2.1 Dielectrophoretic movement
Pohl and co-workers detailly explained the theory of the dielectrophoresis41-43. DEP force (\(F_{\text{DEP}}\)) can be defined according to the difference between the dielectric properties of the particle and its suspension medium44-46.
\(F_{\text{DEP}}=2\pi r^{3}\varepsilon_{m}Re(K\left(\omega\right))\nabla E^{2}\)(1)
The \(F_{\text{DEP}}\) is expressed in Eq (1) . Here, ris the radius of the cell (particle), \(\varepsilon_{m}\) is the permittivity of the surrounding medium, (\(Re(K\left(\omega\right))\)is the real part of the Clausius-Mossotti factor\(K\left(\omega\right)\), and \(E\) is the applied electric field. The Clausius-Mossotti factor is defined as given by in Eq (2) . The subscripts “m ” and “c ” indicate suspending medium and cells, respectively.
\(K\left(\omega\right)\ =\ \frac{(\varepsilon_{c}^{*}\ -\ \varepsilon_{m}^{*}\ )\ }{(\varepsilon_{c}^{*}+\ 2\varepsilon_{m}^{*}\ )}\)(2)
Here, \(\varepsilon_{c}^{*}\) is known as the complex permittivity of a cell and \(\varepsilon_{m}^{*}\) is the complex permittivity of the surrounding medium. The complex permittivity can be expressed as shownEq (3) . Here, \(\varepsilon\) is the permittivity, \(\sigma\)is the conductivity and \(\omega\) (\(\omega=2\pi f\)) includes the electric field frequency (f).
\(\varepsilon^{*}\ =\varepsilon+\frac{\text{jσ}}{\omega}\) (3)
Reaction of the cells to dielectrophoretic forces can be classified according to sign of the \(Re(K\left(\omega\right))\). When strong electric field regions attract cells, the value of the\(Re(K\left(\omega\right)\) is positive, it is referred as positive DEP (pDEP). Contrary, when strong electric field regions repel cells, the value of the \(Re(K\left(\omega\right)\) is negative, and negative DEP (nDEP) occurs. The crossover frequency can be described as the cessation of the particle motion, which is specific for the particles. Mostly, cells experience very weak DEP forces which does not generate a clear movement.