  In soft matter structure couples to flow and vice versa. Complementary to
structural investigations, we here are interested in the determination of
particle velocities of charged colloidal suspensions of different structure
under flow. In a combined effort of theory and experiment we determine the
Fourier transform of the super-heterodyne field auto-correlation function
(power spectrum) which in frequency space is found to be well separated from
homodyne contributions and low frequency noise. Under certain conditions the
power spectrum is dominated by incoherently scattered light, originating from
the unavoidable size polydispersity of colloidal particles. A simple
approximate form for the low-wavenumber self-intermediate scattering function
is proposed, reminiscent to the case of non-interacting particles. We
experimentally scrutinize the range of applicability of these simplified
calculations on employing a parabolic electro-osmotic flow profile. Both for
non-interacting and strongly interacting fluid particle systems, the spectra
are well described as diffusion-broadened velocity distributions comprising an
osmotic flow-averaged superposition of Lorentzians at distinct locations. We
discuss the performance and scope of this approach with particular focus on
moderately strong interactions and on multiphase flow. In addition, we point to
some remaining theoretical challenges in connection to the observed linear
increase of the effective diffusion constant and the integrated spectral power
with increasing electric field strength.
