## 2 Microfluidic Manipulation Techniques
### Electrophoresis  
Electrophoresis (EP) is defined as the motion of a charged particle relative to a stationary fluid, driven by an external electric field [28, 52, 53, 72]. The direction and magnitude of the induced motion depend on the polarity and amount of net electrical charge of the particle, respectively [28, 52]. Generally, electrophoretic force is produced by a pair of electrodes connected to a direct current (DC) power supply [83, 84]. When electrodes are immersed in an ionic solution containing particles and an external DC electric field is provided to the electrodes, the particles experience electrophoretic force, moving toward the electrode possessing opposite polarity (Figure 2). The moving velocity of the  
Figure 1: Dielectrophoretic (DEP) motion of a dielectric particle in a non-uniform electric field. **(a)** Positive dielectrophoresis, in which a dielectric particle moves toward a strong electric field region. **(b)** Negative dielectrophoresis, in which a dielectric particle migrates to a weak electric field region. Reproduced from [40], with the permission of AIP Publishing (2012).  
particles, i.e., electrophoretic velocity (\(v\)), is linearly proportional to the strength of the applied DC electric field (\(E\)) [29; 52].  
\[v=\mu_{ep}E, \tag{5}\]  
where the electrophoretic mobility, \(\mu_{ep}\), is the ability of a charged particle to move in response to an external electric field. It is expressed in two forms based on the relative magnitude of the Debye layer thickness (\(\lambda_{D}\)) to the particle radius (\(r_{p}\)) [28; 29; 72].  
\[\mu_{ep}=\begin{cases}&\frac{\varepsilon_{r}\varepsilon_{o}\varepsilon_{p}}{ \eta_{f}}\left(\lambda_{D}\ll r_{p}\right)\\ &\frac{2\varepsilon_{r}\varepsilon_{o}\varepsilon_{p}}{3\eta_{f}}\left( \lambda_{D}\gg r_{p}\right)\end{cases}, \tag{6}\]  
where \(\varepsilon_{r}\) is the relative permittivity of the particle, \(\varepsilon_{0}\) is the vacuum permittivity of free space, \(\zeta_{p}\) is the zeta potential of the particle's surface, and \(\eta_{f}\) is the viscosity of the surrounding fluid [85]. The variable \(\zeta\) is defined as  
\[\zeta=\frac{\sigma\lambda_{D}r_{p}}{\varepsilon_{r}\varepsilon_{o}\big{(} \lambda_{D}+r_{p}\big{)}}, \tag{7}\]  
When charged particles suspended in a fluid move by electrophoretic force, they are also subject to two other forces [40; 86]: (1) fluid friction force and (2) electrophoretic retardation force. The friction force is the viscous drag force acting on electrophoretically moving particles. It depends on the size and shape of a particle and the viscosity of a surrounding fluid. The drag force increases for larger particles and higher fluid viscosities. The electrophoretic retardation force indicates the force exerted on movable ions in an EDL surrounding a charged particle. The ions have a polarity opposite to that of the particle and accordingly cause a fluid flow heading the opposite direction to the EP in an applied electric field. The flow results in a retardation effect on the electrophoretically induced motion.  
EP has been mainly utilized for particle purification [87; 88; 89; 90] and separation [83; 91; 92; 93; 94; 95; 96]. It has advantages of ease of particle manipulation and simplicity [24; 27]. However, there are also several disadvantages [24]. First, EP is applicable only for charged particles; therefore, the range of relevant applications is not wide. Furthermore, the electrophoretic migration speed is relatively slow because the upper intensity of an applied DC electric field is restricted to avoid undesirable phenomena such as electrolysis.