possibility is that beads alternate between periods of sliding or rolling when they move along the silicon surface resulting in unsteady hydrodynamic resistance on individual beads.

To quantify the phase lag, the angle between the magnetic field and the bead direction was measured at four different speeds. Figure 8 summarizes the results from these measurements, where each data point represents measurements of 60 beads taken across 6 different time points.

These experiments lead to two important observations. First, phase angle lag appears to be inversely related to the magnetic field strength at the chip. It is expected that a weaker magnetic field at the chip more weakly magnetizes the NiFe pillars. This in turn yields a weaker magnetic force pulling the microbeads towards the pillars. As the magnetic force weakens, the drag force causes the microbead to lag more.

Figure 8 shows that the experimental and simulation phase angle lag exhibits nearly a linear relationship with magnetic field rotation speed. It was verified using a high speed camera that the bead in Figure 8 maintained synchronicity with the rotating magnetic field. Thus magnetic field rotation speed can be used as an analog for bead linear velocity. Taking this and the phase angle lag as an indirect measure for drag force, the rotating microbeads appear to be following Stoke’s law, (17) which states that for low Re number flows, the drag force on a spherical particle is linearly related to the velocity of the particle. It is possible the discrepancies between the model and experimental values could be from an unaccounted for traction force between the chip surface and the bead or potentially a discrepancy in the modeled value of the magnetization constant of the NiFe pillars in simulation.

In order to quantify the amount of material capture on the rotating beads, we injected fluorescent nanospheres (Fluosphere, 40 nm diameter, from Life Technologies, formerly Invitrogen, Carlsbad, CA, USA) labeled with biotin which bind to streptavidin coated M-280 beads (2.8 micron diameter). The nanospheres, suspended in a 0.5% solution by volume in PBS + 0.1% Tween-20, were introduced into the channel at a linear velocity of 0.19 mm/s for 5 min. Figure 9 shows that rapid capture has taken place at the surface of the beads.