= Solution
Different materials have different frequency-dependent polarization and conduction. For an $e^{i\omega t}$ convention, a useful relative complex permittivity is $\widetilde\epsilon_r=\epsilon_r-i\sigma/(\epsilon_0\omega)$. Substituting the particle and medium responses into $\widetilde K$ determines whether each population undergoes positive or negative <dielectrophoresis> and with what magnitude.
\b[Choose a frequency at which one population has $\Re\widetilde K>0$ and another has $\Re\widetilde K<0$.] A nonuniform electrode field then sends them towards different regions, allowing collection in separate channels or trapping one while the other passes. Alternatively, different positive-force magnitudes can produce different deflections in a flowing suspension. A crossover where $\Re\widetilde K=0$ can selectively suppress the force on one material.
The useful frequency depends on the surrounding medium as well as the particle. An unchanging, real-permittivity model would not by itself give frequency-selective separation; dielectric dispersion or conductivity contrast is needed. Particle size affects force magnitude, and heating, electro-osmotic flow and surface polarization can complicate a real separation.
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