Dielectrophoretic Force on a Dielectric Sphere

In this section, we present the dielectric force on a dielectric sphere of finite radius a. It may be noted that the induced dipole moment reported in the previous section assumes homogeneous external electrical field Eq. However, the calculation becomes more involved for inhomogeneous case. If the radius R of the sphere is much smaller than the distance Z over which the external electrical field varies, one can still use equation (6.200) for the induced dipole. Let us use the Taylor expansion (here just taken to first order) of the external electrical field EQ(r) around the center coordinate Tq of the sphere  

The vector function/i(e- , e ) appearing above is a generalized Clausius-Mossotti function. Combining equations (6.189), (6.202), and (6.203), we arrive at 

In the last equality, we have used V[E ] = 2E V , which is valid in electrostatics where 

The dielectrophoretic force Fpgp can be written using the Clausius-Mossotti factor as 

This power of 2 of the electric field in equation (6.205) implies that the sign of the DEP force is independent of the sign of EO. The sign of the Clausius-Mossotti factor K ei, p) determines 

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