# Microbeads for Sampling and Mixing in a Complex Sample

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{®}& M-280, Life Technologies, formerly Invitrogen, Carlsbad, CA, USA) introduced into the channel with a syringe pump are trapped at the poles of the now magnetized soft magnetic discs. Rotation of the external permanent magnet will also rotate the induced magnetic poles in the soft magnetic discs which will in turn rotate the trapped microbeads (Figure 1).

**Figure 1.**Magnetic attraction between paramagnetic beads and induced magnetic poles. As the external permanent magnet rotates, the induced poles within the soft magnetic features also rotate, pulling the magnetic microbead.

## 2. Experimental Section

#### 2.1. Computational Modeling

_{і}(

**r**,t), describing the mass density of fluid particles at a lattice node

**r**and time t propagating in the direction i with a constant velocity

**c**

_{і}. The hydrodynamic quantities are calculated as moments of the distribution function, i.e., the density,

_{A}(

**r**,

**c**

_{і}, t), f

_{B}(

**r**,

**c**

_{і}, t) are the mass density of fluid A and fluid B respectively [12,13,14]. The conserved quantities are calculated as moments of the distribution functions, i.e., the mass density,

_{і}(

**r**, t) and ϕ

_{і}(

**r**, t), that describe the relaxation of distribution functions towards their equilibrium values, ρ

_{і}

^{eq}(

**r**, t) and ϕ

_{і}

^{eq}(

**r**, t) respectively. The equilibrium distributions, which are constructed to conserve mass, momentum, and order parameter, are respectively given by

**P**is the pressure tensor,

**u**is the macroscopic fluid velocity, μ is the chemical potential, and Г is a coefficient related to the mobility

**F**(

**r**

_{і}) acting on the node at position

**r**

_{і}includes the magnetic force and the force exerted by the fluid at the fluid-solid interface. We have previously validated our model in the limit of low Reynolds number and used it to examine microchannel flows with rigid and compliant particles [16,17,18,19,20].

**B**is the magnetic field vector, and

_{p}being the bead volume and χ being the difference of magnetic susceptibility between beads and the medium. In the case of bead magnetization saturation, the magnetic force simplifies to Equation (15) [23].

_{d}= a, disk height h = 0.05a, and the spacing s between disks varies from 2a to 1.5a. All these dimensions match experimental measurement.

#### 2.2. Current Device Fabrication and Characterization

#### 2.2.1. PDMS Molding

#### 2.2.2 Chip Fabrication

_{2}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 SiO

_{2}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 SiO

_{2}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.

#### 2.2.3. Chip Preparation

#### 2.2.4. Device Assembly

#### 2.2.5. Magnetic Bead Solution

#### 2.2.6. Magnet and Motor Assembly

**Figure 3.**Images of experimental set-up. Bottom image shows assembled PDMS channel with two inlets and two outlets and chip with NiFe features.

## 3. Results and Discussion

#### 3.1. Computational Modeling of Mixing

**Figure 4.**Comparison of mixing efficiency between pure diffusion (

**a**) and magnetic mixer without channel flow after 100 bead revolutions (

**b**). The concentration is averaged over channel height. The back circles denote the position of static discs, whereas the green circles indicate the instant position of rotating beads. In

**(b)**, left, 2 beads rotation per disk with 2a spacing; middle, 1 bead per disk with 2a spacing; right, 1 bead per disk with 1.5a spacing.

**Figure 5.**Mixing degree versus time for different flow rates (U

_{m}is the maximum velocity of channel flow, V

_{b}denotes the rotation velocity of beads).

#### 3.1.1. Bead Trajectories

**Figure 6.**Trajectories of magnetic beads moving around static disks in a rotating magnetic field. (

**a**) A bead completes one period around the disk during about three periods of the magnetic field (f = 8000 RPM, B = 0.063 T). (

**b**) A bead completes one period around the disk during about four periods of the magnetic field (f = 10,000 RPM, B = 0.074 T). (

**c**) A bead rotates with the frequency equal to that of the external magnetic field and follows nearly circular trajectory around the disk (f = 8000 RPM, B = 0.13 T). The dotted line shows the outer contour of the static disk. The dot indicates the final position of the bead, whereas the arrow shows the direction of magnetic field.

