text: The simplest theoretical model is that of a homogeneous sphere surrounded by a conducting dielectric medium. For a homogeneous sphere of radius  and complex permittivity  in a medium with complex permittivity  the (time-averaged) DEP force is:
  The factor in curly brackets is known as the complex Clausius-Mossotti function and contains all the frequency dependence of the DEP force.  Where the particle consists of nested spheres – the most common example of which is the approximation of a spherical cell composed of an inner part (the cytoplasm) surrounded by an outer layer (the cell membrane) – then this can be represented by nested expressions for the shells and the way in which they interact, allowing the properties to be elucidated where there are sufficient parameters related to the number of unknowns being sought.
  For a more general field-aligned ellipsoid of radius  and length  with complex dielectric constant  in a medium with complex dielectric constant  the time-dependent dielectrophoretic force is given by:
  The complex dielectric constant is , where  is the dielectric constant,  is the electrical conductivity,  is the field frequency, and  is the imaginary unit.  This expression has been useful for approximating the dielectrophoretic behavior of particles such as red blood cells (as oblate spheroids) or long thin tubes (as prolate ellipsoids) allowing the approximation of the dielectrophoretic response of carbon nanotubes or tobacco mosaic viruses in suspension.
  These equations are accurate for particles when the electric field gradients are not very large (e.g., close to electrode edges) or when the particle is not moving along an axis in which the field gradient is zero (such as at the center of an axisymmetric electrode array), as the equations only take into account the dipole formed and not higher order polarization. When the electric field gradients are large, or when there is a field null running through the center of the particle, higher order terms become relevant, and result in higher forces.
  To be precise, the time-dependent equation only applies to lossless particles, because loss creates a lag between the field and the induced dipole. When averaged, the effect cancels out and the equation holds true for lossy particles as well. An equivalent time-averaged equation can be easily obtained by replacing E with E, or, for sinusoidal voltages by dividing the right hand side by 2.
  These models ignores the fact that cells have a complex internal structure and are heterogeneous. A multi-shell model in a low conducting medium can be used to obtain information of the membrane conductivity and the permittivity of the cytoplasm. 
  For a cell with a shell surrounding a homogeneous core with its surrounding medium considered as a layer, as seen in Figure 2, the overall dielectric response is obtained from a combination of the properties of the shell and core.
  where 1 is the core (in cellular terms, the cytoplasm), 2 is the shell (in a cell, the membrane). r1 is the radius from the centre of the sphere to the inside of the shell, and r2 is the radius from the centre of the sphere to the outside of the shell.