^{5}volts are usually employed, which increases the issues concerning operational safety.

#### Fundamentals

and the steady-state momentum equation

$-\nabla \mathrm{p}+\mathsf{\mu}{\nabla}^{2}\mathit{u}+{\rho}_{e}\mathit{E}=0$, where p is the pressure and μ is the dynamic viscosity of the liquid.

${\rho}_{e}\mathit{E}$ denotes the electrical body force with ρ_{e} being the net charge density and **E** the strength of the applied electric field. However, the electrical body force terms can be ignored based on an assumption of a thin electric double layer (EDL); hence, a slip boundary condition can be imposed [38], and such slip velocity can be expressed as [39]

where u_{eo} is the electroosmotic mobility of the fluid and is dependent on the surface potential ζ_{s} and permittivity ε_{m} and viscosity μ of the liquid [40]. This mobility is given by the Smoluchowski equation as

, and the electric field strength can be obtained as

$\mathit{E}=-\nabla \mathsf{\varphi}$. In the presence of electric field, cells experience electrophoresis due to their electrostatic charges. In addition, the formation of nonuniform electric field generated inside the region of the packed beads results in the cell dielectrophoresis effect. Therefore, considering the combined effect of electroosmotic flow, electrophoresis, and dielectrophoresis, the cell velocity can be estimated as [41]

$${\mathit{u}}_{\mathit{p}}=\mathit{u}-{u}_{p}\mathit{E}-\frac{c{\epsilon}_{m}{r}^{2}}{3\mu}\left(\mathit{E}.\nabla \right)\mathit{E}$$

where **u** is the velocity of the fluid, u_{p} is the electrophoretic mobility of the cell of radius r, and c is a correction factor. Since the conductivity of the working fluid is much lower than that of cells, cells experience a negative DEP effect (refer to Supplementary Information S1). In most iDEP devices, the Joule heating effect can play a significant role as

, where Q is the volumetric Joule heating related to the electrical conductivity of the medium (σ) and the electric field strength (**E**).

where f is the shape factor and θ is the angle between the line of electric field and the line joining the center of the cell to the point of interest. Further, the shape factor is given by [43]

where r is the radius and l is the length of the cell. For rod-shaped cells such as E. coli, l >> 2r. Thus, f = 1. According to the theory of electroporation, when the transmembrane potential reaches the critical value of 0.2–1 V [7], nanopores are formed within the cell membrane, thereby allowing exchanges of ions, drugs, molecules, genes, etc. If the applied field strength is very high, the pores do not reseal, and the cell membrane is damaged permanently. Two major theories can be found in the literature, and they are the theory of electromechanical compression [44] and the pore energy model [45]. Schwan’s equation remains valid as long as the conductivity of the cell membrane is several orders higher than the conductivity of the suspending medium [46]. Successful electroporations have been demonstrated with various buffer conductivities ranging from deionized (DI) water to saline solution (i.e., 1.6 S/m) without affecting the viability of the cell [17,47]. However, the use of a highly conductive buffer can generate a significant amount of heat, which can affect the electroporation process.