Mixing Behavior of Fluids with Magnetic
Nano-particles in Microchannel Flows
Zhanhua SILBER-LI1*, Zhenguo LI2 and
Xu ZHENG1
1.LNM, Institute of Mechanics, Chinese academy of sciences, Beijing 100080
2.Department of Modern Mechanics, University of science and technology of China.
* Corresponding author: lili@imech.ac.cn
1. Instruction
The Reynolds number and Peclet number in microfluidics flows are relatively low, thus the fluid mixture is dominated
by diffusion. In a microchannel with 100m in width, if the diffusion coefficient is about D=10-7cm2/s, the mixing length
will be nearly tens centimeters, which brings difficulty to reduce the size of microchip. To improve the fluid mixing in
microfluidic device, several methods have been introduced: the chaotic mixer1, the rough structures on the wall2 or adding
magnetic particles and external magnetic field to improve mixing3. Mixing by magnetic effect is a kind of active method,
which is related with the properties of magnetic particles, liquids and magnetic field strength, etc. Recently, the magnetic
probes, combining of biological molecules and magnetic particles, are widely used in biosensor or medicine transportation,
so it’s important to study the kinetic mechanism of magnetic particles in fluid under magnetic field.
The momentum equation and the diffusion equation of the ferromagnetic fluids are written as follow:

dV
 f g  p   V  0 M H
dt
and
dC
 D C
dt
. The magnetic particles’ concentration and aggregation will
influence the magnetic force and the effective diffusion coefficient D. Friedman et al. 4 have reviewed some relative
theoretical models. Tabeling et al5 have made experiments in the aggregation characteristic of magnetic particles under
parallel magnetic field, and gave out a relation between the aggregation length, flow rate and the shear rate.
This paper presents an experimental study to the influence of magnetic-particles’ concentration to mixing rate in
microchannels, under a steady single point electromagnetic pole. The influence of magnetic-particles’ concentration to
aggregation state of particles under different velocities has been observed initially.
2. Experimental apparatus and methods
Experimental apparatus consist with Olympus fluorescence microscopy IX71 and Andor EMCCD 885 (Fig.1a). Two
object lens are used: 10×/0.7 and 100×oil/1.35. The photo capture frequency is about 35Hz. Y-shape microchannels made
of PDMS are used (Fig.1b). The main-channel is 50m in width, 50m in height and 1cm in length; the sub-channel is same
in width and height. Liquid A is the ferromagnetic fluids and liquid B is di-water. The diameter of magnetic particles is
about 400nm, volume fraction ＝7.8％, and maximum magnetization ＝2×105A/m. Diluted by water,  of the sample I,
II and III are 0.39%, 0.78% and 1.56%, and the corresponding magnetization are 1×104 , 2×104 and 4×104A/m,
respectively. External magnetic field is a steady electromagnetic field. The maximum magnetic field strength is 120Gs
approximately. A sharp iron needle induced the magnetic field into near the channel, the magnetic line direction is vertical
to the flow direction (Fig.1b), and the local magnetic field strength is about 49 Gs. The flow velocity is depended on the
pressure of the liquid column height. The velocities range 13mms-1, and the Re=0.0170.051.
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Fig.1
Experimental setup (a), Schematic diagram (b)
3. Experimental results
3.1 Mixing rate
Fig.2 show the mixing process of sample III with velocity V=2mm s-1. To describe the mixing degree in different spatial
position, the mixing rate  is defined as:   1 
 (C  C )
i
( N  1)
2
 1 , where C is the mean concentration of the entraning
C
liquids. Ci is the concentration at ith position in y axis at a fixed x. Fig.3 shows the relation of the mixing rate versus
dimensionless streamwise position (x/w, w is the width of channel) for three different samples. The mixing rate of Sample II
at x/w =100 is only about 30% without magnetic field. Under the effects of magnetic field, mixing rate tends to 80% at x/w
=45. The mixing length will be shorter, when the concentrations of the liquids increase. The fully mixing length for Sample
III is located at x/w =10.
Fig.2 The mixture images of Sample III (=1.56%)，
Fig.3 Mixing rate vs. dimensionless length x/w
without magnetic field (a), with magnetic field(b)
3.2 Aggregation of magnetic particles under different concentrations
The images of sample III show the aggregation appears under external magnetic field (Fig.4b). The magnetic force,
shear stress, Van der Waals force and gravity force will affect the magnetic particles, but the magnetic force and shear stress
will be dominant in this test. The external magnetic pole is placed very near the upper side wall, and the velocity near wall
is low, so the particles are easy to be adhered. While the chains of magnetic particles can be broken in the middle of the
channel, because
H
decreases and velocity is bigger. It has been obvious that the higher the concentration of the magnetic
particles is, the shorter the aggregation length is.
Fig.4 Aggregation state of ferromagnetic fluid
(=1.56%) without magnetic field (a), with magnetic field (b).
4.Conclusions
The experiments of the mixing process of ferromagnetic fluids (volume fraction = 0.39%-1.56%), in a Y shape
micro-channel (50m×50m×1cm) show that the magnetic particles in Poiseuille flow, the fully mixing length can be
shortens under magnetic field and the aggregation of magnetic particles can be observed.
References:
1. Stroock, A. D., Dertinger, S. K., Ajdari, A., Mezic, I., Stone, H. A. & Whitesides, G. M. 2002, Science 295, 647–651;
2. Stroock, A. D., Dertinger, S. K., Whitesides, G. M. and Ajdari, A., 2002, Anal. Chem, 74, 5306-5312;
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3. Mensing, G. A., Pearce, T. M., Graham, M. D. & Beebe, D. J. 2004 Phil. Trans. R. Soc. Lond. A362, 1059–1068;
4. Friedman G. Yellen B., 2005, Current Opinion in Colloid & Interface Science, 10, 158-166;
5. Degre G., Brunet E., Okkels F. and Tabeling, P., 2004, Conf. of 21th IUTAM, Poland.
Thanks to Chinese Academy of Sciences Major Innovation Project (KJCX2-SW-L2) and National
Natural Science Foundation of China (10272107) for their supports.
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