#### 3.2. Experimental Device Characterization

#### 3.2.1. Dynamics of High Speed Rotation

**Figure 7.**Images of microbead circling around static discs in rotating magnetic field. The alignment of the magnetic field lines is represented by the arrow through the images. The magnetic field rotational speed and magnetic field strength felt at the chip is given beneath the images. These were the two experimental parameters varied for the experiments. (

**a**) Speed: 2500 rpm, Mag. Field: 0188 T; (

**b**) Speed: 10,000 rpm, Mag. Field: 0.18 T; (

**c**) Speed: 2500 rpm, Mag. Field: 0.088 T; (

**d**) Speed: 10,000 rpm, Mag. Field: 0.088T.

**Figure 8.**Experimental and simulated (use the model described previously) phase angle lags for four different magnetic field rotational speed and two different magnetic field strengths. The force plotted here is the horizontal component of the magnetic force which is balanced by the viscous drag force. Each experimental data point represents 60 measurements across 6 time points. Error bars represent one standard deviation.

#### 3.2.2. Microbeads Capture Capacity

**Figure 9.**Capturing performance of rotating magnetic beads. The fluorescence in the image is the presence of biotin-labeled Fluospheres (Invitrogen) bound to the M-280 microbeads after the flow. The image on the right is the brightfield image showing the positions of the M-280 microbeads.

