Controlled dynamics of rotating magnetic

bead chains in microfluidic systems. Y. Gao1, M.A. Hulsen1 and J.M.J. den Toonder1,2

1Eindhoven University of Technology, THE NETHERLANDS

2Philips Research, THE NETHERLANDS

Department of Mechanical Engineering

/Mechanical engineering

Introduction Magnetic micron-sized beads (Fig. 1a) suspended in a non-magnetic fluid can be

used in various ways in microfluidic systems, for example to detect and/or extract

bio-molecules or cells (Fig. 1b) or to mix fluids at micro-scale (Fig. 1c).

Fig. 1 Manipulation of magnetic beads. (a) 2.8 µm sized magnetic bead [1]. (b) Magnetic beads

functionalized with different bio-specific surface coatings. (c) Magnetic beads can be used to mix

fluorescent and non-fluorescent laminar flows [2].

As matter of fact, mass-transport of the bio-molecules and cells can be made

chaotic by controlled actuation of the magnetic beads, which will significantly

enhance the capture efficiencies and shorten the detection time.

Motivation Upon application of a rotating magnetic field, magnetic beads form chains that

periodically break-up and reform (Fig. 2). This repeating topological change of the

chain is the most efficient way to induce chaotic mass-transport of the bio-

molecules and cells.

Fig. 2 2D FEM simulations of a magnetic bead chain inducing chaotic advection at micro-scale in

Newtonian fluid, obtained by Kang et al. [3].

We combine 3D numerical simulations with experimental work to fully control this

repeating topological change of the chain in Newtonian fluids. Also we have

derived a dimensionless number (RT) as a new criterion to characterize this

special region of interest:

where η is the fluid viscosity, ω the angular velocity of the field, µ0 the magnetic

permeability of free space, χp the magnetic bead susceptibility, H0 the magnitude

of the field and N the amount of beads forming the chain.

Numerical and Experimental methods The numerical work is based on the use of dipolar magnetic interactions and

hydrodynamic-interaction tensors to approximate both magnetic and

hydrodynamic interactions between the particles. Experimentally, a set-up (Fig. 3)

was realized capable of actuating the magnetic beads triaxially. Experiments and

simulations were performed with two different bead suspensions (table 1).

Fig. 3 A magnetic actuation set-up was realized capable of generating a user-specified magnetic field

both in the horizontal as well as in the vertical plane. The setup consists of 8 individually controlled

coils (brown) together with 8 soft-iron poles (grey) connected by soft-iron frames (blue and red).

Micromer® Dynabeads®

Particle diameter 3 µm 2.8 µm

Particle surface coating COOH COOH

Particle susceptibility 0.23 0.65

Fluid medium De-ionized water De-ionized water

Applied magnetic field 13 mT 6.5 mT

Results and Discussion RT divides the rotating bead chain dynamics into two global regimes:

(1) if RT < RTc, the chain rotates as a rigid rod following the field.

(2) if RT > RTc, the chain periodically fragments and reforms.

Theoretically, RTc equals 1 and marks the beginning of chain fragmentation and

reformation. In figure 4, RTc‘s are obtained for experimental and simulated rotating

bead chains.

Fig. 4 Quantitative comparisons between numerical and experimental results of rotating bead chains (with

lengths varying from 5 to 17 particles) at the point of fragmentation, characterized by the dimensionless

number RTc.

For simulated bead chains (crosses), RTc ≈ 1 is the boundary between rigid and

dynamic behaviors. Experimentally (squares), RTc’s between 0.6 and 1.3 are found.

Deviations are believed to be caused by uncertainties in the measured values of the

magnetic particle properties and the applied field strengths. In figure 5, results of the

actual rotating behavior of a 14-bead chain are shown from experiments (a, c) and

from simulations (b, d).

Fig. 5 Experimental (a, c) and simulated (b, d) results of a rotating 14-bead chain. The black arrows

indicate the direction of the magnetic field, which rotates in clockwise direction.

At values of RT < RTc, the bead chain rotates as a rigid rod. As RT ≥ RTc the bead chain

breaks up and reconnects at the chain center in a stable and predictable manner.

Conclusion We have developed a 3D numerical method that can accurately predict the dynamical

behavior of rotating magnetic bead chains. A dimensionless number has been derived

that can characterize the corresponding dynamics. We can experimentally control a

rotating magnetic bead chain and design the optimum parameters for real microfluidic

applications to effectively capture low concentrations of bio-molecules.

Literature [1] Figure obtained from Dynal® Magnetic beads

[2] Lee, S. H. (2009). "Effective mixing in a microfluidic chip using magnetic particles." Lab on a Chip 9: 479-482.

[3] Kang, T. G. (2007). "Chaotic mixing induced by a magnetic chain in a rotating magnetic field." Physical Review E

76(6): 11.

Bead chain length

RTc

a

d

c

b

RT=0.7

RT=0.49

RT=1.41

RT=0.92

Antibodies

Immunoassay

Infectious Disease

Test

Adsorbent

Bacteria

detection

Cell trapping

Fluorescenc

e

labeling

Proteins

Proteome

analysis

DNA Probes

SNPs analysis

Gene diagnostic test

a b

c

Table 1. System parameters