**1. Introduction**

Mimicking the microenvironment of biological systems is crucial, especially for diagnostic and tissue engineering purposes. There are several contact-free manipulation methodologies [1] that mimic and control the microenvironments of biological systems, such as magnetophoresis [2], acoustophoresis [3], electrophoresis [4], and thermophoresis [5]. Magnetophoresis is a method that provides contact-free manipulation of particles in a magnetic field. There is no additional equipment required instead of permanent magnets or electromagnets for magnetophoresis; however, sound waves, electrical source, and heat source are required for acoustophoresis, electrophoresis, and thermophoresis, respectively [6].

Magnetophoresis is a contactless manipulation method, which provides the manipulation of particles in the magnetic field provided by either permanent magnets or electromagnets. During manipulation of particles in a magnetic field gradient or/and in a magnetized medium, neither pH nor temperature of sample is

affected [7]. There are two different types of magnetophoresis, such as positive and negative magnetophoresis (**Figure 1A, B**). In the positive magnetophoresis, particles that have magnetic properties migrate within nonmagnetic (diamagnetic) medium. On the other hand, particles that do not have magnetic properties migrate within paramagnetic medium in negative magnetophoresis [8, 9]. The migration of particles in both types of magnetophoresis depends on the magnetic susceptibility differences between particle and medium.

**1.1 History and theory of magnetic levitation**

*Magnetic Levitation Based Applications in Bioscience DOI: http://dx.doi.org/10.5772/intechopen.92148*

(**Figure 2C**) [1].

At balanced height:

*F* ! *<sup>g</sup>* þ *F* !

paramagnetic medium (kg.m�<sup>3</sup>

**Figure 2.**

**151**

In Eq. (4), the gravitational *F*

Magnetic levitation concept appeared within the study named as "An Absolute Micromanometer Using Diamagnetic Levitation" at the end of 1960s. In this study, the diamagnetically levitated ultramicromanometer was described where frictionfree suspension was produced via magnetic induction for graphite disk to measure absolute pressure down to 10�<sup>10</sup> Torr [15]. Later, density-based separation was carried out for minerals [16] and metals [17] by magnetic levitation principle. In another study, improvement of magnetic levitation system has been studied to measure the density differences of liquids and solids [18–20]. On the other hand, magnetic levitation-based approaches also appeared in tissue engineering applications. The magnetic levitation techniques were also used to mimic 3D cellular microenvironment and to form 3D cellular structures by guiding the cells [21–26]. As depicted in **Figure 2**, the diamagnetic particles in paramagnetic medium are density-dependently positioned at specific height, in which each force (gravitational, magnetic buoyant forces, and steric interactions) on diamagnetic particle (**Figure 2B**) is equalized under magnetic field produced by permanent magnets [Eqs. (1) and (4)] [27–29]. The magnetic and gravitational forces act on diamagnetic particles and cause the particles to either float or sink in paramagnetic solution

> *F* ! *<sup>g</sup>* þ *F* !

*<sup>m</sup>* <sup>¼</sup> *Xp* � *Xm μ*0

*V g*! <sup>þ</sup>

! *g*

*<sup>g</sup>* ¼ *ρ<sup>p</sup>* � *ρ<sup>m</sup>*

*V B*! *:*∇ ! *B* !

*Xp* � *Xm μ*0

and magnetic *<sup>F</sup>*

particles are balanced. Here, *ρ<sup>p</sup>* and *ρ<sup>m</sup>* refer to the density of levitating particle and

*The principle of magnetic levitation. (A) Magnetic field between the magnets, which is oriented in anti-Helmholtz configuration. (B) the forces on levitating objects within the magnetic levitation systems. (C) the*

*alignment of levitating objects at specific levitation heights depending on their densities.*

*F* !

*F* !

*<sup>m</sup>* ¼ *ρ<sup>p</sup>* � *ρ<sup>m</sup>*

*<sup>m</sup>* ¼ 0 (1)

forces on levitating

(3)

¼ 0 (4)

*V g*! (2)

*V B*! *:*∇ ! *B* !

! *m*

), respectively; and *Xp* and *Xm* represent the

Magnetic levitation (MagLev) technique, which works with the principle of negative magnetophoresis, manipulates the diamagnetic particles in paramagnetic medium by providing antigravity conditions (**Figure 1C**) [10]. The diamagnetic particles that are suspended in a paramagnetic medium are positioned at specific height called levitation height depending on their densities when the external magnetic field is applied. According to magnetic levitation principle, diamagnetic particles are specifically positioned depending on their densities by balancing all forces on particles, which are gravitational force (from gravity) and magnetic buoyant force (from magnetic field).

In magnetic levitation systems, biological entities (as diamagnetic particles) are also levitated and manipulated in a three-dimensional (3D) space as well as nonbiological particles in the paramagnetic medium [11]. The paramagnetic medium is an important parameter for magnetic levitation-based approaches, because magnetic susceptibility differences between paramagnetic medium (χ > 0) and diamagnetic particle (χ < 0) provide magnetic buoyancy force on diamagnetic particles in the presence of external magnetic field [12]. There are different paramagnetic mediums that are used in magnetic levitation-based approaches, such as ferrofluids [13] and paramagnetic salt solutions [2]. Ferrofluids are the suspension of maghemite (Fe2O3) or magnetite (Fe3O4) that has higher magnetic susceptibility than paramagnetic salt solutions; however, observation of the samples is limited because of their opaque nature [14]. Manganese (II) chloride (MnCl2) and diethylenetriamine-pentaacetic acid (Gd-DTPA) are generally chosen and used paramagnetic agents in magnetic levitation; however, they are used in high concentration to effectively levitate diamagnetic particles because of their low magnetic susceptibilies. The use of paramagnetic salts in high concentration is the main reason for toxicity-based limitations in bioapplications of magnetic levitation technology [2].

#### **Figure 1.**

*Migration of particles with magnetophoresis. (A) Positive magnetophoresis, which means the migration of magnetic particles in diamagnetic fluid. (B) Negative magnetophoresis, which means the migration of diamagnetic particles in paramagnetic fluid. (C) Migration of diamagnetic particles in paramagnetic fluid via magnetic levitation principle.*
