Post on 12-Mar-2021
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