  Here we study characteristic length scales in an aqueous suspension of
symmetric oppositely charged colloid subject to a uniform electric field by
Brownian Dynamics simulations. We consider a sufficiently strong electric field
where the like charges in the system form macroscopic lanes. We construct
spatial correlation functions characterizing structural order and that of
particles of different mobilities in-plane transverse to the electric field at
a given time. We call these functions as equal time density correlation
function (ETDCF). The ETDCF between particles of different charges,
irrespective of mobilities, are called structural ETDCFs, while those between
particles of different mobilities are called the dynamic ETDCF. We extract the
characteristic length of correlation by fitting the envelopes of the ETDCFs to
exponential dependence. We find that structural ETDCF and the dynamical-ETDCFs
of the slow particles increase with time. This suggests that the slow particles
undergo microphase separation in the background of the fast particles which
drive the structural pattern in the plane transverse to the lanes. The ETDCFs
can be measured for colloidal systems directly following particle motion by
video-microscopy and may be useful to understand patterns out of equilibrium.
