**4. Magnetophoresis**

Magnetophoresis (MAG) is the motion of particles under the influence of a nonuniform magnetic field, as the particles being magnetized cause them to be attracted toward the regions of high magnetic flux density or repelled away [8]. Magnetic field is generated by either a permanent magnet or an electromagnetic coil.

#### **4.1. Fundamentals of MAG**

Magnetophoretic force experienced by a particle is governed by

$$F\_{MAG} = \frac{\left(\chi\_r - \chi\_n\right)V\_r}{\mu\_0} (\mathbf{B} \cdot \nabla)\mathbf{B} \tag{7}$$

The motional direction is controlled by the difference of magnetic susceptibility between the

magnet (Reprinted with permission from Lee et al. [27]. Copyright 2016 Springer Nature).

**Figure 2.** (a) Magnetophoresis. Bioparticles A (purple) are pushed toward the region with maximum magnetic flux density (pMAG) due to positive magnetic susceptibility difference between the bioparticles and the suspending medium (*χpA*-*χ<sup>m</sup>* > 0), while bioparticles B (yellow) experience the opposite (*χpB*-*χ<sup>m</sup>* < 0), thus being repelled away from the region (FpMAG, positive magnetophoretic force; FnMAG, negative magnetophoretic force) (Reprinted with permission from Md Ali et al. [13]. Copyright 2016 Royal Society of Chemistry). (b) Manipulation of model organism by magnetophoresis. Multilayered magnetic silica film-coated yeast is manipulated in microfluidic device equipped with external permanent

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with minimum magnetic field flux gradient, and this is called as negative MAG (nMAG). The

Common practices in magnetophoretic manipulation of bioparticle employ either (1) immunomagnetic manipulation [28] or (2) diamagnetic manipulation [29], in which paramagnetic bounded to bioparticle is exploited in the former, while in the latter, paramagnetic- or ferrofluid-suspending medium is utilized. In immunomagnetic bioparticle manipulation, paramagnetic micro-/nanoparticles, e.g., iron oxide microparticles and streptavidin paramagnetic particles, which have higher susceptibility compared to suspending medium are used. Target bioparticles are bounded to paramagnetic micro-/nanoparticles through antibodies, benefiting from binding affinity with bioparticles. Under influence of magnetic field, the microparticlebioparticle complexes can be manipulated. While in diamagnetic bioparticle manipulation, a suspending medium with higher magnetic susceptibility compared to target bioparticle is utilized. In this method, the magnetic field manipulates the suspending medium rather than

Lee et al. [27] magnetically functionalize living yeast cells, *Saccharomyces cerevisiae* (*S. cerevisiae*), as micro-magnets, by performing coating of several groups of them with different thicknesses of magnetic silica film (single layer up to seven layers), to control the magnetization degree of the cells as shown in **Figure 2b**. By doing so, multiple subgroups are being formed which can be manipulated independently in the pool of heterogeneous cell mixtures. Magnetophoretic separation of erythrocytes, i.e., maturing RBCs from the mixture with reticulocytes and immature RBCs, in hematopoietic stem cell (HSC) culture, has been performed by Jin




particle and the medium, i.e., *χ<sup>p</sup>*

magnetic susceptibility difference (*χ<sup>p</sup>*

the bioparticles themselves.

conceptual mechanism is shown in **Figure 2a**.

**4.2. Magnetophoretic manipulation of bioparticles**

(*χp*

where *FMAG* is the effective magnetic force upon the particle; *χ<sup>p</sup>* and *χm* are the magnetic susceptibility of the particle and the medium, respectively; *Vp* is the particle volume, *B* is the magnetic flux density, and *μ*<sup>0</sup> is the free space permeability [8].

Biological Particle Control and Separation using Active Forces in Microfluidic Environments http://dx.doi.org/10.5772/intechopen.75714 89

**Figure 2.** (a) Magnetophoresis. Bioparticles A (purple) are pushed toward the region with maximum magnetic flux density (pMAG) due to positive magnetic susceptibility difference between the bioparticles and the suspending medium (*χpA*-*χ<sup>m</sup>* > 0), while bioparticles B (yellow) experience the opposite (*χpB*-*χ<sup>m</sup>* < 0), thus being repelled away from the region (FpMAG, positive magnetophoretic force; FnMAG, negative magnetophoretic force) (Reprinted with permission from Md Ali et al. [13]. Copyright 2016 Royal Society of Chemistry). (b) Manipulation of model organism by magnetophoresis. Multilayered magnetic silica film-coated yeast is manipulated in microfluidic device equipped with external permanent magnet (Reprinted with permission from Lee et al. [27]. Copyright 2016 Springer Nature).

The motional direction is controlled by the difference of magnetic susceptibility between the particle and the medium, i.e., *χ<sup>p</sup>* -*χm*. For a positive magnetic susceptibility difference (*χp* -*χ<sup>m</sup>* > 0), the suspended particles are pushed to region with maximum magnetic field flux gradient, and this situation is known as positive MAG (pMAG). In contrast, under negative magnetic susceptibility difference (*χ<sup>p</sup>* -*χ<sup>m</sup>* < 0) situation, the particles are pushed to regions with minimum magnetic field flux gradient, and this is called as negative MAG (nMAG). The conceptual mechanism is shown in **Figure 2a**.

Common practices in magnetophoretic manipulation of bioparticle employ either (1) immunomagnetic manipulation [28] or (2) diamagnetic manipulation [29], in which paramagnetic bounded to bioparticle is exploited in the former, while in the latter, paramagnetic- or ferrofluid-suspending medium is utilized. In immunomagnetic bioparticle manipulation, paramagnetic micro-/nanoparticles, e.g., iron oxide microparticles and streptavidin paramagnetic particles, which have higher susceptibility compared to suspending medium are used. Target bioparticles are bounded to paramagnetic micro-/nanoparticles through antibodies, benefiting from binding affinity with bioparticles. Under influence of magnetic field, the microparticlebioparticle complexes can be manipulated. While in diamagnetic bioparticle manipulation, a suspending medium with higher magnetic susceptibility compared to target bioparticle is utilized. In this method, the magnetic field manipulates the suspending medium rather than the bioparticles themselves.
