AC Dielectrophoretic Force on a Dielectric Sphere

We have considered DC voltages driving the DEP trap in the previous section. However, there are many advantages in using AC voltage bias instead (1) Any charge monopoles (ions) in 

Let us assume a simple harmonic time variation exp(-/wf) of the applied potential. The applied potential 0(r, t) and the associated electrical field E r, t) = -V (r, t) are denoted as 

For perfect dielectric, the surface charge density is equal to zero, as stated in equation (6.197c). However, with nonzero conductivities and AC fields, it becomes nonzero and in fact time dependent. The time derivative of given by charge conservation and Ohm s law  

Taking the time derivative of equation (6.219) using E-fields from equation (6.218b), substituting in equation (6.220), and multiplying with i/co, we have 

is the relative permittivity, a is the conductivity, and is the frequency of the electric field. Now, we may observe that the boundary condition in the AC case equation (6.221) has the same mathematical form as the boundary condition equation (6.197c) in the DC case. We can therefore use the result of equation (6.205) directly using the complex dielectric functions in the Clausius-Mossotti factor, which is where the boundary condition has been used  

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