 Solution

Different materials have different frequency-dependent polarization and conduction. For an $e^{i\omega t}$ convention, a useful relative complex permittivity is ${\widetilde{ϵ}}_r={ϵ}_r-i\sigma /({ϵ}_0\omega )$. Substituting the particle and medium responses into $\tilde{K}$ determines whether each population undergoes positive or negative dielectrophoresis and with what magnitude.

Choose a frequency at which one population has $\Re \tilde{K}>0$ and another has $\Re \tilde{K}<0$. 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 $\Re \tilde{K}=0$ 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.