Magnetic Mixing - Michael A. Beauregard

Microfluidic devices consist of channels that are of dimensions that make most liquids, when flowed through these channels, flow in a laminar pattern. Achieving mixing in a microfluidic channel can have a plethora of applications including increasing rates of reaction or dilution and culturing cells. Magnetic mixing can accomplish these goals through three main resources: singular stir bars or beads, groups of magnetic beads, and ferrofluids.

Singular Stir Bars and Beads

Stir bars can range widely in size. Larger stir bars usually need to be incorporated into a larger, macroscopic container called a continuously stirred tank reactor (CSTR). The spinning motion of the bar or bead is accomplished using an external magnetic field. The effluent of the macroscopic reactor can then be fed into a microfluidic device for further experimentation and analysis. CSTRs follow the design equation below:

[math]\displaystyle{ C(t) = C_o e^{-F t/V} }[/math] [1]

[math]\displaystyle{ C(t) = Concentration at time t }[/math]
[math]\displaystyle{ C_o = Initial concentration }[/math]
[math]\displaystyle{ F = flowrate }[/math]
[math]\displaystyle{ V = CSTR volume }[/math]

Figure 1. Macroscopic CSTR with black stir bead

A CSTR in conjunction with a microfluidic device would need to have a volume on the scale of ~1mL to make use of appropriate flowrates. Tan, et al. characterizes the use of different CSTR shapes of 1mL volume and shows that they can be used for cell cultures on a small scale [2].

Stir bars can also be shrunk down to ~500µm in length and ~30µm in width [3]. This allows them to fit inside microfluidic channels. The stir bar is attached to an axel at its center. The axel is sandwiched between a glass base layer and a PDMS top layer so that the stir bar does not move when liquid is flowed into the channel. An external magnetic field must be strong enough to overcome the frictional forces of liquid moving through the channel to spin the stir bar. The stir bar is located at the interface of two liquids downstream of a Y junction where the two liquids met. Due to laminar flow, only areas in the channel that come into direct contact with the mixing bar become mixed. Liquid at the very edges of the channel continue to rely purely on diffusion for mixing.

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  Figure 2. Micro stir bar (left) and its placement into a microfluidic device (right)

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  Figure 3. Flow pattern resulting from a micro stir bar

Magnetic Beads

Magnetic beads can be used to achieve thorough mixing in very small spaces [4]. Lee et al. developed a method where 4µm magnetic beads are flowed into a 4.2nL compartment of a microfluidic device. The beads remain in the mixing chamber due to a combination of their size and an externally applied magnetic field. Smaller beads would flow out of the mixing compartment and larger beads would conglomerate into a single mass that would not move. The correct beads would align and rotate just as a macroscopic stir bar would. When the beads were not rotating, they provided a mixing efficiency of 66%. When the beads were moving, they provided a mixing efficiency of 96%. The beads were also biocompatible.

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  Figure 4. Flow pattern resulting from the mixing of 4µm diameter beads inside a CSTR (center) at increasing mixing rates from a-c

Ferrofluids

Ferrofluids still contain solid magnetic particles, but they are ~10nm in diameter, giving them properties more similar to a liquid when in an aqueous suspension [5]. Wen et al. used a microfluidic technique where a channel of biocompatible ferrofluid met a channel of dye via a Y intersection. [6] The channel paralleled a coil of wire. Different extents of mixing could be seen depending on the frequency of the alternating current flowing through the wire, the strength of the resulting magnetic field, and the amount of time that the microfluidic channel spent next to the wire coil.

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  Figure 6. Salomon et al. fabricated an array of nanocantilevers on the scale of 10⁵ nanocantilevers/cm².

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  Figure 7. Two methods of printing were used, resulting in both inked surfaces of BSA underneath the cantilevers and solely around the cantilevers. (1) Inking the stamp with IgG. (2) Washing and drying the stamp. (3) Cleaning outside the stamp grooves. (3B) Inking the stamp with BSA. (4) Printing after aligning the stamp and the chip. (4A) Incubating the chip with BSA. (5) Result.

References

1. Hill, C. G.; Root, T. W. Introduction to Chemical Engineering Kinetics and Reactor Design, 2nd ed.; Wiley, 2014.
2. Tan, C. K.; Davies, M. J.; Mccluskey, D. K.; Munro, I. R.; Nweke, M. C.; Tracey, M. C.; Szita, N. Journal of Chemical Technology & Biotechnology2015, 90 (10), 1927–1936.
3. Lu, L.-H.; Ryu, K. S.; Liu, C. Journal of Microelectromechanical Systems2002, 11 (5), 462–469.
4. Lee, S. H.; Noort, D. V.; Lee, J. Y.; Zhang, B.-T.; Park, T. H. Lab Chip2009, 9 (3), 479–482.
5. Ferrofluids http://education.mrsec.wisc.edu/background/ferrofluid/ (accessed Feb 17, 2017).
6. Wen, C.-Y.; Yeh, C.-P.; Tsai, C.-H.; Fu, L.-M. Electrophoresis2009, 30 (24), 4179–4186.
7. Hardt, S.; Schönfeld Friedhelm. Microfluidic technologies for miniaturized analysis systems; Springer: New York, 2011.