Length-scales of dynamic heterogeneity in a driven binary colloid

Here we study the characteristic length scales in an aqueous suspension of a symmetric oppositely charged colloid subjected to a uniform electric field by Brownian dynamics simulations. We consider the in-plane structure in the presence of a sufficiently strong electric field where the like charges in the system form macroscopic lanes. We construct spatial correlation functions characterizing the structural order and that of particles of different mobilities in the plane transverse to the electric field at a given time. We call these functions equal time density correlation functions (ETDCFs). The ETDCFs between particles of different charges, irrespective of mobilities, are the structural ETDCFs, while those between particles of different mobilities are the dynamic ETDCFs. We extract the characteristic length of correlation by fitting the envelopes of the ETDCFs to exponential dependences. We find that the correlation length scales of the structural ETDCFs and the dynamic ETDCFs of the slow particles increase with time in a concurrent manner. This suggests that the clustering of particles tends to build up dynamically correlated slow particles in the plane transverse to the lanes. The ETDCFs can be measured for colloidal systems by directly following the particle motion by video-microscopy and may be useful to understand the patterns out of equilibrium.