## 4. Conclusion and Future Work

## Acknowledgments

## References

- Dwivedi, H.P.; Jaykus, L.A. Detection of pathogens in foods: The current state-of-the-art and future directions. Crit. Rev. Microbiol.
**2011**, 37, 40–63. [Google Scholar] [CrossRef] - Suh, Y.K.; Kang, S. A review on mixing in microfluidics. Micromachines
**2010**, 1, 82–111. [Google Scholar] [CrossRef] - Ramadan, Q.; Samper, V.; Poenar, D.; Yu, C. Magnetic-based microfluidic platform for biomolecular separation. Biomed. Devices
**2006**, 8, 151–158. [Google Scholar] - Deng, T.; Whitesides, G.M. Manipulation of magnetic microbeads in suspension using micromagnetic systems fabricated with soft lithography. Appl. Phys. Lett.
**2001**, 78, 1775–1777. [Google Scholar] [CrossRef] - Lee, H.; Purdon, A.M.; Chu, V.; Westervelt, R.M. Controlled assembly of magnetic nanoparticles from magnetotactic bacteria using microelectromagntes arrays. Nano Lett.
**2004**, 4, 995–998. [Google Scholar] [CrossRef] - Wirix-Speetjens, R.; de Boeck, J. On-chip magnetic particle transport by alternating magnetic field gradients. IEEE Trans. Magn.
**2004**, 40, 1944–1946. [Google Scholar] [CrossRef] - Mao, W.; Peng, Z.; Hesketh, P.J.; Alexeev, A. Microfluidic mixing using an array of superparamagnetic beads. In Proceedings of the American Physical Society Meeting, Dallas, TX, USA, 21 March 2011.
- Alexeev, A.; Verberg, R.; Balzas, A.C. Modeling the motion of microcapsules on compliant polymeric surfaces. Macromolecules
**2005**, 38, 10244–10260. [Google Scholar] [CrossRef] - Alexeev, A.; Verberg, R.; Balazs, A.C. Designing compliant substrates to regulate the motion of vesicles. Phys. Rev. Lett.
**2006**, 96. [Google Scholar] [CrossRef] - Succi, S. The Lattice Boltzmann Equation for Fluids Dynamics and Beyond; Clarendon Press: Oxford, UK, 2001. [Google Scholar]
- Ladd, A.J.C.; Verberg, R. Lattice-Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys.
**2001**, 104, 1191–1251. [Google Scholar] [CrossRef] - Verberg, R.; Pooley, C.; Yeomans, J.; Balzas, A. Pattern formation in binary fluids confined between rough, chemically heterogeneous surfaces. Phys. Rev. Lett.
**2004**, 93, 184501–185504. [Google Scholar] - Verberg, R.; Yeomans, J.M.; Balazs, A.C. Modeling the flow of fluid/particle mixtures in microchannels: Encapsulating nanoparticles within monodisperse droplets. J. Chem. Phys.
**2005**, 123, 224706–224714. [Google Scholar] [CrossRef] - Swift, M.R.; Orlandini, E.; Osborn, W.; Yeomans, J. Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys. Rev. E
**1996**, 54, 5041–5052. [Google Scholar] [CrossRef] - Bouzidi, M.; Firdaouss, M.; Lallemand, P. Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys. Fluids
**2001**, 13, 3452–3459. [Google Scholar] [CrossRef] - Alexeev, A.; Verberg, R.; Balazs, A.C. Modeling the interactions between deformable capsules rolling on a compliant surface. Soft Matter
**2006**, 2, 499–509. [Google Scholar] [CrossRef] - Alexeev, A.; Verberg, R; Balazs, A.C. Patterned surfaces segregate compliant microcapsules. Langmuir
**2007**, 23, 983–987. [Google Scholar] [CrossRef] - Masoud, H; Alexeev, A. Modeling magnetic microcapsules that crawl in microchannels. Soft Matter
**2010**, 6, 794–799. [Google Scholar] [CrossRef] - Mao, W.; Alexeev, A. Hydrodynamic sorting of microparticles by size in ridged microchannels. Phys. Fluids.
**2011**. [Google Scholar] [CrossRef] - Arata, J.P.; Alexeev, A. Designing microfluidic channel that separates elastic particles upon stiffness. Soft Matter
**2009**, 5, 2721–2724. [Google Scholar] [CrossRef] - Furlani, E.P. Permanent Magnet and Electromechanical Devices: Materials, Analysis, and Applications; Academic Press: San Diego, CA, USA, 2001. [Google Scholar]
- Furlani, E.P. Analysis of particle transport in a magnetophoretic microsystem. J. Appl. Phys.
**2006**, 99, 024912–024922. [Google Scholar] [CrossRef] - Rosensweig, R.E. Ferrohydrodynamics; Dover Publications: Mineola, NY, USA, 1997. [Google Scholar]
- Peng, Z. Parallel Manipulation of Individual Magnetic Microbeads for Lab-on-a-Chip Applications. Ph.D. Thesis, School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA, 2011. [Google Scholar]
- Peng, Z.; Guo, W.; Cannon, J.L.; Hesketh, P.J. A magnetophoresis system for controlled transport and trapping of magnetic beads. In Proceedings of Transactions of microTAS 2010, Groningen, The Netherlands, 3–7 October 2010.

© 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Owen, D.; Mao, W.; Alexeev, A.; Cannon, J.L.; Hesketh, P.J.
Microbeads for Sampling and Mixing in a Complex Sample. *Micromachines* **2013**, *4*, 103-115.
https://doi.org/10.3390/mi4010103

**AMA Style**

Owen D, Mao W, Alexeev A, Cannon JL, Hesketh PJ.
Microbeads for Sampling and Mixing in a Complex Sample. *Micromachines*. 2013; 4(1):103-115.
https://doi.org/10.3390/mi4010103

**Chicago/Turabian Style**

Owen, Drew, Wenbin Mao, Alex Alexeev, Jennifer L. Cannon, and Peter J. Hesketh.
2013. "Microbeads for Sampling and Mixing in a Complex Sample" *Micromachines* 4, no. 1: 103-115.
https://doi.org/10.3390/mi4010103