Pattern formation of charged particles in an electric field.

The application of an electric field to a suspension of charged particles can lead to the formation of patterns due to electrohydrodynamic instabilities which remain poorly understood. We elucidate this behavior by visualizing the dynamics of charged carbon black particles suspended in a nonpolar solvent in response to an electric field. As the particles are transported across a microfluidic channel, an instability occurs in which the initially uniform, rapidly advancing particle front develops fingers. Furthermore, when the direction of the applied field is repeatedly switched, the particles localize into a remarkably well-defined periodic pattern which reflects an interplay between the fingering instability and particle diffusion.