Theory of the dielectrophoretic behavior of clustered colloidal particles in two dimensions

Clustering behaviors in real colloidal suspensions can often be seen. In such clusters, the separation between the suspended particles is so close that we cannot neglect the multiple image effect on the dielectrophoresis of the particles. Since the exact multiple image method, so far, exists in two-dimensional cases, rather than in three-dimensional cases, as an initial model we have investigated the cluster colloidal suspension, in which many circular or cylindrical particles are randomly distributed in a sheet cluster. We have applied the multiple image method and the Maxwell-Garnett approximation (MGA) to study the dielectrophoretic (DEP) spectrum of the cluster. The dipole factor of a particle in the cluster has been exactly expressed in the spectral representation, thus simplifying the study. To ones interest, the multiple image method has been found to be in a good agreement with the MGA, even though they were founded in the light of different physical thoughts. To this end, it is found that the multiple image method predicts two characteristic frequencies, at which the dielectric dispersion occurs in the DEP spectrum. By choosing the appropriate material or geometrical parameters, the lower characteristic frequency can be achieved