## 2 Microfluidic Manipulation Techniques  
### Dielectrophoresis  
Among the various mechanisms to manipulate particles using electrically induced forces, dielectrophoresis (DEP) is the most frequently utilized in microfluidic systems [29; 40; 48; 51; 65; 66; 67; 68; 69; 70]. DEP is defined as the motion of neutral or semi-conducting particles produced by the application of a non-uniform electric field [40; 51; 71; 72]. Under the presence of an electric field, a particle experiences polarization resulting in a net dipole moment within the particle. If the electric field is not uniform, the Coulomb forces acting on the two poles become unequal. Then, the net resulting force causes the particle to move (Figure 1). The particle migration phenomenon is termed DEP, and the related DEP force is generally expressed in a time-averaged manner using the following equation [40; 51]:  
\[F_{DEP}=\frac{1}{2}Re[\widetilde{p}\cdot\
abla]E^{*}, \tag{1}\]  
where \(\widetilde{p}\) is the effective dipole moment of a particle, \(E^{*}\) is the complex conjugate of an applied electric field, and \(Re\) and \(\
abla\) represent the real part in brackets and the differential operator, respectively. For a spherical particle with radius \(r\), the equation is re-written as [51]  
\[F_{DEP}=2\pi r^{3}\varepsilon_{m}Re[K(\omega)]\
abla|E_{rms}|^{2}, \tag{2}\]  
where \(\varepsilon_{m}\) is the absolute electrical permittivity of suspending medium, \(K(\omega)\) is the Clausius-Mossotti (CM) factor, \(\omega\) is the angular frequency of an applied electric field, and \(E_{rms}\) is the root mean square (\(rms\)) of electric field strength. The CM factor is expressed as the difference of complex permittivity of a particle (\(\varepsilon_{p}\)*) and surrounding medium (\(\varepsilon_{m}\)*) as follows [51]:  
\[K(\omega)=\frac{\varepsilon_{p}^{*}-\varepsilon_{m}^{*}}{\varepsilon_{p}^{*}+ \varepsilon_{m}^{*}}, \tag{3}\]  
\[\varepsilon^{*}=\varepsilon-i\frac{\sigma}{\omega}, \tag{4}\]  
where \(i=\sqrt{-1}\), and \(\sigma\) is the electrical conductivity of a particle or medium. The DEP force is generally produced by an inhomogeneous electrode system such as castellated or interdigitated planar microelectrodes providing a non-uniform electric field [29; 69; 70; 73; 74; 75]. The intensity of the applied electric field is highest in the region between two closely spaced electrodes. Particles experiencingelectric field gradients are either attracted to or repelled from a high electric field region by the DEP force. The direction of the particle movement is determined by the frequency-dependent dielectric properties of a particle and the suspending medium [51] and is apparent from the sign of \(Re[K(\omega)]\) in Equation (2). If a particle is more polarizable than the surrounding medium, i.e., if \(Re[K(\omega)]>0\), the particle moves toward a strong electric field region experiencing positive DEP (p-DEP) (Figure 1a). Conductive particles in insulating fluids exhibit p-DEP behavior over all frequencies [51, 66]. On the contrary, if a particle is less polarizable than the surrounding medium, i.e., if \(Re[K(\omega)]<0\), it migrates to a weak electric field region, repelled from a strong electric field region by negative DEP (n-DEP) (Figure 1b). Generally, polymer particles such as polystyrene or latex beads show n-DEP in a conductive electrolyte solution over megahertz frequencies [51, 67, 76]. DEP has often been utilized for particle separation [66, 68, 77], transport [78], and sorting [79] in various fields because of several important advantages [24, 40, 74]. DEP can accumulate a large quantity of particles at a region close to or far from electrode edges immediately with application of a non-uniform electric field. Also, the object of manipulation is not limited to either a conductive or dielectric particle. DEP-based manipulation depends on the relative polarizability of a particle with respect to the surrounding medium, which relates to the electrical permittivity and conductivity of a particle and suspending medium [51].